几何非线性损伤粘弹性中厚板的动力学行为分析

根据Timoshenko几何变形假设和Boltzmann叠加原理，推导出控制损伤粘弹性Timoshenko中厚板的非线性动力方程以及简化的Galerkin截断方程组；然后利用非线性动力系统中的数值方法求解了简化方程组．通过分析可知，板在谐载荷的作用下，具有非常丰富的动力学特性．同时研究了板的几何参数、材料参数及载荷参数对损伤粘弹性中厚板动力学行为的影响．

Dynamical behaviors of nonlinear viscoelastic thick plates with damage

Based on the deformation hypothesis of Timoshenko's plates and the Boltzmann's superposition principles for linear viscoelastic materials, the nonlinear equations governing the dynamical behavior of Timoshenko's viscoelastic thick plates with damage were derived,and the Galerkin method was applied to simplify the equations. The numerical methods in nonlinear dynamical systems were used to solve the simplified systems. It could be seen that there are plenty of dynamical properties for dynamical systems formed by this kind of viscoelastic thick plates with damage under a transverse harmonic load. The influences of load, geometry and material parameters on the dynamical behavior of the nonlinear system were investigated,and the effect of damage on the dynamical behavior of plate was discussed.