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

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 integro-partial-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.