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Applied Mathematics and Mechanics

, Volume 24, Issue 3, pp 247–255 | Cite as

Two-mode Galerkin approach in dynamic stability analysis of viscoelastic plates

  • Zhang Neng-hui
  • Cheng Chang-jun
Article

Abstract

The dynamic stability of viscoelastic thin plates with large deflections was investigated by using the largest Liapunov exponent analysis and other numerical and analytical dynamic methods. The material behavior was described in terms of the Boltzmann superposition principle. The Galerkin method was used to simplify the original integropartial-differential model into a two-mode approximate integral model, which further reduced to an ordinary differential model by introducing new variables. The dynamic properties of one-mode and two-mode truncated systems were numerically compared. The influence of viscoelastic properties of the material, the loading amplitude and the initial values on the dynamic behavior of the plate under in-plane periodic excitations was discussed.

Key words

viscoelastic plate dynamic stability von Kármán's hypothesis Galerkin method chaos Hopf bifurcation 

Chinese Library Classification

O345 

2000 MR Subject Classification

74D10 74H55 74K20 74S30 

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Zhang Neng-hui
    • 1
    • 2
  • Cheng Chang-jun
    • 1
    • 2
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghaiPR China
  2. 2.Department of MechanicsShanghai UniversityShanghaiPR China

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