非线性粘弹性板的失稳条件

研究了给定面内周期激励作用下简支各向同性均匀粘弹性板平衡失稀问题，板的材料特性由Leaderman非线性本构关系描述，将板的动力学方程进行（Galerkin截断得到简化数学模型为弱非线性系统，采用平均法得到系统的平均化方程，对平均化方程进行稳定性分析得到了板平衡失稳的解析条件，对原系统用数值仿真进行研究，数值结果表明，随着激励幅值的增加或粘弹性材料系数的减少，系统平衡点推失稳，激励幅值和粘弹性材料系数的临界值均与解析结果接近。

Instability Conditions of Nonlinear Viscoelastic Plates

The instability of an isotropic homogeneous simply-supported rectangular plate under a prescribed periodic in-plane load was investigated. The material is assumed to be viscoelastic and obey the Leaderman nonlinear constitutive relation. The simplified dynamic model obtained by the Galerkin truncated method is a weak nonlinear system. The averaging method was employed to establish the averaged equation. The linearized stability analysis was carried out to get the condition of instability. The numerical simulations of the origin system was presented. Numerical results indicate that the equilibrium becomes unstable with the increase of the excitation parameter or with the decrease of the material coefficient. The critical values of them are closed to the analytical results.