基于高阶剪切理论的层合板非线性动力稳定性

Analysis of nonlinear dynamic stability of composite laminates based on higher order shear deformation theory

基于R eddy提出的层合板高阶剪切变形简化理论对复合材料层合板的非线性动力稳定性问题进行了研究.推导了考虑几何非线性、非线性惯性和阻尼效应的M eth ieu方程,给出了该方程解的解析表达式,并研究了参数振动解的稳定性.通过典型数例讨论发现:层合板的第一参数振动是其主要的参数振动;对于非保守体系,阻尼对参数振动的振幅影响不大,而对牵引则有着显著的影响.

Nonlinear dynamic stability associated with composite laminates subjected to dynamic loads has been studied. On the basis of Reddy＇s simple higher order shear deformation theory,a dynamic instability equation, called Methieu equation, is deduced, which considers nonlinear elastic, inertial and damping effects. The analytical expressions of solution corresponding to the equations are given. Dynamic instability of the parameter vibration is investigated. Numerical results for dynamic stability analysis of typical thick laminates show that the first parameter vibration is essential for the study of nonlinear dynamic stability, and that the damping effect upon the amplitude of parameter vibration is weak, however on the maximum deepness of traction, is significant for non-conservative system.