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  • nonlinear  (11)
  • nonlinear oscillations  (9)
  • 1
    ISSN: 1573-269X
    Keywords: Laminated spherical caps ; static and dynamic analysis ; transverse shear deformation ; nonlinear
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Based on Timoshenko-Mindlin kinematic hypothesis, the shallow shell theory is extended to include the transverse shear deformation for the nonlinear axisymmetric dynamic analysis of the symmetric cross-ply shallow spherical shell. Using the orthogonal point collocation method and the Newmark scheme, an iterative solution is formulated. The numerical results for the nonlinear static and dynamic responses and dynamic buckling of these shallow spherical shells with circular holes under uniformly distributed static or dynamic normal impact loads are presented and compared with available data.
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  • 2
    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.
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  • 3
    ISSN: 1573-269X
    Keywords: higher order finite elements ; panel flutter ; nonlinear ; postbuckling ; chaos ; dynamic response
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Higher order elements were first design for linear problems where, in certain situations, they present advantages over the lower order elements. A method to efficiently extend their use to geometrical nonlinear problems as panel flutter and postbuckling behavior is presented. The chaotic and limit-cycle oscillations of an isotropic plate are obtained based on direct integration of the discretized equation of motion. The plate is modeled using the von Karman theory and the geometrical nonlinearities are separated in a nonlinear term of the first kind which manifests especially in the prebuckling and buckling regimes, and a nonlinear term of the second kind which is responsible for the postbuckling behavior. A fifth order, fully compatible element has been used to model thin plates while the inplane loads where introduced through a membrane element. The aerodynamics was modeled using the first order 'piston theory’. The method introduces the concept of a deteriorated form of the second geometric matrix which is equivalent to neglecting higher order terms in the strain energy of the plate. This allows for a drastic reduction in the computational effort with no observable loss of accuracy. Well established results in the literature are used to validate the method.
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  • 4
    ISSN: 1573-269X
    Keywords: Ship dynamics ; nonlinear oscillations ; parametric excitation ; effects of bending and torsional elasticity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An enhanced mechanical model for simulating ship body oscillations and both the induced fluxural and twisting vibrations of the hull in the case of longitudinal seas is presented. The onset of parametric rolling, which may result from nonlinearly coupled heave-pitch-roll motions, and the effects of bending and torsional elasticity of the hull are considered in detail. It is shown that in the above sea conditions the flexural and/or twisting vibrations are likely to occur under a mechanism similar to that of parametric rolling.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 6 (1994), S. 301-316 
    ISSN: 1573-269X
    Keywords: Valve mechanism of internal combustion engine ; parametric and forcing excitation ; nonlinear oscillations ; local and global bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we study in detail problems of nonlinear oscillations of valve mechanism at internal combustion engine. The practical measurement indicates that stiffness of valve mechanism is not constant but is a function of the rotational angle of the cam. For simplicity of analysis we replace valve mechanism of internal combustion engine with a nonlinear oscillator of single degree of freedom under combined parametric and forcing excitation. We use the method of multiple scales and normal form theory to study local and global bifurcations of valve mechanism at internal combustion engine.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 20 (1999), S. 309-317 
    ISSN: 1573-269X
    Keywords: nonlinear oscillations ; chaos ; control ; input-output linearization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The control of chaotic oscillations is investigated in this paper. A control methodology, termed input-output linearization, is modified by locally linearizing the nonlinear control law in the small neighborhood of the control goal. Its suitability for controlling chaotic oscillators is analyzed. The forced Duffing oscillator is treated as a numerical example of controlling chaotic motion to a given fixed point and a given period-2 motion. The control signals and time needed to achieve the desired goals of the modified method are compared with those of the original method. The robustness of the control law is demonstrated.
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  • 7
    ISSN: 1573-269X
    Keywords: viscoelasticity ; harmonic balance ; foam ; nonlinear ; system identification ; polynomial stiffness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Identification of the vibrational behavior of polyurethanefoams used in automotive seats is described. The dynamic system consistsof a rigid block mounted on a 3″ cube of foam material, which serves asthe only flexible component. When constrained to undergo linearunidirectional motion, the dynamic system is modeled as a single degreeof freedom system, governed by an integro-differential equation. Inaddition to a relaxation kernel representing the linear viscoelasticbehavior of the foam, the model includes a polynomial type stiffness toaccount for the foam's strain-based nonlinearities. The relaxationkernel is assumed to be of an exponential type. Experimentalmethodologies for obtaining repeatable, accurate measurements of thesystem's response to an impulse and to single frequency harmonic baseexcitations are described. Analysis methods are then investigated forextracting the relevant linear, nonlinear, and viscoelastic parameters.Characterization of these foam properties as functions of compressionlevel is also presented.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 22 (2000), S. 393-413 
    ISSN: 1573-269X
    Keywords: piecewise linear ; nonlinear ; vibration ; absorber
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper explores the potential of the piecewise linearvibration absorber in a system subject to narrow band harmonic loading.Such a spring is chosen because the design of linear springs is commonknowledge among engineers. The two-degrees-of-freedom system is solvedby using the Incremental Harmonic Balance method, and response aspectssuch as stiffness crossing frequency and jump behaviour are discussed.The effects of mass, stiffness, natural frequency ratios, and stiffnesscrossing positions on the suppression zone are probed. It is shown thata hardening absorber can deliver a wider bandwidth than a linear oneover a range of frequencies. The absorber parameters needed to producegood designs have been determined and the quality of the realizedsuppression zone is discussed. Design guidelines are formulated to aidthe parameter selection process.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 15 (1998), S. 225-244 
    ISSN: 1573-269X
    Keywords: Localization ; cyclic systems ; disorder ; nonlinear
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dynamics of weakly coupled, nonlinear cyclic assemblies are investigated in the presence of weak structural mistuning. The method of multiple scales is used to obtain a set of nonlinear algebraic equations which govern the steady-state, synchronous (‘modal-like’) motions for the structures. Considering a degenerate assembly of uncoupled oscillators, spatially localized modes are computed corresponding to motions during which vibrational energy is spatially confined to one oscillator (strong localization) or a subset of oscillators (weak localization). In the limit of weak substructural coupling, asymptotic solutions are obtained which correspond to (i) spatially extended, (ii) strongly localized, and (iii) weakly localized modes for fully coupled systems. Throughout the analysis, the influence of structural mistunings on the resulting solutions are discussed. Additionally, numerical solutions (including linearized stability characteristics) are obtained for prototypical two- and three-degree-of-freedom (DoF) systems with various structural mistunings. The numerical results provide insight into the strong influence of structural irregularities on the dynamical behavior of nonlinear cyclic systems, and demonstrate that the combined influences of structural mistunings and nonlinearities do not lead to uniform improvement of motion confinement characteristics.
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  • 10
    ISSN: 1573-269X
    Keywords: Beam ; gravity effect ; method of multiple scales ; nonlinear oscillations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A critical problem in designing large structures for space applications, such as space stations and parabolic antennas, is the limitation of testing these structures and their substructures on earth. These structures will exhibit very high flexibilities due to the small loads expected to be encountered in orbit. It has been reported in the literature that the gravitational sag effect under dead weight is of extreme importance during ground tests of space-station structural components [1–4]. An investigation of a horizontal, pinned-pinned beam with complete axial restraint and undergoing large-amplitude oscillations about the statically deflected position is presented here. This paper presents a solution for the frequency-amplitude relationship of the nonlinear free oscillations of a horizontal, immovable-end beam under the influence of gravity. The governing equation of motion used for the analysis is the Bernoulli-Euler type modified to include the effects of mid-plane stretching and gravity. Boundary conditions are simply supported such that at both ends there is no bending moment and no transverse and axial displacements. These boundary conditions give rise to an initial tension in the statically deflected shape. The displacement function consists of an assumed space mode using a simple sine function and unknown amplitude which is a function of time. This assumption provides for satisfaction of the boundary conditions and leads to an ordinary differential equation which is nonlinear, containing both quadratic and cubic functions of the amplitude. The perturbation method of multiple scales is used to provide an approximate solution for the fundamental frequency-amplitude relationship. Since the beam is initially deflected the small-amplitude fundamental natural frequency always increases relative to the free vibration situation provided in zero gravity. The nonlinear equation provides for interactions between frequency and amplitude in that both hardening and softening effects arise. The coefficient of the quadratic term in the nonlinear equation arises from the static (dead load) portion of the deflection. This quadratic term, depending upon its magnitude, introduces a softening effect that overcomes the hardening term (due to initial axial tension developed by deflection) for large slenderness ratios. For very large slender, immovable-end beams, the fundamental natural frequency is greater than that of beams without axial constraints undergoing small amplitude oscillations. This phenomenon is attributed to the stiffening effect of the statically-induced axial tension. However, the stiffening effect of axial tension in beams with slenderness ratios greater than approximately 392 undergoing large-amplitude symmetric-mode oscillations is overpowered by the presence of gravitational loading.
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