Differential quadrature method for analyzing nonlinear dynamic characteristics of viscoelastic plates with shear effects

Li, J.-J.; Chang-jun, Cheng

doi:10.1007/s11071-009-9631-8

Cited by 14 publications

(9 citation statements)

References 29 publications

(51 reference statements)

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“…The natural vibrations of a viscoelastic beam are investigated and the results obtained are compared with the results of field experiments. In [16][17][18], forced vibration analysis of isotropic thin circular plate resting on nonlinear viscoelastic foundation is investigated. The system coupled nonlinear partial differential equations are transformed to system of nonlinear ordinary differential equation using Galerkin decomposition method.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of high-rise structures taking into account the viscoelastic properties of the material

et al. 2021

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The article deals with forced vibrations of a high-rise axisymmetric structure, represented as a viscoelastic beam of an annular section with a variable slope of the generatrices and variable thickness. The research was conducted to analyze the behavior of a high-rise structure for various kinematic effects. The task is to determine the displacements of the points of a high-rise structure at different time points under different kinematic effects. The methods were developed and a computer program was built; forced vibrations of high-rise axisymmetric structures under various kinematic actions, considering viscoelastic properties of the material, were investigated in linear, nonlinear, and viscoelastic formulations. The study of the dynamic behavior of a high-rise structure, taking into account the nonlinear and dissipative properties (different in nature) of the material, shows that the combined consideration of all these properties brings the resulting pattern closer to the one observed in reality. That is, the amplitude of the structure’s oscillations does not grow infinitely, but gradually decreases over time, and the maximum possible consideration of nonlinear and dissipative properties leads to the fastest damping of oscillations.

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Section: Introductionmentioning

confidence: 99%

Dynamics of high-rise structures taking into account the viscoelastic properties of the material

et al. 2021

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“…Solid and laminated plates with viscoelastic behaviour have been analysed in many papers, like [1][2][3][4][5][6][7][8][9][10][11][12]. In these papers Green-Rivlin, Kelvin-Voigt or GHM viscoelastic models were applied.…”

Section: Introductionmentioning

confidence: 99%

Influence of elastic supports on non-linear steady-state vibrations of Zener material plates

Litewka¹,

Lewandowski²

2018

AIP Conference Proceedings

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Abstract. The paper reports numerical results of analyses of steady-state harmonic vibrations of von Kármán non-linear plates made from Zener material with various elastic support conditions. Influences of shear deformation and rotary inertia are taken into account, thus the model is able to predict the behaviour of plates with a moderate thickness. The amplitude equation for the plate is obtained using the time-averaged principle of virtual work for the assumed harmonic form of excitation and plate displacements as well as the harmonic balance method for Zener material and non-linear elastic supports. Plates are discretised using 8-noded rectangular plate finite elements. The discretised amplitude equation is solved for the response curves using a path-following method. Results of two numerical examples are presented and the qualitative and quantitative influence of support elastic properties is discussed.

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“…Naser et al [22] concerned with the dynamic behavior of laminated beam, plate and shell structures consisting of a viscoelastic damping layer constrained between two structural layers, as well as, Finite element models for modal, harmonic and transient analyses were developed. Li and Cheng [23] provided a method in nonlinear dynamics are synthetically applied to reveal plenty and complex dynamical phenomena of viscoelastic plates. At the same time, the influences of load and material parameters on dynamic behavior were investigated.…”

Section: Introductionmentioning

confidence: 99%

Thermoviscoelastic dynamic response for a composite material thin narrow strip

Dai

Liu

2015

J Mech Sci Technol

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Based on von Karman nonlinear strain-displacement relationships and classical thin plate theory, a list of nonlinear dynamic equilibrium equations for a viscoelastic composite material thin narrow strip under thermal and mechanic loads are deduced. According to the material constitutive relationship and the relaxation modulus in the form of the Prony series, combing with the Newmark method and the Newton-cotes integration method, a new numerical algorithm for direct solving the whole problem in the time domain is established. By applying this numerical algorithm, the viscoelastic composite material thin narrow strip as the research subject is analyzed systematically, and its rich dynamical behaviors are revealed comprehensively. To verify the accuracy of the present work, a comparison is made with previously published results. Finally, the viscoelastic composite material thin narrow strip under harmonic excitation load and impact load are discussed in detail, and many valuable thermoviscoelastic dynamic characteristics are revealed.

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Differential quadrature method for analyzing nonlinear dynamic characteristics of viscoelastic plates with shear effects

Cited by 14 publications

References 29 publications

Dynamics of high-rise structures taking into account the viscoelastic properties of the material

Dynamics of high-rise structures taking into account the viscoelastic properties of the material

Influence of elastic supports on non-linear steady-state vibrations of Zener material plates

Thermoviscoelastic dynamic response for a composite material thin narrow strip

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