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  • Springer  (98)
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  • 1
    ISSN: 1572-8900
    Keywords: Capillary zone electrophoresis ; oligomers ; lactic acid ; glycolic acid ; 3-hydroxybutyric acid ; water solubility ; stability ; degradation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In an attempt to increase the range of analytical techniques able to monitor ultimate degradation stages of degradable, biodegradable, and bioresorbable polymers, capillary zone electrophoresis (CZE) was used to analyze tentatively oligomers formed during thermal condensation of lactic, glycolic, anddl-3-hydroxybutyric acids. The influence of the buffer and of capillary coating are discussed in terms of electroosmotic flow. Typical analyses were first performed using a 0.1M borate buffer (pH 8.9) with anodic injection. In the case of lactic acid, seven peaks were well separated, while only three peaks were observed for glycolic acid. A more complex situation was found fordl-3-hydroxybutyric acid oligomers. The first five peaks were split. The major component of each doublet was attributed to hydroxy-terminated oligomers, whereas the satellite peaks were assigned to oligomers bearing a C=C double bond at the noncarboxylic terminus. CZE of pH-sensitive lactic acid oligomers was also performed in 0.05M phosphate buffer (pH 6.8) with cathodic injection after physical coating of the fused-silica capillary with DEAE-Dextran. The buffer-soluble fraction present in lactic acid oligomers was extracted from a dichloromethane solution. Extracts issued from different batches of lactic acid condensates gave a constant water-solubility pattern whose cutoff was at the level of the decamer. CZE was also used to monitor thein vitro aging of aqueous solutions of these water-soluble oligomers. The lactyllactic acid dimer appeared more stable than higher oligomers, thus showing that ultimate stages of the degradation did not proceed at random. These physicochemical characteristics were used to complement the degradation pathway based on diffusion of oligomers duringin vitro aging of large size lactic acid plates made by compression molding. CZE data showed that lactic acid was the only component which was released in the aqueous medium during degradation.
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  • 2
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    Journal of polymers and the environment 3 (1995), S. 199-203 
    ISSN: 1572-8900
    Keywords: Chemiluminescence ; oxidation ; stability ; acrylonitrile-butadiene-styrene
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The thermal oxidative stability of various formulations based on emulsion-grade ABS was studied by the chemiluminescence technique. Emulsion products were found to be essentially less stable than ionic mass polymerization resins. Among the antioxidants studied, Santonox R is clearly more efficient than Irganox 1076 and Irganox 3114, and its superiority is reflected primarily in improved induction period values. The introduction of Tinuvin 770 and Tinuvin 328 UV stabilizers into emulsion resins does not change the durability of the products. In mixtures where both Irganox 1076 and UV stabilizers are present, a certain antagonistic effect was noted at high UV stabilizer concentrations.
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  • 3
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    Celestial mechanics and dynamical astronomy 74 (1999), S. 19-57 
    ISSN: 1572-9478
    Keywords: stability ; Hamiltonian ; two centers ; oblate planet ; galactic disks ; dipole
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Relative equilibria occur in a wide variety of physical applications, including celestial mechanics, particle accelerators, plasma physics, and atomic physics. We derive sufficient conditions for Lyapunov stability of circular orbits in arbitrary axisymmetric gravitational (electrostatic) and magnetic fields, including the effects of local mass (charge) and current density. Particularly simple stability conditions are derived for source‐free regions, where the gravitational field is harmonic (∇2U = 0) or the magnetic field irrotational (∇ × B = 0). In either case the resulting stability conditions can be expressed geometrically (coordinate‐free) in terms of dimensionless stability indices. Stability bounds are calculated for several examples, including the problem of two fixed centers, the J2 planetary model, galactic disks, and a toroidal quadrupole magnetic field.
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  • 4
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    Celestial mechanics and dynamical astronomy 75 (1999), S. 251-285 
    ISSN: 1572-9478
    Keywords: unrestricted problem ; rotational motion ; rigid body dynamics ; libration points ; stability ; resonances
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present an analysis of the model introduced by Kokoriev and Kirpichnikov (1988) for the study of unrestricted planar motion of a point mass and a symmetric rigid body whose gravity field is approximated by two point masses (a dumb-bell model). To show possible generalization of the model, we give a systematic derivation of equations of motion for a more general unrestricted problem of a point and a rigid body possessing a plane of dynamical symmetry. We give a simple description of bifurcation of triangular libration points, and we perform an analysis of their linear stability. We propose to extend the model of Kokoriev and Kirpichnikov (1988) to a case when the symmetric body is oblate. In the proposed model the gravity field of moving and rotating body is approximated by two complex masses at complex distance (a complex dumb-bell model). An analysis of bifurcation of the triangular libration points in this model is also presented.
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  • 5
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    Celestial mechanics and dynamical astronomy 78 (2000), S. 227-241 
    ISSN: 1572-9478
    Keywords: stability ; normal form ; spin-orbit resonance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider a model of spin-orbit interaction, describing the motion of an oblate satellite rotating about an internal spin-axis and orbiting about a central planet. The resulting second order differential equation depends upon the parameters provided by the equatorial oblateness of the satellite and its orbital eccentricity. Normal form transformations around the main spin-orbit resonances are carried out explicitly. As an outcome, one can compute some invariants; the fact that these quantities are not identically zero is a necessary condition to prove the existence of nearby periodic orbits (Birkhoff fixed point theorem). Moreover, the nonvanishing of the invariants provides also the stability of the spin-orbit resonances, since it guarantees the existence of invariant curves surrounding the periodic orbit.
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  • 6
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    Celestial mechanics and dynamical astronomy 63 (1995), S. 205-225 
    ISSN: 1572-9478
    Keywords: Restricted three body problem ; Lagrangian points ; resonances ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The problem of stability of the Lagrangian pointL 4 in the circular restricted problem of three bodies is investigated close to the 1 : 2 commensurability of the long and short period libration. By stability we define boundedness of the solution for a given initial finite displacement from the equilibrium point as function of the mass parameter μ close to the commensurability. A rigorous treatment close to the resonance condition is possible using a transformation that diagonalizes the matrix related to the linear part of the equations of motion. The so obtained equations are further transformed to action angle type variables. Then using an isolated resonance approach, only the slowly varying terms are kept in the equations and two independent isolating first integrals can be found. These integrals finally enable us to solve the stability problem in an exact way. The so obtained results are compared to numeric integration of the equations of motion and are found to be in perfect agreement.
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  • 7
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    Celestial mechanics and dynamical astronomy 61 (1995), S. 181-196 
    ISSN: 1572-9478
    Keywords: Periodic solutions ; stability ; restricted three-body problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.
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  • 8
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    Celestial mechanics and dynamical astronomy 67 (1997), S. 181-204 
    ISSN: 1572-9478
    Keywords: Hamiltonian systems ; symplectic mappings ; normal forms ; resonances ; stability ; three degrees of freedom
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We analyze four-dimensional symplectic mappings in the neighbourhood of an elliptic fixed point whose eigenvalues are close to satisfy a third-order resonance. Using the perturbative tools of resonant normal forms, the geometry of the orbits and the existence of elliptic or hyperbolic one-dimensional tori (fixed lines) is worked out. This allows one to give an analytical estimate of the stability domain when the resonance is unstable. A comparison with numerical results for the four-dimensional Hénon mapping is given.
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  • 9
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    Celestial mechanics and dynamical astronomy 61 (1995), S. 1-19 
    ISSN: 1572-9478
    Keywords: Three body problem ; stability ; surface of section ; commensurability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The model of the circular restricted problem of three bodies is used to investigate the sensitivity of the third body motion when it is given a positional or velocity deviation away from the L4 triangular libration point. The x-axis is used as a criteria for defining the stability of the third body motion. Poincaré's surfaces of section are used to compare the regions of periodic, quasi-periodic and stochastic motion to the trajectories found using the definition of stability (not crossing the x-axis) defined in this study. Values of the primary/secondary mass ratios (μ) ranging from 0 to the linear critical value 0.038521... are investigated. Using this new form of stability measure, it is determined that certain values of μ are more stable than others. The results of this study are compared, and found, to give agreeable results to other studies which investigate commensurabilities of the long and short period terms of periodic orbits.
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  • 10
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    Celestial mechanics and dynamical astronomy 61 (1995), S. 261-285 
    ISSN: 1572-9478
    Keywords: galactic dynamics ; periodic orbits ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the stability of axial orbits in analytical galactic potentials as a function of the energy of the orbit and the ellipticity of the potential. The problem is solved by an analytical method, the validity of which is not limited to small amplitudes. The lines of neutral stability divide the parameter space in regions corresponding to different organizations of the main families of orbits in the symmetry planes.
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  • 11
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    Celestial mechanics and dynamical astronomy 66 (1996), S. 191-202 
    ISSN: 1572-9478
    Keywords: resonance ; restricted problem ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The stability of triangular libration points, when the bigger primary is a source of radiation and the smaller primary is an oblate spheroid. has been investigated in the resonance cases ω1 = 2ω2 and ω1 = 3ω2. The motion is unstable for all the values of parameters q and A when ω1 = 2ω2 and the motion is unstable and stable depending upon the values of the parameters q and A when ω1 = 3ω2. Here q is the radiation parameter and A is the oblateness parameter.
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  • 12
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    Celestial mechanics and dynamical astronomy 69 (1997), S. 271-281 
    ISSN: 1572-9478
    Keywords: restricted three-body problem ; libration points ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The existence and stability of triangular libration points in the relativistic restricted three-body problem has been studied. It is found that L4,5 are unstable in the whole range 0 ≤ µ ≤ 1/2 in contrast to the classical restricted three-body problem where they are stable for 0 〈 µ 〈 µ0, where µ is the mass parameter and µ0 = 0.03852....
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  • 13
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    Celestial mechanics and dynamical astronomy 69 (1997), S. 317-330 
    ISSN: 1572-9478
    Keywords: artificial satellite ; Nekhoroshev's theory ; normal form ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the significance of long time stabilty predictions in the light of Nekhoroshev's theory by studying the orbits of artificial satellites. As a simplified model problem we consider the so-called J2problem for an earth's satellite, neglecting luni-solar perturbations and nonconservative effects. We consider a wide range of orbits, excluding those which are too close to the critical inclination. Most of the orbits turn out to be stable for times larger than the estimated age of the solar system, thus proving that, as far as dissipation can be neglected, stability in Nekhoroshev's sense may be effective for physically realistic systems.
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  • 14
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    Celestial mechanics and dynamical astronomy 70 (1998), S. 41-58 
    ISSN: 1572-9478
    Keywords: three-body problem ; libration points ; stability ; normal forms.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we consider the problem of motion of an infinitesimal point mass in the gravity field of an uniformly rotating dumb-bell. The aim of our study is to investigate Liapunov stability of Lagrangian libration points of this problem. We analyze the stability of libration points in the whole range of parameters ω, μ of the problem. In particular, we consider all resonance cases when the order of resonance is not greater than five.
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  • 15
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    Optical review 6 (1999), S. 28-36 
    ISSN: 1349-9432
    Keywords: optical propagation equation ; stability ; picosecond pulse ; 3-dimensional computation ; Fresnel’s distribution ; fast Fourier transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a new simulation code able to simulate the entire propagation of laser pulse, from the amplifiers level up to the focusing stage. This algorithm has some new characteristics that we intend to present. It computes the three-dimensional optical propagation equation using no approximation other than its picosecond expression. The stability has been carefully studied so that it can be applied to any geometry. This is a great improvement since, up to now only cylindrical geometry was accessible for accuracy. In this paper we also present a method using Fast Fourier Transform able to evaluate with a high accuracy, Fresnel’s distribution of a focused laser pulse. The advantages provided by our algorithm are its rapidity and its high physical understanding of the focusing phenomena.
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  • 16
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    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 809-816 
    ISSN: 1420-9039
    Keywords: 34D20 ; 34D35 ; 35Q72 ; 73H10 ; 73K03 ; Elastic string ; stability ; energy-momentum ; axial motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish “orbitai” stability (modulo this collection of relative equilibria). For a well-defined class of “soft” materials, there is an upper bound on the axial speed sufficient for stability; “stiff” materials are shown to be orbitally stable at any axial speed.
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  • 17
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    Archive of applied mechanics 67 (1997), S. 447-456 
    ISSN: 1432-0681
    Keywords: Key words rotation ; stability ; energy criterion ; variational analysis ; functional analysis ; eigenvalue problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Stability of a heavy rotating rod with a variable cross section is studied by energy method. Bifurcation points for the system of equilibrium equations are analyzed. It is shown that for the case when the rotation speed exceeds the critical one, the trivial solution ceases to be the minimizer of the potential energy, so that rod loses stability, according to the energy criteria. Also, a new estimate of the maximal rod deflection in the post-critical state is obtained.
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  • 18
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    Archive of applied mechanics 65 (1995), S. 507-521 
    ISSN: 1432-0681
    Keywords: rod vibrations ; stability ; tip mass ; non-conservative forces ; non-selfadjoint problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Separable and non-selfadjoint boundary-value problems representing the vibration of linearly elastic unidimensional systems are considered. The elastic system is modelled as a continuous distributed-parameter system where singularities in the mass distribution function can be neatly taken into account. Specifically, extending Green's function approach, the free vibration, stability and forced vibration of fixed-free rods with a tip mass and under the action of uniformly distributed non-conservative loads have been investigated analytically.
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  • 19
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    Archive of applied mechanics 65 (1995), S. 99-109 
    ISSN: 1432-0681
    Keywords: Key words Bars ; voids ; viscoelasticity ; stability ; critical load
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  Dynamic stability of an elastic bar with voids is considered. Using the Lyapunov approach some new sufficient stability conditions are obtained and explicit expressions for the critical load are derived.
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  • 20
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    Archive of applied mechanics 65 (1995), S. 133-141 
    ISSN: 1432-0681
    Keywords: Shear deformation ; elastically supported beams ; axial compression ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary The influence of shear deformation on the buckling behavior of a beam supported laterally by a Winkler elastic foundation is studied. A full investigation of the bifurcation points at which, under axial load, the beam becomes critical with respect to one or two simultaneous buckling modes is made. The configurations and stabilities of the equilibrium paths that bifurcate from the critical points are derived. From the results of theoretical analysis, it becomes evident that shear deformation has a considerable effect upon the equilibriums and stabilities of the post-buckling of the beam. The results for the Bernoulli-Euler beam can be obtained as a limiting case for those of the present beam by letting the shear stiffness tend to infinity.
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  • 21
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    Archive of applied mechanics 65 (1995), S. 178-193 
    ISSN: 1432-0681
    Keywords: Periodic motion ; modal treatment ; itrations ; time variance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Übersicht Lineare, periodisch zeitvariante Bewegungsgleichungen treten im Hubschrauber- und Windturbinenbau auf. Der Getriebebau und die Rotordynamik liefern weitere Beispiele. In diesem Bericht wird ein systematischer Weg zu ihrer Lösung dargestellt. Mit dem Ansatz von Hill wird die homogene Lösung über die Lösung eines Eigenwertproblems gewonnen. Nach Anpassung an die Anfangsbedingungen liefert sie die Fundamentalmatrix des Systems. Ähnlich wie bei zeitinvarianten Systemen, existieren auch bei zeitvarianten Systemen Orthogonalitätsbedingungen, die die Eigenvektoren erfüllen. Die Eigenvektoren selbst sind allerdings zeitabhängig. Benutzt man die Eigenvektoren als Ansatzvektor zur Berechnung der erzwungenen Schwingungen (Transformation mit der zeitvarianten Modalmatrix des Systems), so gelingt es, die Bewegungsgleichungen des Systems in entkoppelte, zeitinvariante zu überführen. Sie lassen sich in bekannter Weise lösen. Dieses Vorgehen wird auf eine moderne Windkraftanlage angewandt. Sie wurde zunächst mit 372 Freiheitsgraden modelliert, die aber auf 18 vor der numerischen Weiterbehandlung kondensiert wurden. Das Stabilitätsverhalten und die Antwortspektren auf stochastische Anregung durch den Wind wurden auf dem oben beschriebenen Weg ermittelt.
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  • 22
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    Archive of applied mechanics 65 (1995), S. 178-193 
    ISSN: 1432-0681
    Keywords: Key words Periodic motion ; modal treatment ; itrations ; time variance ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Übersicht  Lineare, periodisch zeitvariante Bewegungsgleichungen treten im Hubschrauber- und Windturbinenbau auf. Der Getriebebau und die Rotordynamik liefern weitere Beispiele. In diesem Bericht wird ein systematischer Weg zu ihrer Lösung dargestellt. Mit dem Ansatz von Hill wird die homogene Lösung über die Lösung eines Eigenwertproblems gewonnen. Nach Anpassung an die Anfangsbedingungen liefert sie die Fundamentalmatrix des Systems. Ähnlich wie bei zeitinvarianten Systemen, existieren auch bei zeitvarianten Systemen Orthogonalitätsbedingungen, die die Eigenvektoren erfüllen. Die Eigenvektoren selbst sind allerdings zeitabhängig. Benutzt man die Eigenvektoren als Ansatzvektor zur Berechnung der erzwungenen Schwingungen (Transformation mit der zeitvarianten Modalmatrix des Systems), so gelingt es, die Bewegungsgleichungen des Systems in entkoppelte, zeitinvariante zu überführen. Sie lassen sich in bekannter Weise lösen. Dieses Vorgehen wird auf eine moderne Windkraftanlage angewandt. Sie wurde zunächst mit 372 Freiheitsgraden modelliert, die aber auf 18 vor der numerischen Weiterbehandlung kondensiert wurden. Das Stabilitätsverhalten und die Antwortspektren auf stochastische Anregung durch den Wind wurden auf dem oben beschriebenen Weg ermittelt.
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    Archive of applied mechanics 66 (1996), S. 291-299 
    ISSN: 1432-0681
    Keywords: stability ; elasticity ; singularities ; bifurcation ; material instabilities
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Branching analysis for the homogeneous deformations of a compressible elastic unit cube under dead loading is performed. Critical conditions for branching of the equilibrium paths are derived and the post-critical equilibrium paths are described. Special attention is given to the compound branching.
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  • 24
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    Archive of applied mechanics 65 (1995), S. 133-141 
    ISSN: 1432-0681
    Keywords: Key words Shear deformation ; elastically supported beams ; axial compression ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  The influence of shear deformation on the buckling behavior of a beam supported laterally by a Winkler elastic foundation is studied. A full investigation of the bifurcation points at which, under axial load, the beam becomes critical with respect to one or two simultaneous buckling modes is made. The configurations and stabilities of the equilibrium paths that bifurcate from the critical points are derived. From the results of theoretical analysis, it becomes evident that shear deformation has a considerable effect upon the equilibriums and stabilities of the post-buckling of the beam. The results for the Bernoulli-Euler beam can be obtained as a limiting case for those of the present beam by letting the shear stiffness tend to infinity.
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  • 25
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    Archive of applied mechanics 70 (2000), S. 17-29 
    ISSN: 1432-0681
    Keywords: Key words free-surface flow ; solidification ; strip casting ; steady state ; nonuniqueness ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary The paper is concerned with a one-dimensional analysis of plane open-channel flow with continuous solidification. The process is of relevance for recent developments in the casting of steel and other metals. The bottom of the channel consists of a rotating casting roll and a horizontal cooling table, where the solidified material is withdrawn with given velocity. The study is restricted to the region downstream of the top of the casting roll. Surface tension is neglected. In the main part of the analysis inviscid fluid flow is considered since the Reynolds number is very large in the applications. It is found that the steady-state solutions are nonunique in a certain parameter range. In addition to a continuous solution, there are two solutions including hydraulic jumps, with one hydraulic jump being located on the casting roll, the other one on the cooling table. Regarding the stability of the non unique solutions, the evolution of disturbances is investigated numerically as an initial-value problem. It is concluded that the hydraulic jump on the cooling table is unstable, while the other discontinuous solution as well as the continuous solution are stable for sufficiently small disturbances. Which stable solution is attained in the steady state, depends on the history of the process. Friction at the liquid/solid interface is taken into account in the last part of the analysis. A constant friction coefficient is assumed. It is found that the history of the process determines the steady-state solution if, and only if, the friction coefficient is sufficiently small. For larger values of the friction coefficient, the steady-state solution is unique and independent of the history of the transient process. Furthermore, for sufficiently large friction coefficients, stable hydraulic jumps are found, in contrast to the inviscid case, also on the cooling table.
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  • 26
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    Archive of applied mechanics 65 (1995), S. 507-521 
    ISSN: 1432-0681
    Keywords: Key words rod vibrations ; stability ; tip mass ; non-conservative forces ; non-selfadjoint problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  Separable and non-selfadjoint boundary-value problems representing the vibration of linearly elastic unidimensional systems are considered. The elastic system is modelled as a continuous distributed-parameter system where singularities in the mass distribution function can be neatly taken into account. Specifically, extending Green’s function approach, the free vibration, stability and forced vibration of fixed-free rods with a tip mass and under the action of uniformly distributed non-conservative loads have been investigated analytically.
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  • 27
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    Archive of applied mechanics 66 (1996), S. 264-272 
    ISSN: 1432-0681
    Keywords: asymptotic expansion ; stability ; boundary layer ; laminar flow ; heat transfer
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary By means of a combined method it is demonstrated for regular perturbation problems how the higher order terms of an asymptotic expansion may be determined from numerical solutions of the non-expanded basic equations. The method is applied to heat transfer effects in a laminar boundary layer and to the analysis of its stability. All first- and second-order coefficients of the problem are determined from numerical solutions of the basic set of equations.
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    Archive of applied mechanics 66 (1996), S. 264-272 
    ISSN: 1432-0681
    Keywords: Key words asymptotic expansion ; stability ; boundary layer ; laminar flow ; heat transfer
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  By means of a combined method it is demonstrated for regular perturbation problems how the higher order terms of an asymptotic expansion may be determined from numerical solutions of the non-expanded basic equations. The method is applied to heat transfer effects in a laminar boundary layer and to the analysis of its stability. All first- and second-order coefficients of the problem are determined from numerical solutions of the basic set of equations.
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    Archive of applied mechanics 69 (1999), S. 47-54 
    ISSN: 1432-0681
    Keywords: Key words Bifurcation ; stability ; multibody system dynamics ; singularity theory ; Liapunov's direct method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary In this paper, the global behavior of relative equilibrium states of a three-body satellite with flexible connection under the action of the gravitational torque is studied. With geometric method, the conditions of existence of nontrivial solutions to the relative equilibrium equations are determined. By using reduction method and singularity theory, the conditions of occurrence of bifurcation from trivial solutions are derived, which agree with the existence conditions of nontrivial solutions, and the bifurcation is proved to be pitchfork-bifurcation. The Liapunov stability of each equilibrium state is considered, and a stability diagram in terms of system parameters is presented.
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    Archive of applied mechanics 65 (1995), S. 99-109 
    ISSN: 1432-0681
    Keywords: Bars ; voids ; viscoelasticity ; stability ; critical load
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Dynamic stability of an elastic bar with voids is considered. Using the Lyapunov approach some new sufficient stability conditions are obtained and explicit expressions for the critical load are derived.
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    Journal of intelligent and robotic systems 27 (2000), S. 195-209 
    ISSN: 1573-0409
    Keywords: wall-climbing robot ; electromagnetic grippers ; stability ; additional support element ; sliding and turning over conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Legged-climbing robot is considered. Each foot of the robot has an electromagnet system for robot"s holding on a metal surface. This surface can be both vertical and inclined, including negative slope. Analytical calculation of robot stability under turn over or sliding conditions has been made. Critical slopes have been determined. One of these slopes corresponds to minimal reserve of robot stability towards sliding and another to minimal reserve of robot stability towards turning-over. As total reserve of stability of a robot is always equal to the minimal one of these reserves. Additional support elements of elastic material with high coefficient of friction, along with electromagnet, allows to increase minimal reserve of robot stability towards sliding. The use of such support elements leads to redistributing force of normal support reaction between electromagnet (which surface has low coefficient of friction) and additional support element (which surface has high coefficient of friction). It is just what leads to increasing the total friction force and as a consequence to increasing of minimal reserve of robot stability towards sliding.
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    Journal of intelligent and robotic systems 23 (1998), S. 27-43 
    ISSN: 1573-0409
    Keywords: autonomous control ; actuator delays ; stability
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper, we consider the control design problem of vehicle following systems with actuator delays. An upper bound for the time delays is first constructed to guarantee the vehicle stability. Second, sufficient conditions are presented to avoid slinky-effects in the vehicle following. Next, zero steady state achieved by the proposed controller is proven. Finally, simulations are given to examine our claims.
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    Letters in mathematical physics 53 (2000), S. 313-320 
    ISSN: 1573-0530
    Keywords: partial differential equations ; nonlinearities ; symmetries ; stability ; minimization
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    Topics: Mathematics , Physics
    Notes: Abstract We suggest a simple but general method of establishing symmetry properties of stable solutions of nonlinear elliptic equations. The method relies on characterization of symmetry breaking with a help of zero modes and on a generalization of the Perron–Frobenius theory.
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    Journal of statistical physics 88 (1997), S. 691-711 
    ISSN: 1572-9613
    Keywords: Quasicrystals ; nonperiodic tilings ; classical lattice-gas models ; ground states ; stability
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    Topics: Physics
    Notes: Abstract We give strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions, but rather are generic in some regions of phase space. We show this by constructing classical lattice-gas models with translation-invariant finite-range interactions and with a unique quasiperiodic ground state which is stable against small perturbations of two-body potentials. More generally, we provide a criterion for stability of nonperiodic ground states.
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    Journal of statistical physics 91 (1998), S. 285-305 
    ISSN: 1572-9613
    Keywords: Chapman–Enskog expansion ; Burnett equation ; Boltzmann equation ; stability
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    Topics: Physics
    Notes: Abstract This paper continues the author's study of procedures for rewriting the well-known Chapman–Enskog expansion used in the kinetic theory of gases. The usual Chapman–Enskog expansion, when used in isothermal fluid motion, will introduce nonlinear instability at super-Burnett order O(ε3) truncation. The procedure given here eliminates the truncation instability and produces the desired dissipation inequality.
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    Journal of statistical physics 95 (1999), S. 835-850 
    ISSN: 1572-9613
    Keywords: quasicrystals ; nonperiodic tilings ; classical lattice-gas models ; nonperiodic ground states ; nonperiodic Gibbs states ; stability ; frustration
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    Topics: Physics
    Notes: Abstract One of the fundamental problems of quasicrystals is to understand their occurrence in microscopic models of interacting particles. We review here recent attempts to construct stable quasicrystalline phases. In particular, we compare two recently constructed classical lattice-gas models with translation-invariant interactions and without periodic ground-state configurations. The models are based on nonperiodic tilings of the plane by square-like tiles. In the first model, all interactions can be minimized simultaneously. The second model is frustrated; its nonperiodic ground state can arise only by the minimization of the energy of competing interactions. We put forward some hypotheses concerning stabilities of nonperiodic ground states. In particular, we introduce two criteria, the so-called strict boundary conditions, and prove their equivalence to the zero-temperature stability of ground states against small perturbations of potentials of interacting particles. We discuss the relevance of these conditions for the low-temperature stability, i.e., for the existence of thermodynamically stable nonperiodic equilibrium states.
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    Journal of statistical physics 95 (1999), S. 867-902 
    ISSN: 1572-9613
    Keywords: kinetics of phase transitions ; domain coarsening ; asymptotic behavior ; self-similarity ; stability ; chaos
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    Topics: Physics
    Notes: Abstract The classical Lifshitz–Slyozov–Wagner theory of domain coarsening predicts asymptotically self-similar behavior for the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field. Here we consider the long-time behavior of measure-valued solutions for systems in which particle size is uniformly bounded, i.e., for initial measures of compact support. We prove that the long-time behavior of the size distribution depends sensitively on the initial distribution of the largest particles in the system. Convergence to the classically predicted smooth similarity solution is impossible if the initial distribution function is comparable to any finite power of distance to the end of the support. We give a necessary criterion for convergence to other self-similar solutions, and conditional stability theorems for some such solutions. For a dense set of initial data, convergence to any self-similar solution is impossible.
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    Journal of statistical physics 101 (2000), S. 731-746 
    ISSN: 1572-9613
    Keywords: attractive Bose–Einstein condensates ; nonlinear Schrödinger equation ; stability ; ground state ; variational arguments
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    Topics: Physics
    Notes: Abstract We propose the critical nonlinear Schrödinger equation with a harmonic potential as a model of attractive Bose–Einstein condensates. By an elaborate mathematical analysis we show that a sharp stability threshold exists with respect to the number of condensate particles. The value of the threshold agrees with the existing experimental data. Moreover with this threshold we prove that a ground state of the condensate exists and is orbital stable. We also evaluate the minimum of the condensate energy.
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    Journal of intelligent and robotic systems 20 (1997), S. 131-155 
    ISSN: 1573-0409
    Keywords: robot adaptive control ; basis function-like networks ; stability ; discrete variable structure
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Stable neural network-based sampled-data indirect and direct adaptivecontrol approaches, which are the integration of a neural network (NN)approach and the adaptive implementation of the discrete variable structurecontrol, are developed in this paper for the trajectory tracking control ofa robot arm with unknown nonlinear dynamics. The robot arm is assumed tohave an upper and lower bound of its inertia matrix norm and its states areavailable for measurement. The discrete variable structure control servestwo purposes, i.e., one is to force the system states to be within the stateregion in which neural networks are used when the system goes out of neuralcontrol; and the other is to improve the tracking performance within the NNapproximation region. Main theory results for designing stable neuralnetwork-based sampled data indirect and direct adaptive controllers aregiven, and the extension of the proposed control approaches to the compositeadaptive control of a flexible-link robot is discussed. Finally, theeffectiveness of the proposed control approaches is illustrated throughsimulation studies.
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    Journal of intelligent and robotic systems 22 (1998), S. 23-38 
    ISSN: 1573-0409
    Keywords: robot dynamic model ; stiffness matrix ; constant disturbance ; integrator backstepping ; Liapunov functions ; Barbalat lemma ; stability
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A robust regulator for flexible-joint robots is proposed, which yields constant torque disturbance rejection acting on the links. The design uses the integrator backstepping technique [4,5] to cancel nonlinearities and disturbance not in the range space of the control. Stability of the closed loop system is shown using iterative Liapunov functions.
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    Journal of intelligent and robotic systems 19 (1997), S. 411-436 
    ISSN: 1573-0409
    Keywords: assembly planning ; stability ; robot ; forward ; operations
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The paper presents an approach to sequence planning consisting in determining assembly sequences defined in terms of mating and non-mating operations and based on a dynamic expansion of the assembly tree obtained using a knowledge base management system. The planner considers the case of a single-robot assembly workcell. The use of stability and the detailed definition of sequences also by means of several non-mating operations are shown to be powerful instruments in the control of the tree expansion. Forward assembly planning has been chosen, in order to minimize the number of stability checks. Backtracking is avoided by combining precedence relations and stability analysis. Hard and soft constrains are introduced to drive the tree expansion. Hard constraints are precedence relations and stability analysis. All operations are associated to costs, which are used as soft constraints. The operation based approach enables one to manage even non-mating operations and to easily overcome the linearity constraint. Costs enable the planner to manage the association among tools and components. The first section of the paper concerns Stability Analysis that is subdivided into Static and Dynamic Stability Analysis. The former is mainly involved in analyzing gravity effects; the latter is mainly involved in evaluate inertia effects due to manipulation. Stability Analysis is implemented in a simplified form. Fundamental assumptions are: no rotational equilibrium condition is considered; for each reaction force only direction and versus, but not magnitude, are considered; friction is neglected. The second section discusses the structure of the planner and its implementation. The planner is a rule based system. Forward chaining and hypothetical reasoning are the inference strategies used. The knowledge base and the data base of the system are presented and the advantages obtained using a rule based system are discussed. The third section shows two planning examples, showing the performance of the system in a simple case and in an industrial test case, the assembly of a microwave branching filter composed of 26 components.
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    Journal of intelligent and robotic systems 26 (1999), S. 91-100 
    ISSN: 1573-0409
    Keywords: robots ; neural networks ; adaptiveness ; stability ; approximation
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract An indirect adaptive control approach is developed in this paper for robots with unknown nonlinear dynamics using neural networks (NNs). A key property of the proposed approach is that the actual joint angle values in the control law are replaced by the desired joint angles, angle velocities and accelerators, and the bound on the NN reconstruction errors is assumed to be unknown. Main theoretical results for designing such a neuro-controller are given, and the control performance of the proposed controller is verified with simulation studies.
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    Acta mechanica solida Sinica 9 (1996), S. 179-183 
    ISSN: 0894-9166
    Keywords: crack growth ; stability ; cusp catastrophe ; J-integral ; three-point bending specimen
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This paper presents an attempt at the application of catastrophe theory to the stability analysis ofJ-controlled crack growth in three-point bending specimens. By introducing the solutions ofJ- integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.
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    ISSN: 1432-0770
    Keywords: Key words: Hebbian learning rule ; attractor dynamics ; symmetric connections ; multiplicative normalization ; self-organization ; stability
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    Topics: Biology , Computer Science , Physics
    Notes: Abstract. While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs.
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    Computational mechanics 23 (1999), S. 8-19 
    ISSN: 1432-0924
    Keywords: Keywords: Material characteristic length ; strain-rate gradient ; dominant growth rate ; viscoplastic material ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract We study thermomechanical deformations of a viscoplastic body deformed in simple shear. The strain gradients are taken as independent kinematic variables and the corresponding higher order stresses are included in the balance laws, and the equation for the yield surface. Three different functional relationships, the power law, and those proposed by Wright and Batra, and Johnson and Cook are used to relate the effective strain rate to the effective stress and temperature. Effects of strain hardening of the material and elastic deformations are neglected. The homogeneous solution of the problem is perturbed and the stability of the problem linear in the perturbation variables is studied. Following Wright and Ockendon's postulate that the wavelength whose initial growth rate is maximum determines the minimum spacing between adjacent shear bands, the shear band spacing is computed. It is found that the minimum shear band spacing is very sensitive to the thermal softening coefficient/exponent, the material characteristic length and the nominal strain-rate. Approximate analytical expressions for the critical wave length for heat conducting nonpolar materials and locally adiabatic deformations of gradient dependent materials are also derived.
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    Journal of nonlinear science 5 (1995), S. 373-418 
    ISSN: 1432-1467
    Keywords: Hamiltonian system with symmetry ; relative equilibria ; perturbation ; linearization ; stability
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    Topics: Mathematics , Physics
    Notes: Summary A relative equilibrium of a Hamiltonian system with symmetry is a point of phase space giving an evolution which is a one-parameter orbit of the action of the symmetry group of the system. The evolutions of sufficiently small perturbations of a formally stable relative equilibrium are arbitrarily confined to that relative equilibrium's orbit under the isotropy subgroup of its momentum. However, interesting evolution along that orbit, here called drift, does occur. In this article, linearizations of relative equilibria are used to construct a first order perturbation theory explaining drift, and also to determine when the set of relative equilibria near a given relative equilibrium is a smooth symplectic submanifold of phase space.
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    International journal of fracture 105 (2000), S. 57-79 
    ISSN: 1573-2673
    Keywords: Interface toughness ; interface debonding ; stability ; adhesive interface ; bimaterial.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper, we studied the interface debonding when a crack perpendicularly approaches an interface between two dissimilar elastic materials. An interface toughness law was first defined according to an adhesive model governing the interface fracture. By analysing the interaction between the normally approaching crack and the interface crack and by tacking account of the adhesive forces at ends of the interfacial crack, a model for studying the interface debonding and the debonding stability was established. It is observed that the interface debonding toughness depends strongly on the mixed mode locally produced over the plastic adhesive zone of the interface. Moreover, the interface debonding may be unstable, i.e. the interface debonding length may jump from an initial value to a certain final value under critical remote loading. This jump may be surprisedly important in certain cases. These results agree with the experimental works gathered so far and can be used to explain the mechanism of 'crack arrestor' formed by an interface.
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    Interface science 3 (1996), S. 303-316 
    ISSN: 1573-2746
    Keywords: epitaxy ; Krudjumov-Sachs ; stability
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract In this paper we address the problems related to critical misfit and thickness in epilayer-substrate combinations of comparable bond strengths; specifically the case in which a pseudomorphic monolayer (ML) is stable and the critical thickness is about three MLs or less. Of particular interest are the average energies related to misfit strain f KS and misfit dislocations (MDs)—in the latter case the individual contributions of the oscillatory strains 〈V〉 and the epilayer-substrate disregistry 〈V〉MD. The individual energies are of interest because they may play different roles in the realization of specific growth modes. The analytical approach involves the following assumptions: (a) a rigid substrate as source of a periodic epilayer atom-substrate interaction potential which we model in terms of a low order truncated Fourier series; and (b) an epilayer which (i) deforms harmonically with zero strain gradient normal to the film plane, (ii) grows in Kurdjumov-Sachs (KS) orientation due to small misfit. f KS and in the layer-by-layer growth mode. Arguments are presented claiming that this interfacial situation may be approximated by a one-dimensional problem in which epilayer stiffness constants and equilibrium structure, as well as epilayer-substrate interaction depend on epilayer thickness; which poses a complex problem. An approximate solution could be obtained by assuming these quantities to be independent of thickness and proximities of the vacuum and the substrate. The most prominent conclusions are that the equilibrium density of MDs and hence the transition from misfit accommodation by MS to one containing MDs is a catastrophic process and that sustained minimum energy may require the overcoming of an energy barrier. While elementary implementation of the results to equilibrium growth mode theory suggests—independently of the catastrophic nature—that energetically favored misfit strain relief by misfit dislocations may, or may not, effect a transition to Stranski-Krastanov growth, a crude numerical calculation favors the transition. A proper implementation of the results require extensive numerical calculations and is planned for the near future.
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    Oxidation of metals 46 (1996), S. 169-184 
    ISSN: 1573-4889
    Keywords: XPS ; steel ; stability ; oxide ; sulfur
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract X-ray photoelectron spectroscopy measurements show that exposure of an Fe−Cr−Ni alloy to H2S and O2 under ultrahigh vacuum (UHV) conditions leads to the thermal instability of the Fe oxide without affecting the Cr oxide. An atomically clean metal surface, predominantly Fe in composition and free of internal sulfur, was exposed to H2S under controlled conditions in order to form a sulfided monolayer. Adsorbed S inhibited surface oxidation at temperatures between 325 K and 825 K. The presence of adsorbed S did not, however, inhibit the surface segregation of Cr for temperatures 〉600 K, compared to a S-free sample. Upon annealing of a sulfided sample to 900 K in UHV, the Fe oxide largely disappears, while no change is observed in the Cr oxide. The S-free sample shows no significant change in either the Fe or Cr oxides upon annealing. The results presented in this paper show that sulfidation of an alloy surface prior to oxidation and surface segregation can adversely affect the thermal stability of the Fe oxide without affecting the Cr oxide overlayer resulting from surface segregation and preferential oxidation.
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    Acta mechanica Sinica 12 (1996), S. 124-134 
    ISSN: 1614-3116
    Keywords: jet ; stability ; breakup ; atomization
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet. With respect to the spatial growing disturbance mode, the numerical results obtained from the solution of the dispersion equation reveal that a dimensionless parameterJ e exists. AsJ e〉1, the axisymmetric disturbance mode is most unstable; and whenJ e〈1, the asymmetric disturbances come into being, their growth rate increases with the decrease, ofJ e, till one of them becomes the most unstable disturbance. The breakup of a low-speed liquid jet results from the developing of axisymmetric disturbances, whose instability is produced by the surface tension; while the atomization of a high-speed liquid jet is brought about by the evolution of nonaxisymmetric disturbance, whose instability is caused by the aerodynamic force on the interface between the jet and the ambient gas.
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    Acta mechanica Sinica 14 (1998), S. 274-282 
    ISSN: 1614-3116
    Keywords: time delay ; stability ; frozen time approach ; retarded dynamic systems
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    Notes: Abstract By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involving arbitrary time delays, respectively. It is found that the asymptotic stability of these retarded dynamic systems is governed by the maximal and minimal singular values of the coefficient matrices and their time derivatives.
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    Acta mechanica Sinica 16 (2000), S. 264-272 
    ISSN: 1614-3116
    Keywords: nonlinear dynamics ; bifurcation ; stability ; fluid-solid interaction
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.
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    Acta mechanica Sinica 13 (1997), S. 366-376 
    ISSN: 1614-3116
    Keywords: vibro-impact ; stability ; multiplicity
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation are analytically derived. The stability condition of a periodic impacting motion is given by analyzing the propagation of small, arbitrary perturbation from that motion. In numerical simulations, the periodic impacting motions are classified according to the system states before and after an impact. The numerical results show that there exist many types of vibro-impacts and the bifurcation of periodic vibro-impacts is not smooth.
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    Acta mechanica Sinica 14 (1998), S. 226-233 
    ISSN: 1614-3116
    Keywords: jet ; stability ; dispersion equation ; swirling gas
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet injected into a gas with swirl. Here, the dimensionless parameterJ e is again introduced, in the meantime, another dimensionless parameterE called as circulation is also introduced to represent the relative swirling intensity. With respect to the spatial growing disturbance mode, the numerical results obtained from solving the dispersion equation reveal the following facts. First, at the same value ofE, in pace with the changing ofJ e , the variation of disturbance and the critical disturbance mode still keep the same characters. Second, the present results are the same as that of S.P. Lin whenJ e 〉1; but in the range ofJ e 〈1, it's no more the case, the swirl decreases the axisymmetric disturbance, yet increases the asymmetric disturbance, furthermore the swirl may make the character of the most unstable disturbance mode changed (axisymmetric or asymmetric); the above action of the swirl becomes much stronger whenJ e ≪1.
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    Applied mathematics and mechanics 16 (1995), S. 195-202 
    ISSN: 1573-2754
    Keywords: nonlinear ; stability ; Lyapunov function
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In the paper Lyapumov function for a fourth order linear system is given and stability of the trivial solutions to a class of fourth order nonlinear systems is studied.
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    Applied mathematics and mechanics 16 (1995), S. 635-642 
    ISSN: 1573-2754
    Keywords: analytic mechanics ; nonholonomic system ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The stability for the equilibrium states of Chaplygin's systems is considered. The equations of motion of Chaplygin's systems and the existence conditions of their equilibrium states are given. Some criteria of stability for the equilibrium. states of Chaplygin's systems are obtained. Two examples are finally given.
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    Applied mathematics and mechanics 17 (1996), S. 869-877 
    ISSN: 1573-2754
    Keywords: thermohaline double-diffusive system ; periodic solution ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A shortout analytic method of stability in strong nonlinear autonomous system is introduced into stability analysis of the thermohaline double-diffusive system. Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions. For linear periodic solution in infinitesimal motion, the existence range of monotomic branch and oscillatory branch are outilined. The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μ is smaller than critical value µ c in this case of 0〈rs-rsc≪1. The stability conclusions under different direction of vortex are drawn out.
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  • 58
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    Applied mathematics and mechanics 19 (1998), S. 163-168 
    ISSN: 1573-2754
    Keywords: nonlinear equation ; stability ; Newton's method ; auto-adjustable damping method ; the vector of damping factors
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The general approach for solving the nonlinear equations is linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For the strongly nonlinear problems, the solution obtained in the iterative process is always difficult, even divergent due to the numerical instability. It can not fulfill the engineering requirements. Newton's method and its variants can not settle this problem. As a result, the application of numerical simulation for the strongly nonlinear problems is limited. An auto-adjustable damping method has been presented in this paper. This is a further improvement of Newton's method with damping factor. A set of vector of damping factor is introduced. This set of vector can be adjusted continuously during the iterative process in accordance with the judgement and adjustment. An effective convergence coefficient and quichening coefficient are employed to relax the restricted requirements for the initial values and to shorten the iterative process. Then, the numerical stability will be ensured for the solution of complicated strongly nonlinear equations. Using this method, some complicated strongly nonlinear heat transfer problems in airplanes and aeroengines have been numerically simulated successfully. It can be used for the numerical simulation of strongly nonlinear problems in engineering such as nonlinear hydrodynamics and aerodynamics, heat transfer and structural dynamic response etc.
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    Applied mathematics and mechanics 19 (1998), S. 861-867 
    ISSN: 1573-2754
    Keywords: rotating fluids ; motion of body ; small disturbances ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the disturbances to a uniformly rotating ideal fluid with a sphere moving steadily along the axis of rotation are analysed by using linearization theory, the equations of disturbance, pressure and disturbance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric. The equation of disturbance stream function is analysed with the method of normal modes, and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral disturbances are obtained. The conclusion is drawn that three are three kinds of possible forms of neutral disturbances.
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    Applied mathematics and mechanics 20 (1999), S. 912-916 
    ISSN: 1573-2754
    Keywords: delay ; neural network ; stability ; TN911.23 ; O332
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, by using Liapunov functional, some sufficient conditions are obtained for the stability of the equilibrium of a neural network model with delay of the type $$u'_i \left( t \right) = - b_i u_i \left( t \right) + \sum\limits_{j = 1}^n {T_{ij} f_j } \left( {\mu _j u_j \left( {t - \tau _j } \right)} \right) + c_i ,\tau _j \geqslant 0,i = 1,2 \cdots ,n.$$
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    Studia geophysica et geodaetica 42 (1998), S. 320-327 
    ISSN: 1573-1626
    Keywords: MHD ; stability ; bifurcations
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences , Physics
    Notes: Abstract A series of numerical studies on the behaviour of magnetic fields and motions in a spherical body of an electrically conducting incompressible fluid have been carried out. The magnetic field was assumed to be maintained by a given electromotive force inside the body and to continue as a potential field in outer space. In view of the motion an external forcing was taken into account, and boundary conditions were considered which correspond to a stress-free surface. The stability of several steady states has been studied as well as the evolutions starting from unstable states. In this paper a configuration with a poloidal magnetic field and a differential rotation, both symmetric about the same axis, is considered. This configuration is stable only for sufficiently small Hartmann numbers but evolves, if disturbed, in the case of larger Hartmann numbers toward a non-axisymmetric state. In this case the well-known symmetrization effect of differential rotation in magnetic fields is destroyed.
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    Applied mathematics and mechanics 19 (1998), S. 457-462 
    ISSN: 1573-2754
    Keywords: neural networks ; equilibrium ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, some sufficient conditions are obtained for the global asymptotic stability of the equilibrium of neural networks with interneuronal transmission delays of the type $$x'_i (t) = - b_i x_i (t) + \sum\limits_{j = 1}^n {\omega _{\ddot y} f_j (x_j (t - \tau _j )) + p_i (t 〉 0;i = 1,2, \cdots ,n)} $$
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    Applied mathematics and mechanics 20 (1999), S. 1384-1388 
    ISSN: 1573-2754
    Keywords: nonlinear dynamic system ; bifurcation ; stability ; TB123 ; O322
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A computation algorithm based on the Poincaré Mapping in combination with Pseudo-Arc Length Continuation Method is presented for calculating the unstable response with saddle-node bifurcation, and the singularity, which occurs using the general continuation method combined with Poincaré Mapping to follow the path, is also proved. A normalization equation can be introduced to avoid the singularity in the process of iteration, and a new iteration algorithm will be presented too. There will be two directions in which the path can be continued at each point, but only one can be used. The method of determining the direction will be presented in the paper. It can be concluded that is method is effective in analysis of nonlinear dynamic system with saddle-node bifurcations.
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    Applied mathematics and mechanics 20 (1999), S. 233-240 
    ISSN: 1573-2754
    Keywords: viscoelasticity ; cylindrical shell ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the dynamic stability of a viscoelastic circular cylindrical shell subject to an axial compressive force and a uniformly distributed radial compressive load is discussed. By using the Laplace transformation, stability conditions of viscoelastic shell under constant loads are yielded. By using synthetically the classical dynamic methods, the various dynamical properties for the dynamical system defined by the viscoelastic shell and the effect of parameters on the stability of structure are obtained.
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    Mechanics of composite materials 35 (1999), S. 495-506 
    ISSN: 1573-8922
    Keywords: layered structure ; shells ; frames ; stringers ; nonlinearity ; stability ; pulsed loading ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Nonlinear three-dimensional problems of dynamic deformation, buckling, and posteritical behavior of composite shell structures under pulsed loads are analyzed. The structure is assumed to be made of rigidly joined plates and shells of revolution along the lines coinciding with the coordinate directions of the joined elements. Individual structural elements can be made of both composite and conventional isotropic materials. The kinematic model of deformation of the structural elements is based on Timoshenko-type hypotheses. This approach is oriented to the calculation of nonstationary deformation processes in composite structures under small deformations but large displacements and rotation angles, and is implemented in the context of a simplified version of the geometrically nonlinear theory of shells. The physical relations in the composite structural elements are based on the theory of effective moduli for individual layers or for the package as a whole, whereas in the metallic elements this is done in the framework of the theory of plastic flow. The equations of motion of a composite shell structure are derived based on the principle of virtual displacements with some additional conditions allowing for the joint operation of structural elements. To solve the initial boundary-value problem formulated, an efficient numerical method is developed based on the finite-difference discretization of variational equations of motion in space variables and an explicit second-order time-integration scheme. The permissible time-integration step is determined using Neumann's spectral criterion. The above method is especially efficient in calculating thin-walled shells, as well as in the case of local loads acting on the structural element, when the discretization grid has to be condensed in the zones of rapidly changing solutions in space variables. The results of analyzing the nonstationary deformation processes and critical loads are presented for composite and isotropic cylindrical shells reinforced with a set of discrete ribs in the case of pulsed axial compression and external pressure.
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    Mechanics of composite materials 36 (2000), S. 475-480 
    ISSN: 1573-8922
    Keywords: stability ; three-dimensional theory ; tribotechnics ; elastoplastic deformations ; viscoelasticity ; surface ; tracking and dead loads ; laminated coating ; piecewise-homogeneous model ; active loading
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The problem of surface instability of laminated coatings with inelastic properties is considered within the framework of a model of piecewise-homogeneous media on the basis of the three-dimensional linearized theory of stability. A general statement of the problem is formulated and the basic characteristic equations are derived. The solutions of particular problems are obtained for elastoplastic and viscoelastic models of solids.
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  • 67
    ISSN: 1435-1536
    Keywords: Cholesterol ; membrane fluidity ; muramyldipeptide ; phospholipid ; stability
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Application of the muramyldipeptide derivative B30-MDP to liposomal vaccines will aid in the development of improved high immunogenicity vaccines. To give full play to the effectiveness of B30-MDP as a liposomal vaccine, it is important to evaluate the effect of cholesterol, dimyristoylphosphatidylcholine (DMPC) or distearoylphosphatidylcholine (DSPC) incorporation on the chemical stability of B30-MDP and physicochemical properties of B30-MDP/lipid mixed vesicles from the view point of pharmaceutics. The observed degradation rate constants of B30-MDP by hydrolysis in B30-MDP/cholesterol mixed vesicles were increased with increasing concentration of cholesterol, however, those in B30-MDP/DMPC and B30-MDP/DSPC mixed vesicles were unchanged with increasing concentration of DMPC and DSPC. The degradation behavior of B30-MDP was then compared with physicochemical properties of B30-MDP/lipid mixed vesicles, such as membrane fluidity and particle size. It was apparent that the degradation of B30-MDP in B30-MDP/cholesterol mixed vesicles was influenced by the particle size, but not by the fluidity of the membranes. In the case of B30-MDP/phospholipid mixed vesicles, MDP/phospholipid mixed vesicles, the degradation of B30-MDP was not influenced by either the membranes' fluidity or the particle size of the mixed vesicles. It is considered that the degradation of B30-MDP in the mixed vesicles is dependent on the membrane state, and the addition of cholesterol to B30-MDP vesicle inhibits the mutual interaction of MDP regions, whereas the addition of phospholipids hardly influences the mutual interaction of MDP regions, possibly owing to phase separation between B30-MDP and phospholipids.
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    Flow, turbulence and combustion 62 (1999), S. 137-162 
    ISSN: 1573-1987
    Keywords: laminar wall jet ; heat transfer ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The hydrodynamic stability of a low speed, plane, non-isothermal laminar wall jet at a constant temperature boundary condition was investigated theoretically and experimentally. The mean velocity and temperature profiles used in the stability analysis were obtained by implementing the Illingworth–Stewartson transformation that allows one to extend the classical Glauert solution to a thermally non-uniform flow. The stability calculations showed that the two unstable eigenmodes coexisting at moderate Reynolds numbers are significantly affected by the heat transfer. Heating is destabilizing the flow while cooling is stabilizing it. However, the large-scale instabilities associated with the inflection point of the velocity profile still amplify in spite of the high level of the stabilizing temperature difference. The calculated stability characteristics of the wall jet with heat transfer were compared with experimental data. The comparison showed excellent agreement for small amplitudes of the imposed perturbations. The agreement is less good for the phase velocities of the sub-harmonic wave and this is attributed to experimental difficulties and to nonlinear effects.
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    Earth, moon and planets 87 (1999), S. 103-115 
    ISSN: 1573-0794
    Keywords: Accretion ; exoplanetary system ; extrasolar planets ; numerical integration ; orbital migration ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A number of extrasolar planets have been detected in close orbits around nearby stars. It is probable that these planets did not form in these orbits but migrated from their formation locations beyond the ice line. Orbital migration mechanisms involving angular momentum transfer through tidal interactions between the planets and circumstellar gas-dust disks or by gravitational interaction with a residual planetesimal disk together with several means of halting inward migration have been identified. These offer plausible schemes to explain the orbits of observed extrasolar giant planets and giant planets within the Solar System. Recent advances in numerical integration methods and in the power of computer workstations have allowed these techniques to be applied to modelling directly the mechanisms and consequences of orbital migration in the Solar System. There is now potential for these techniques also to be applied to modelling the consequences of the orbital migration of planets in the observed exoplanetary systems. In particular the detailed investigation of the stability of terrestrial planets in the habitable zone of these systems and the formation of terrestrial planets after the dissipation of the gas disk is now possible. The stability of terrestrial planets in the habitable zone of selected exoplanetary systems has been established and the possibility of the accretion of terrestrial planets in these systems is being investigated by the author in collaboration with Barrie W. Jones (Open University), and with John Chambers (NASA-Ames) and Mark Bailey of Armagh Observatory, using numerical integration. The direct simulation of orbital migration by planetesimal scattering must probably await faster hardware and/or more efficient algorithms.
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    Flow, turbulence and combustion 54 (1995), S. 313-321 
    ISSN: 1573-1987
    Keywords: riblets ; stability ; Tollmien-Schlichting ; Görtler
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The onset of transition in the boundary layer over a grooved surface is studied by introducing the presence of grooves into the standarde 9 model with the aid of a previously obtained equivalent boundary condition. Under conditions of self-similarity and smallness of the grooves, Tollmien-Schlichting waves are found to be excited at a slightly smaller Reynolds number and Görtler vortices at a slightly larger one than on a smooth surface.
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    Colloid & polymer science 275 (1997), S. 155-161 
    ISSN: 1435-1536
    Keywords: Key words HCO-10 ; vesicles ; encapsulation ; stability ; solubilization
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  The characteristics of poly(oxyethylene) hydrogenated caster oil ether (HCO-10) vesicles were studied for the standpoints of encapsulation efficiency, stability, solubilization and permeability or barrier efficiency. The vesicles of 5% HCO-10 had 6.24% of calcein-entrapment efficiency and 240 nm of mean diameter. The stability of HCO-10 vesicle suspensions was dependent on their concentrations. In the vesicle suspensions of 10% HCO-10 or more, both the size of the vesicles and the fluidity of the suspensions obviously varied with incubation time, indicating that a flocculation occurred; whereas, the vesicle suspension of 5% HCO-10 was relatively stable. The solubilization process of HCO-10 vesicles by SDS was similar to that of EggPC liposomes. The rate constants for permeation of Cl ion and calcein were 2.46×10-3 s-1 and 5.79×10-5 s-1, respectively, suggesting that HCO-10 vesicles possessed some barrier potential for Cl ion and calcein although they were smaller than those of liposomes. Furthermore, the efflux of the solute such as calcein from HCO-10 vesicles was maximum at 37 °C, where the vesicle membrane was presumably destabilized by dehydration of EOs in HCO-10 molecules.
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  • 72
    ISSN: 1435-1536
    Keywords: Key words Heterophase polymerization ; emulsion ; polymer particle ; stability ; styrene conversion
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  Heterophase polymerization of styrene in the presence of di-p-tolyl-o-carbalkoxyphenylcarbinol (DTC) soluble in monomer and insoluble in water, as stabilizer, was investigated. The factors affecting polymer particle diameter, their size distribution and stability were investigated. It was suggested that polymer particles are formed from monomer droplets. The polystyrene suspension with narrow particle size distribution synthesized in the presence of DTC, was used for immunochemical research.
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    Colloid & polymer science 105 (1997), S. 38-40 
    ISSN: 1435-1536
    Keywords: α-haematite hydrosols ; stability ; urea ; ionic adsorption sequence ; water structure
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The effect of urea on the stability of α-haematite hydrosols in the presence of various monovalent ions was studied on each side of the pzc (pH 8.2) by measurements of the critical coagulation concentration (CCC) of the hydrosol. It was observed that for pHs lower than the pzc, the effect of urea depends strongly on the nature of coagulating ion and on the pH:The CCC values of IO 3 − increases with urea concentrations but those of ClO 4 − and Cl− decreases. For pHs higher than the pzc, an inversion of the cationic adsorption sequence was observed. This behavior is in a good agreement with the well-known action of urea on the structure of water and also with the general property of the α-haematite water interface.
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    Rheologica acta 34 (1995), S. 417-429 
    ISSN: 1435-1528
    Keywords: Electrorheology ; nonlinear ; simulations ; stability ; steady shear
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Particle-level simulations are employed to investigate the transition from linear to nonlinear rheological behavior for electrorheological suspensions under start-up of steady shear flow. This transition is found to first arise from the very slight rearrangement of structures, as opposed to the gross rupture of particulate columns. Linear stability analysis shows that these rearrangements occur when the structures are sheared into electrostatically unstable configurations. The rearrangements also produce a second type of relaxation phenomenon that appears at low frequencies and finite strain amplitudes. Incorporating more realistic force descriptions into the idealized simulation model shifts the transition to nonlinear deformation to smaller strain amplitudes, approaching experimentally observed values. The role of the rearrangement of unstable structures on the oscillatory shear flow response is investigated in the following paper, Part II.
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    Rheologica acta 34 (1995), S. 430-439 
    ISSN: 1435-1528
    Keywords: Electrorheology ; nonlinear ; simulations ; stability ; viscoelasticity
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    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract In the preceding paper, Part 1, the transition from linear to nonlinear behavior for electrorheological (ER) suspensions under start-up of steady shear flow was found to first arise from the slight rearrangement of unstable structures. In this paper, we investigate the transition to nonlinear behavior for ER suspensions under oscillatory shear flow, focusing on the role of the rearrangement of unstable structures, and employing experimental and simulation results. Again, we find that nonlinear deformation first arises from these rearrangements, as opposed to the gross rearrangement or rupture of particulate chains. The Fourier transform of the simulated time-dependent shear stress is employed to quantify the dependence of the critical strain on the deformation frequency and electric field strength. The predicted behavior is consistent with experimental trends. Methods for verifying the predictions are discussed, as well as possible avenues for exploiting this information in improved operating strategies and improved ER fluids.
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    Rheologica acta 36 (1997), S. 367-383 
    ISSN: 1435-1528
    Keywords: Viscoelastic flow ; arrays of cylinders ; stability ; porous media
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    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (Wec), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above Wec which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above Wec a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplifieds spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.
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    Rheologica acta 36 (1997), S. 367-383 
    ISSN: 1435-1528
    Keywords: Key words Viscoelastic flow ; arrays of cylinders ; stability ; porous media
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (We c ), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above We c which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above We c a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplified spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.
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    Journal of biological physics 20 (1995), S. 223-227 
    ISSN: 1573-0689
    Keywords: protocells ; microsphere ; thermal proteinoid ; stability ; surface energy ; bulk energy ; electrostatic energy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract The stability of protocells is discussed in terms of macroscopic energies. It is shown that bulk and surface energy contributions alone cannot lead to stable protocells. If electrostatic energy, due to transmembrane voltage, is taken into account, stable hollow spheres are proved to exist. For several reasons, however, this result should not be regarded as an ultimate explanation.
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    Journal of statistical physics 87 (1997), S. 1145-1164 
    ISSN: 1572-9613
    Keywords: Fisher-Kolmogorov equation ; traveling fronts ; fixed points ; population dynamics ; bifurcations ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The one-dimensional reaction-diffusion equations for the process (D) $$A + B \to 2A,B + C \to 2B,C + A \to 2C$$ are extended to include the counteracting reactions (R) $$A + 2B \to 3B,B + 2C \to 3C,C + 2A \to 3A$$ which have a reaction rate α relative to the direct process (D). This process can be seen as a three-component version of the reaction which is described by the Fisher-Kolmogorov equation. The fixed points of the equations are studied as a function of α. It is shown that the equations admit solutions which consist of a series of traveling fronts. Other solutions exist which are traveling periodic waves. A very remarkable fact is that for these waves exact expressions can be constructed.
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    International journal of thermophysics 19 (1998), S. 461-470 
    ISSN: 1572-9567
    Keywords: small-angle neutron scattering ; stability ; vesicles
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Small-angle neutron scattering (SANS) was used to investigate the structure of mixed colloids of egg yolk phosphatidylcholine (EYPC) with the bile salt, cholylglycine (CG), in D2O as a function of pressure (P) and temperature (T). At atmospheric pressure, the system forms an isotropic phase of mixed, single-bilayer vesicles (SLVs). Increasing the external hydrostatic pressure brought about significant changes in particle morphology. At T=25°C, application of a pressure of 3.5 MPa resulted in collapse of the SLVs. A further increase in P, up to 51.8 MPa, resulted in a transition from a phase of ordered (stacked), collapsed vesicles to one of stacked, ribbon-like particles. A similar collapse of the vesicles was observed at a higher temperature (T=37°C) with increasing P, but at this temperature, no ribbon phase was found at the highest pressure explored.
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    International journal of infrared and millimeter waves 19 (1998), S. 1721-1734 
    ISSN: 1572-9559
    Keywords: optical phase-locked loop ; stability ; phase jitter ; four-wave mixing ; semiconductor laser amplifier
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper, the properties of the optical phase-locked loop(PLL) based on the four-wave mixing in the semiconductor laser amplifiers (SLAs) are discussed. The components that achieve the function of detecting the bit phase of the input optical signal are concerned and discussed in detail together as a function module named as the optical bit phase detector referred to the general electronic PLL. Therefore, most of the properties of the optical PLL can be analyzed by applying the general phase-locked theory. Here the stability of the optical PLL is discussed. It's shown that the variance of input signal power in the practical application will cause optical PLL system unstable because of its long loop delay. The influence on the output phase jitter of the optical PLL is also investigated.
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    Applied mathematics and mechanics 21 (2000), S. 987-994 
    ISSN: 1573-2754
    Keywords: stability ; chaos ; averaging method ; Galerkin method ; viscoelastic column ; O322
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The dynamical stability of a homogeneous, simple supported column, subjected to a periodic axial force, is investigated. The viscoelastic material is assumed to obey the Leaderman nonlinear constitutive relation. The equation of motion was derived as a nonlinear integro-partial-differential equation, and was simplified into a nonlinear integro-differential equation by the Galerkin method. The averaging method was employed to carry out the stability analysis. Numerical results are presented to compare with the analytical ones. Numerical results also indicate that chaotic motion appears.
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  • 83
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    Applied mathematics and mechanics 19 (1998), S. 135-146 
    ISSN: 1573-2754
    Keywords: nonholonomic system ; Lagrange's theorem ; manifold ; stability ; Liapunov's direct method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The stability problem for the manifold of equilibrium positions of a class of nonholonomic systems is studied in this paper. Based on Liapunov's direct method and the definition of stability. Lagrange's theorem of holonomic systems is extended to a class of nonholonomic conservative systems and dissipative systems, and a new expression is made to the relation between asymptotic stability for the manifold of equilibrium positions of this class of nonholonomic systems and dissipative forces. Two examples are finally given to illustrate the application of the theorems.
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  • 84
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    Applied mathematics and mechanics 21 (2000), S. 1177-1186 
    ISSN: 1573-2754
    Keywords: elastic foundation ; pipe conveying fluid ; coupled-mode flutter ; stability ; power series method ; 0353
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by power series method. Compared with pipe without considering elastic foundation, the numerical results show that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe. And the increase of foundation parameters may increase the critical flow velocity of static instability and dynamic instability of pipe, thereby delays the occurrence of divergence and flutter instability of pipe. For higher mass ratio β, in the combination of certain foundation parameters, pipe behaves the phenomenon of restabilization and redivergence after the occurrence of static instability, and then coupled-mode flutter takes place.
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  • 85
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    Applied mathematics and mechanics 21 (2000), S. 1390-1400 
    ISSN: 1573-2754
    Keywords: suspended solid particles ; continuum phase-coupled model ; stability ; moving jet ; numerical computation ; O359
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The spatial stability equation of moving jet containing dense suspended solid particles was derived out by means of the continuum phase-coupled model. The stability curves of moving jet for different downstream distances, Reynolds number of flow-field, particle properties and velocities of jetting device are got by the finite difference method based on the asymptotic method and the Eulerian conservative difference scheme. Founded on the analysis of the obtained stability curves it is found that the positive velocity of jetting device widens the unstable frequency range of flow-field but the effect of the negative one is contrary. In addition, particles existing in the flow-field curb the instability of flow-field and the effect enhances with the decrease of Reynolds number of flow-field. These conclusions benefit learning the development of moving two-phase jet.
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  • 86
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    Applied mathematics and mechanics 21 (2000), S. 209-216 
    ISSN: 1573-2754
    Keywords: composite material ; rotational shell ; stability ; nonlinear ; O347.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract By adopting the energy method, a new method to calculate the stability of the composite shell of revolution is presented. This method takes the influence of nonlinear prebuckling deformations and stresses on the buckling of the shell into account. The relationships between the prebuckling deformations and strains are calculated by nonlinear Kármán equations. The numerical method is used to calculate the energy of the total system. The nonlinear equations are solved by combining gradient method and amendatory Newton iterative method. The computer program is also developed. An example is given to demonstrate the accuracy of the method presented.
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  • 87
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    Applied mathematics and mechanics 21 (2000), S. 237-242 
    ISSN: 1573-2754
    Keywords: system identification ; damped least square ; recursive algorithm ; convergence ; stability ; O231 ; O241
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The recursive least square is widely used in parameter identification. But it is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. It is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.
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    Journal of porous materials 3 (1996), S. 41-46 
    ISSN: 1573-4854
    Keywords: Iron Pillared Clay (Fe-PILC) ; acid-treatment ; base-treatment ; montmorillonite ; stability ; porosity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Fe-PILCs were treated in a mild acid and basic environment (low concentrated acids and bases at ambient temperatures) for two days to evaluate their influence on the structure and porosity. All modified Fe-PILCs were analyzed for different parameters such as surface area, micropore volume, interlayer distance and total amount of Fe2O3. Acid treatment has a positive influence on the surface area and micropore volume. However, a complete destruction of the structure was noticed after modification with solutions of equilibrium pH(pHeq) below 1.82. This collapse is accompanied by a serious loss of Fe2O3 as observed from EPMA-analysis. Besides an increased surface area and micropore volume, base modified Fe-PILCs show, independent of the pHeq used, XRD-peaks, indicating no structural breakdown during the treatment. This paper proposes on a model to explain the behaviour of Fe-PILCs in mild acid and basic environment.
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    Applied mathematics and mechanics 16 (1995), S. 1161-1169 
    ISSN: 1573-2754
    Keywords: shell ; stability ; critical load
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper gives the resultant forces and moments, strain energy and work of external forces on the basis of the deformation theory of flexible body. Therefore, in accordance with the principle of virtual displacement, the energy criterion of critical load is obtained and the equilibrium equation and boundary conditions of stability problem are derived.
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    Applied mathematics and mechanics 17 (1996), S. 65-75 
    ISSN: 1573-2754
    Keywords: impacting vibration ; stability ; codimension two bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract Bifurcation problems of a spring-mass system vibrating against an infinite large plane are studied in this paper. It is shown that there exist phenomena of codimension two bifurcations when the ratios of frequencies are in the neigborhood of the same special values and the coefficient of restitution approach unity. By theory of normal forms, we reduce Poincare maps to normal forms, and find flip bifurcations, Hopf bifurcations of fixed points and that of period two points. The theoretical solutions are verified by numerical computations.
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    Applied mathematics and mechanics 17 (1996), S. 1039-1049 
    ISSN: 1573-2754
    Keywords: nonlinear differential equations of the fourth order ; Lyapunov function ; stability ; boundedness ; intrinsic method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, we first present constructing a Lyapunov function for (1.1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡0, and the boundedness result of the solutions of (1.1) for case p≠0. These results improve several well-known results.
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    Applied mathematics and mechanics 20 (1999), S. 564-567 
    ISSN: 1573-2754
    Keywords: generalized Birkhoff's system ; equilibrium state ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and then the linear approximate method and direct method of stability in equilibrium state are studied. Some results on equilibrium of generalized Birkhoff's autonomous system are obtained on the basis of Lyapunov's thorem. Last, the application of the results is illustrated with an example.
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    Journal of elasticity 48 (1997), S. 218-239 
    ISSN: 1573-2681
    Keywords: stability ; nonlinear elasticity ; Mooney-Rivlin material ; incompressible material ; thick-walled tube
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The problem of instability of a hyperelastic, thick-walled cylindrical tube was first studied by Wilkes [1] in 1955. The solution was formulated within the framework of the theory of small deformations superimposed on large homogeneous deformations for the general class of incompressible, isotropic materials; and results for axially symmetrical buckling were obtained for the neo-Hookean material. The solution involves a certain quadratic equation whose characteristic roots depend on the material response functions. For the neo-Hookean material these roots always are positive. In fact, here we show for the more general Mooney–Rivlin material that these roots always are positive, provided the empirical inequalities hold. In a recent study [2] of this problem for a class of internally constrained compressible materials, it is observed that these characteristic roots may be real-valued, pure imaginary, or complex-valued. The similarity of the analytical structure of the two problems, however, is most striking; and this similarity leads one to question possible complex-valued solutions for the incompressible case. Some remarks on this issue will be presented and some new results will be reported, including additional results for both the neo-Hookean and Mooney–Rivlin materials.
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  • 94
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    Journal of elasticity 53 (1998), S. 199-213 
    ISSN: 1573-2681
    Keywords: thermoelasticity ; stability ; strong ellipticity.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A notion of material stability is introduced and discussed in the setting of nonlinear thermoelasticity. Necessary and sufficient conditions are established for the stability of a general thermoelastic material. The adiabatic theory and the theory that accounts for heat conduction are considered separately.
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    Multibody system dynamics 3 (1999), S. 287-299 
    ISSN: 1573-272X
    Keywords: multibody dynamics ; symbol manipulation ; linearization ; stability ; Floquet theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract It is shown that use of AUTOLEV, a symbol manipulation computer program for mechanics analyses, can greatly facilitate the stability analysis of motions of multibody systems.
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  • 96
    ISSN: 1573-2681
    Keywords: stability ; eigenvalue inequalities ; nonsmooth eigenvalue problems ; 35A15 ; 35R35 ; 73K20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Necessary conditions for the stability of elastic bodies subjected to nonmonotone multivalued boundary conditions are derived. These conditions are assumed to be derived from nonconvex and nonsmooth, quasidifferentiable energy functions. A ‘difference convex’ approximation of the potential energy function is written based on an appropriate quasidifferential formulation. Under appropriate assumptions for the convex and the concave parts we prove the existence of at least one nontrivial solution to the nonlinear eigenvalue problem.
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    Journal of elasticity 61 (2000), S. 49-81 
    ISSN: 1573-2681
    Keywords: collagen structure ; stability ; rupture criterion ; growth mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Intracranial saccular aneurysms remain an enigma; it is not known why they form, why they enlarge, or why only some of them rupture. Nonetheless, there is general agreement that mechanics plays an essential role in each aspect of the natural history of these potentially deadly lesions. In this paper, we review recent findings that discount limit point instabilities under quasi-static increases in pressure and resonance under dynamic loading as possible mechanisms of enlargement of saccular aneurysms. Indeed, recent histopathological data suggest that aneurysms enlarge due to a stress-mediated process of growth and remodeling of collagen, the primary load-bearing constituent within the wall. We submit that advanced theoretical, experimental, and numerical studies of this process are essential to further progress in treating this class of pathologies. The purpose of this review is to provide background and direction that encourages elasticians to contribute to this important area of research.
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    Mechanics of time-dependent materials 2 (1998), S. 335-349 
    ISSN: 1573-2738
    Keywords: Lyapunov exponents ; numerical methods ; random processes ; reliability ; rods ; stability ; viscoelasticity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The stability and reliability of a nonlinear viscoelastic rod under a stochastic excitation is investigated. The loads are assumed to be in the form of random stationary processes. The solution is obtained with the help of a numerical method, which is based on the method of the statistical simulation of random input processes and on the numerical solution of the system of nonlinear and linearized integro-differential equations. These equations describe a nonperturbed and perturbed motion of the rod. The estimation of the stability is carried out with the help of top Lyapunov exponents.
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