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  • Articles  (28)
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  • Springer  (28)
  • American Geophysical Union
  • American Institute of Physics (AIP)
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  • 1
    Electronic Resource
    Electronic Resource
    On the Bifurcation of Flows of a Heat-Conducting Fluid between Two Rotating Permeable Cylinders (1997)
    Springer
    Georgian mathematical journal 4 (1997), S. 567-578 
    Details
    ISSN: 1572-9176
    Keywords: Flow ; bifurcation ; perturbation ; axisymmetric flow ; permeable cylinders
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sufficient conditions are found for the bifurcation of flow of a viscous heat-conducting fluid between two rotating permeable cylinders.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022159609975
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  • 2
    Electronic Resource
    Electronic Resource
    On a certain two-sided symmetric condition in magnetic field analysis and computations (1997)
    Springer
    Applications of mathematics 42 (1997), S. 147-159 
    Details
    ISSN: 1572-9109
    Keywords: magnetic field ; variational formulation ; two-sided existence and uniqueness condition ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity models used in electrotechnical practice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022295111737
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  • 3
    Electronic Resource
    Electronic Resource
    Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method (1997)
    Springer
    Applications of mathematics 42 (1997), S. 259-277 
    Details
    ISSN: 1572-9109
    Keywords: Parameter identification ; parabolic problem ; finite element method ; Crank-Nicolson scheme
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The identification problem of a functional coefficient in a parabolic equation is considered. For this purpose an output least squares method is introduced, and estimates of the rate of convergence for the Crank-Nicolson time discretization scheme are proved, the equation being approximated with the finite element Galerkin method with respect to space variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023012328209
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  • 4
    Electronic Resource
    Electronic Resource
    Spatial Patterns for reaction-diffusion systems with conditions described by inclusions (1997)
    Springer
    Applications of mathematics 42 (1997), S. 421-449 
    Details
    ISSN: 1572-9109
    Keywords: reaction-diffusion systems ; variational inequalities ; inclusions ; bifurcation ; stationary solutions ; spatial patterns
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022203129542
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  • 5
    Electronic Resource
    Electronic Resource
    Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities (1997)
    Springer
    Czechoslovak mathematical journal 47 (1997), S. 469-486 
    Details
    ISSN: 1572-9141
    Keywords: reaction-diffusion systems ; unilateral conditions ; bifurcation ; quasivariational inequalities ; spatial patterns
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022411501260
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  • 6
    Electronic Resource
    Electronic Resource
    Dynamic analysis of arrest of buckle propagation on a beam on a nonlinear elastic foundation by FEM (1997)
    Springer
    Acta mechanica solida Sinica 10 (1997), S. 28-35 
    Details
    ISSN: 0894-9166
    Keywords: buckle propagation ; arrest of buckle ; beam on a nonlinear foundation ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasistatic analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02207607
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  • 7
    Electronic Resource
    Electronic Resource
    Effect of temperature on the fracture modes of BHW-35 steel under mode-II loading (1997)
    Springer
    Acta mechanica solida Sinica 10 (1997), S. 76-85 
    Details
    ISSN: 0894-9166
    Keywords: finite element method ; mode- II loading ; J integral
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Finite element method (FEM) has been used to analyze the stress and strain fields and the stress tri-axial levels around the tip of the crack under mode- II loading. The results show that: under mode- II loading, the direction of the maximum tensile stress and that of the maximum tri-axial levels (R o ) exist at an angle of −75. 3° from the original crack plane; the maximum shear stress andR o = 0 exist along the original crack plane. Mode- II loading experiment using BHW-35 steel at different temperatures show that there are two kinds of fracture mode, opening mode (or tensile mode) and sliding mode (or shear mode). A decrease in temperature causes the fracture mode to change from shear mode to tensile mode. For BHW-35 steel, this critical temperature is about −90 C. Actually, under any kind of loading mode (mode I . mode II , mode III or mixed mode), there always exist several kinds of potenital fracture modes (for example, opening mode, sliding mode, tearing mode or mixed mode). The effect of temperature under mode- II loading is actually related to the change of the elastic-plastic properties of the material.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02207612
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  • 8
    Electronic Resource
    Electronic Resource
    Measurement of Stress Intensity Factors of a Mixed-Mode Interface Crack by a Speckle Photography (1997)
    Springer
    Optical review 4 (1997), S. 253-260 
    Details
    ISSN: 1349-9432
    Keywords: speckle photography ; Young’s fringe ; two-dimensional Fourier transform ; finite element method ; stress intensity factor ; interface crack ; mixed mode ; displacement extrapolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The image-processing system based on a two-dimensional Fourier transform is presented for the analysis of Young’s fringes pattern created from a double-exposure speckle photograph. The fringe spacing and orientation are determined using only one Young’s fringes pattern without any other diffraction halo patterns. The stress-intensity factors of a mixed-mode interface crack were measured by speckle photography. A compact normal and shear specimen with an interface crack was employed. This specimen enables us to carry out the experiment under various kinds of mixed-mode loading. A steel and an epoxy resin were used as dissimilar materials. The displacement along the crack lines at the free surface was measured by speckle photography. The K1 and K11 values were determined by a least squares method using displacement data along the crack lines. Three-dimensional finite element analysis was carried out on the same specimen. An accuracy of stress intensity factors obtained by the speckle photography was discussed by comparison of results obtained by the finite element analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s10043-997-0253-4
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  • 9
    Electronic Resource
    Electronic Resource
    Dynamic behavior of piles embedded in transversely isotropic layered media (1997)
    Springer
    Acta mechanica Sinica 13 (1997), S. 241-252 
    Details
    ISSN: 1614-3116
    Keywords: pile-soil system ; soil anisotropy ; transversely isotropic layered media ; dynamic behavior ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Dynamic behavior of single pile embedded in transversely isotropic layered media is investigated using the finite element method combined with dynamic stiffness matrices of the soil derived from Green's function for ring loads. The influence of soil anisotropy on the dynamic behavior of piles is examined through a series of parametric studies
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487706
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  • 10
    Electronic Resource
    Electronic Resource
    Deformation localization and shear band fracture in strong anisotropy sheet tension (1997)
    Springer
    Acta mechanica Sinica 13 (1997), S. 143-152 
    Details
    ISSN: 1614-3116
    Keywords: deformation localization and shear band fracture ; planar anisotropy ; sheet metal tension ; finite element method
    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 tensile deformation localization and the shear band fracture behaviors of sheet metals with strong anisotropy are numerically simulated by using Updating Lagrange finite element method, Quasi-flow plastic constitutive theory[1] and B-L planar anisotropy yield criterion[2]. Simulated results are compared with experimental ones. Very good consistence is obtained between numerical and experimental results. The relationship between the anisotropy coefficientR and the shear band angle θ is found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487920
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  • 11
    Electronic Resource
    Electronic Resource
    Evolution of single elliptic vortex rings (1997)
    Springer
    Acta mechanica Sinica 13 (1997), S. 17-25 
    Details
    ISSN: 1614-3116
    Keywords: elliptic vortex ring ; pseudo-spectral method ; bifurcation ; vortex reconnection
    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 evolution of single elliptic vortex rings for initial aspect ratio (AR)=2,4,6 has been studied. The incompressible Navier-Stokes equations are solved by a dealiased pseudo-spectral method with 643 grid points in a periodic cube. We find that there are three kinds of vortex motion asAR increases and bifurcation occurs at certainAR. The processes of advection, interaction and decay of vortex ring are discussed. Numerical results coincide with experiments and other authors' numerical simulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487827
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  • 12
    Electronic Resource
    Electronic Resource
    Numerical bifurcation and stability analysis for steady-states of reaction diffusion equations (1997)
    Springer
    Numerical algorithms 14 (1997), S. 211-225 
    Details
    ISSN: 1572-9265
    Keywords: bifurcation function ; elliptic boundary value problem ; finite element method ; reduction to an alternative problem ; stability of steady-states ; 35J25 ; 65N35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Solutions $$u \in H_0^1 (\Omega ) \cap H^2 (\Omega )$$ of a semilinear elliptic boundary value problem, $$Au + f(x,u,\lambda ) = 0$$ (with $$f_u (x,u,\lambda )$$ bounded below) can be put into a one-to-one correspondence with zeros $$c \in \mathbb{R}^d $$ of a function $$c \to B(c,\lambda ) \in \mathbb{R}^d $$ . Often d is small. The function $$B(c,\lambda )$$ is called the bifurcation function. It can also be shown that the eigenvalues of the matrix $$B_c (c,\lambda )$$ characterize the stability properties of the solutions of the elliptic problem as rest points of $$u_t + Au + f(x,u,\lambda ) = 0$$ . A finite element method that can be used for computing B and B c has recently been proposed. An overview of these results and the finite element method is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019117130906
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  • 13
    Electronic Resource
    Electronic Resource
    The optimal control variational principle and finite elements analysis for viscoplastic dynamics (1997)
    Springer
    Applied mathematics and mechanics 18 (1997), S. 61-68 
    Details
    ISSN: 1573-2754
    Keywords: viscoplastic dynamics ; optimal control ; variational principle ; finite element 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 This paper presents the optimal control variational principle for Perzyna model which is one of the main constitutive relation of viscoplasticity in dynamics. And it could also be transformed to solve the parametric quadratic programming problem. The FEM form of this problem and its implementation have also been discussed in the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02457502
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  • 14
    Electronic Resource
    Electronic Resource
    On the problem of the number of bifurcation solutions at singular point (1997)
    Springer
    Applied mathematics and mechanics 18 (1997), S. 969-973 
    Details
    ISSN: 1573-2754
    Keywords: homotopy ; continuation method ; bifurcation ; isolated singularity
    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, it is proved that the solutions of a nonlinear equation are isolated under the condition that the singular points are isolated. It shows that there must have and only have finite solutions branching from bifurcation point. This is important for the numerical analysis of bifurcation problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00189288
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  • 15
    Electronic Resource
    Electronic Resource
    A modified Hellinger-Reissner variational functional including only two independent variables for large displacement of thin shallow shell (1997)
    Springer
    Applied mathematics and mechanics 18 (1997), S. 663-670 
    Details
    ISSN: 1573-2754
    Keywords: variational principle ; shallow shell ; large displacement ; finite element 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 variational functional of the Hellinger-Reissner variational principle for the large displacement problem of a thin shallow shell with an arbitrary shape is first established. Then the functional of the modified principle suitable for the finite element method is derived. In the functional only two independent variables, the deflection ω and the stress function F are included. The displacement expressions in the middle surface on the boundary of the shell is also derived by means of the previous two variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00127014
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  • 16
    Electronic Resource
    Electronic Resource
    Nonlinear stability analysis of a clamped rod carrying electric current (1997)
    Springer
    Applied mathematics and mechanics 18 (1997), S. 825-834 
    Details
    ISSN: 1573-2754
    Keywords: magnetoelasticity ; bifurcation ; limit point ; numerical method ; straight rod carrying electric current
    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 is devoted to the analysis of the nonlinear stability of a clamped rod carrying electric current in the magnetic field which is produced by the current flowing in a pair of inifinitely long parallel rigid wires. The natural state of the rod is in the plane of the wires and is equidistant from them. Firstly under the assumption of spatial deformation, the governing equations of the problem are derived, and the linearized problem and critical currents are discussed. Secondly, it is proved that the buckled states of the rod are always in planes. Finally, the global responses of the bifurcation problem of the rod are computed numerically and the distributions of the deflections, axial forces and bending moments are obtained. The results show that the buckled states of the rod may be either supercritical or subcritical, depending on the distancz between the rod and the wires. Furthermore, it is found that there exists a limit point on the branch solution of the supercritical buckled state. This is distinctively different from the buckled state of the elastic compressive rods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00133340
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  • 17
    Electronic Resource
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    Interweaving Kohonen Maps of Different Dimensions to Handle Measure Zero Constraints on Topological Mappings (1997)
    Springer
    Neural processing letters 5 (1997), S. 83-89 
    Details
    ISSN: 1573-773X
    Keywords: finite element method ; Kohonen ; neural networks ; self-organizing ; topological mapping
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The usual “Kohonen” algorithm uses samples of points in a domain to develop a topological correspondence between a grid of “neurons” and a continuous domain. “Topological” means that near points are mapped to near points. However, for many applications there are additional constraints, which are given by sets of measure zero, which are not preserved by this method, because of insufficient sampling. In particular, boundary points do not typically map to boundary points because in general the likelihood of a sample point from a two-dimensional domain falling on the boundary is typically zero for continuous data, and extremely small for numerical data. A specific application, (assigning meshes for the finite element method), was recently solved by interweaving a two-dimensional Kohonen mapping on the entire grid with a one-dimensional Kohonen mapping on the boundary. While the precise method of interweaving was heuristic, the underlying rationale seems widely applicable. This general method is problem independent and suggests a direct generalization to higher dimensions as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009670110038
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  • 18
    Electronic Resource
    Electronic Resource
    Conservation and bifurcation of an invariant torus of a vector field (1997)
    Springer
    Mathematical notes 61 (1997), S. 29-37 
    Details
    ISSN: 1573-8876
    Keywords: invariant tori ; quasiperiodic motion ; bifurcation ; noncritical matrices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider small perturbations with respect to a small parameter ε≥0 of a smooth vector field in ℝn+m possessing an invariant torusT m. The flow on the torusT m is assumed to be quasiperiodic withm basic frequencies satisfying certain conditions of Diophantine type; the matrix Ω of the variational equation with respect to the invariant torus is assumed to be constant. We investigate the existence problem for invariant tori of different dimensions for the case in which Ω is a nonsingular matrix that can have purely imaginary eigenvalues.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02355005
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  • 19
    Electronic Resource
    Electronic Resource
    Saddle-point method and resurgent analysis (1997)
    Springer
    Mathematical notes 61 (1997), S. 227-241 
    Details
    ISSN: 1573-8876
    Keywords: resurgent functions ; saddle-point method ; resurgent equations ; alient derivatives ; Stokes lines ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The topological part of the theory of the parameter-dependent Laplace integral is known to consist of two stages. At the first stage, the integration contour is reduced to a sum of paths of steepest descent for some value of the parameter. At the second stage, this decomposition (and hence the asymptotic expansion of the integral) is continued to all other parameter values. In the present paper, the second stage is studied with the help of resurgent analysis techniques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02355733
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  • 20
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    The Influence of Laterally Inhomogeneous Contacts on the Impedance of Solid Materials: A Three-Dimensional Finite-Element Study (1997)
    Springer
    Journal of electroceramics 1 (1997), S. 73-89 
    Details
    ISSN: 1573-8663
    Keywords: impedance ; porous electrode ; inhomogeneous contact ; finite element method ; potential distribution ; current constriction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The total impedance of samples with electrodes exhibiting only partial contact (porous electrodes) is investigated using the finite element method in three dimensions. Emphasis is put on porous electrodes built up of arrays of small perfect contacts. An equivalent circuit to analyze the impedance spectra is put on a firm basis enabling the reliable determination of bulk properties of “imperfectly” contacted samples. Approximations are given to estimate the contact geometry impedance. The results are also applicable to other imperfect contact problems as occurring at grain boundaries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009902532596
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  • 21
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    Bifurcation, Bursting, and Spike Frequency Adaptation (1997)
    Springer
    Journal of computational neuroscience 4 (1997), S. 257-277 
    Details
    ISSN: 1573-6873
    Keywords: bifurcation ; bursting ; singular perturbation ; spike frequency adaptation ; stomatogastric ganglion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Medicine , Physics
    Notes: Abstract Many neural systems display adaptive properties that occur on timescales that are slower than the time scales associated withrepetitive firing of action potentials or bursting oscillations. Spike frequency adaptation is the name givento processes thatreduce the frequency of rhythmic tonic firing of action potentials,sometimes leading to the termination of spiking and the cell becomingquiescent. This article examines these processes mathematically,within the context of singularly perturbed dynamical systems.We place emphasis on the lengths of successive interspikeintervals during adaptation. Two different bifurcation mechanisms insingularly perturbed systems that correspond to the termination offiring are distinguished by the rate at which interspike intervalsslow near the termination of firing. We compare theoreticalpredictions to measurement of spike frequency adaptation in a modelof the LP cell of the lobster stomatogastric ganglion.
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    URL: http://dx.doi.org/10.1023/A:1008871803040
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  • 22
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    Finite Element Approximation of Vector-Valued Hemivariational Problems (1997)
    Springer
    Journal of global optimization 10 (1997), S. 17-35 
    Details
    ISSN: 1573-2916
    Keywords: vector-valued hemivariational inequality ; finite element method ; nonconvex energy function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we develop a finite element approximationfor vector-valuedhemivariational inequalities.This class of hemivariational problems wasintroducedin [12],[13]. We study two differentproblems: unconstrained oneand constrained one witha nonempty, closed, convex constraint set K. We shall show firstly that the discrete problemsare solvable by usingconsequences of Kakutanifixed point theorem and secondly that the solutionsof the discrete problemsare close on subsequences to the continuous ones.
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    URL: http://dx.doi.org/10.1023/A:1008234502169
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  • 23
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    Chaotic Oscillation of Saddle Form Cable-Suspended Roofs under Vertical Excitation Action (1997)
    Springer
    Nonlinear dynamics 12 (1997), S. 57-68 
    Details
    ISSN: 1573-269X
    Keywords: Saddle form cable-suspended roofs ; truncated spectral model ; bifurcation ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is to investigate the dynamic behaviour of saddle form cable-suspended roofs under vertical excitation action. The governing equations of this problem are system of nonlinear partial differential and integral equations. We first establish a spectral equation, and then consider a model with one coefficient, i.e., a perturbed Duffing equation. The analytical solution is derived for the Duffing equation. Successive approximation solutions can be obtained in likely way for each time to only one new unknown function of time. Numerical results are given for our analytical solution. By using the Melnikov method, it is shown that the spectral system has chaotic solutions and subharmonic solutions under determined parametric conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008241710683
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  • 24
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    Bifurcation Control of Parametrically Excited Duffing System by a Combined Linear-Plus-Nonlinear Feedback Control (1997)
    Springer
    Nonlinear dynamics 12 (1997), S. 263-274 
    Details
    ISSN: 1573-269X
    Keywords: Parametric excitation ; nonlinear systems ; bifurcation ; bifurcation control ; stabilization ; nonlinear control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a parametrically excited Duffing system we propose a bifurcation control method in order to stabilize the trivial steady state in the frequency response and in order to eliminate jump in the force response, by employing a combined linear-plus-nonlinear feedback control. Because the bifurcation of the system is characterized by its modulation equations, we first determine the order of the feedback gain so that the feedback modifies the modulation equations. By theoretically analyzing the modified modulation equations, we show that the unstable region of the trivial steady state can be shifted and the nonlinear character can be changed, by means of the bifurcation control with the above feedback. The shift of the unstable region permits the stabilization of the trivial steady state in the frequency response, and the suppression of the discontinuous bifurcation due to the change of the nonlinear character allows the elimination of the jump in the quasistationary force response. Furthermore, by performing numerical simulations, and by comparing the responses of the uncontrolled system and the controlled one, we clarify that the proposed bifurcation control is available for the stabilization of the trivial steady state in the frequency response and for the reduction of the jump in the nonstationary force response.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008270815516
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  • 25
    Electronic Resource
    Electronic Resource
    Three-to-One Internal Resonances in Hinged-Clamped Beams (1997)
    Springer
    Nonlinear dynamics 12 (1997), S. 129-154 
    Details
    ISSN: 1573-269X
    Keywords: Three-to-one resonance ; internal resonance ; beam vibrations ; bifurcation ; crises
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The nonlinear planar response of a hinged-clamped beam to a primary excitation of either its first mode or its second mode is investigated. The analysis accounts for mid-plane stretching, a static axial load and a restraining spring at one end, and modal damping. For a range of axial loads, the second natural frequency is approximately three times the first natural frequency and hence the first and second modes may interact due to a three-to-one internal resonance. The method of multiple scales is used to attack directly the governing nonlinear partial-differential equation and derive two sets of four first-order nonlinear ordinary-differential equations describing the modulation of the amplitudes and phases of the first two modes in the case of primary resonance of either the first or the second mode. Periodic motions and periodically and chaotically modulated motions of the beam are determined by investigating the equilibrium and dynamic solutions of the modulation equations. For the case of primary resonance of the first mode, only two-mode solutions are possible, whereas for the case of primary resonance of the second mode, single- and two-mode solutions are possible. The two-mode equilibrium solutions of the modulation equations may undergo a supercritical or a subcritical Hopf bifurcation, depending on the magnitude of the axial load. A shooting technique is used to calculate limit cycles of the modulation equations and Floquet theory is used to ascertain their stability. The limit cycles correspond to periodically modulated motions of the beam. The limit cycles are found to undergo cyclic-fold bifurcations and period-doubling bifurcations, leading to chaos. The chaotic attractors may undergo boundary crises, resulting in the destruction of the chaotic attractors and their basins of attraction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008229503164
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  • 26
    Electronic Resource
    Electronic Resource
    The Study of a Parametrically Excited Nonlinear Mechanical System with the Continuation Method (1997)
    Springer
    Nonlinear dynamics 14 (1997), S. 1-22 
    Details
    ISSN: 1573-269X
    Keywords: Nonlinear ; bifurcation ; continuation method ; parametric resonance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dynamic behavior of a one-degree-of-freedom, parametrically excited nonlinear system is investigated. The Galerkin method is applied to the principal and fundamental parameteric resonance of the system. The continuation method is used to study the change of harmonic oscillation with respect to the variation of excitation frequency. The numerical stability analysis of the trivial solution is carried out and the stable and unstable regions of the trivial solution are given. They are found to agree with the results obtained by the analytical method of Galerkin. Periodic solutions are traced and the coexistence of multi-periodic solutions is observed With the change of excitation frequency the large amplitude periodic-2 oscillation is found to be in the same closed branch with the small amplitude periodic-2 solution. In addition, the bifurcation pattern of the trivial solution is found to change from subcritical Hopf bifurcation into supercritical Hopf bifurcation with the increase of excitation amplitude. Combined with the conventional numerical integration method, new complex dynamic behavior is detected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008269317038
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  • 27
    Electronic Resource
    Electronic Resource
    Nonlinear Oscillations of a Nonresonant Cable under In-Plane Excitation with a Longitudinal Control (1997)
    Springer
    Nonlinear dynamics 14 (1997), S. 139-156 
    Details
    ISSN: 1573-269X
    Keywords: Cables ; active control ; nonlinear oscillations ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The nonlinear oscillations of a controlled suspended elastic cable under in-plane excitation are considered. Active control realized by longitudinal displacement of one support is introduced in order to reduce the transverse in-plane and out-of-plane vibrations. Linear and quadratic enhanced velocity feedback control laws are chosen and their effects on the cable motion are investigated using a two degree-of-freedom model. Perturbation analysis is performed to determine the in-plane steady-state solutions and their stability under an out-of-plane disturbance. The analysis is extended to the bifurcated two-mode steady-state oscillations in the region of parametric excitation. The dependence of the control effectiveness on the system parameters is investigated in the case of the first symmetric mode and the range of oscillation amplitudes in which the proposed control ensures a dissipation of energy is determined. Although control based only on in-plane response quantities is effective in reducing oscillations with a prevailing in-plane component, addition of out-of-plane measures has to be considered when the motion is characterized by two comparable components.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008255409438
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  • 28
    Electronic Resource
    Electronic Resource
    Perturbation Methods for Bifurcation Analysis from Multiple Nonresonant Complex Eigenvalues (1997)
    Springer
    Nonlinear dynamics 14 (1997), S. 193-210 
    Details
    ISSN: 1573-269X
    Keywords: Perturbation methods ; stability ; bifurcation ; codimension two ; periodic and quasi-periodic solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown that the logical bases of the static perturbation method, which is currently used in static bifurcation analysis, can also be applied to dynamic bifurcations. A two-time version of the Lindstedt–Poincaré Method and the Multiple Scale Method are employed to analyze a bifurcation problem of codimension two. It is found that the Multiple Scale Method furnishes, in a straightforward way, amplitude modulation equations equal to normal form equations available in literature. With a remarkable computational improvement, the description of the central manifold is avoided. The Lindstedt–Poincaré Method can also be employed if only steady-state solutions have to be determined. An application is illustrated for a mechanical system subjected to aerodynamic excitation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008201828000
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