粘弹性板的非线性动力稳定性分析方法  

ANALYSIS METHOD OF NONLINEAR DYNAMIC STABILITY FOR VISCOELASTIC PLATES

作　　者：彭凡[1] 傅衣铭[1] 

机构地区：[1]湖南大学工程力学系,长沙410082

出　　处：《动力学与控制学报》2005年第4期60-65,共6页Journal of Dynamics and Control

基　　金：湖南省自然科学基金资助项目(05JJ30008)~~

摘　　要：将微分积分型参数振动方程组转化成微分型,且基于增量谐波平衡法的一般应用途径,分析了受面内周期激励的粘弹性板的非线性动力稳定特性,揭示了主要动力不稳定区域的整体下移以及缩小和标准线性固体材料的粘性参数、板的振动频率之间的关系.同时给出了增量谐波平衡法直接应用于非线性微分积分型参数振动方程的简化途径,并通过两种应用途径所得结果的对比,检验了这种简化途径的有效性.Based on the general approach of Incremental Harmonic Balance method （IHBM）, the behavior of non-linear dynamic stability for viscoelastic plates subjected to in-plane periodic excitation was investigated by converting the integro-differential governing equations to differential ones. The dependence of the downward shift and contraction of principal instable regions on the viscose parameters of standard linear solid and vibration frequency of plates was examined. A simplified approach of direct application of Incremental Harmonic Balance method to integro-differential equation of motion was given, and this approximate method was validated through the comparison of results obtained respectively by two kinds of application of IHBM.

关 键 词：粘弹性板 非线性 动力稳定性 增量谐波平衡法 

分 类 号：O345[理学—固体力学] TU311.2[理学—力学]