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

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Abstract

The integro-partial differential equations governing the dynamic behavior of viscoelastic plates taking account of higher-order shear effects and finite deformations are presented. From the matrix formulas of differential quadrature, the special matrix product and the domain decoupled technique presented in this work, the nonlinear governing equations are converted into an explicit matrix form in the spatial domain. The dynamic behaviors of viscoelastic plates are numerically analyzed by introducing new variables in the time domain. The methods in nonlinear dynamics are synthetically applied to reveal plenty and complex dynamical phenomena of viscoelastic plates. The numerical convergence and comparison studies are carried out to validate the present solutions. At the same time, the influences of load and material parameters on dynamic behaviors are investigated. One can see that the system will enter into the chaotic state with a paroxysm form or quasi-periodic bifurcation with changing of parameters.

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Authors and Affiliations

  1. Department of Mechanics, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, P.R. China

    J.-J. Li & C.-J. Cheng

Authors
  1. J.-J. Li
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  2. C.-J. Cheng
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Correspondence to C.-J. Cheng.

Additional information

Sponsored by: the Major Research Plan of the National Natural Science Foundation of China (No. 90816001), the National Science Foundation for Post-doctoral Scientists of China (No. 20080440613); the Shanghai Postdoctoral Sustentation Fund, China (No. 09R21412700), the Shanghai Leading Academic Discipline Project (No. S30106).

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Li, JJ., Cheng, CJ. Differential quadrature method for analyzing nonlinear dynamic characteristics of viscoelastic plates with shear effects. Nonlinear Dyn 61, 57–70 (2010). https://doi.org/10.1007/s11071-009-9631-8

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  • DOI: https://doi.org/10.1007/s11071-009-9631-8

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