变形对夹层圆板非线性振动影响及其周期解

为了解决载荷作用下夹层圆板非线性振动的大挠度方程求解问题,采用基于空间模态假设和变分法,导出时间模态的控制方程.采用伽辽金法推导出静挠度和动挠度耦合作用下夹层圆板的非线性动力方程,从而求解出解的时间模态的渐进表达式.最后采用Lindestedt-Poincare摄动法求解中心点附近的周期解并绘制出幅频特性曲线.结果表明:当横向激扰使夹层圆板产生较大幅度的受迫振动的同时,由于载荷作用下变形的存在,其产生的附加动挠度就会与变形产生非线性耦合现象,因而由此产生的变形必将影响夹层圆板的动力学特性.该成果对非线性振动问题的研究具有一定的参考价值和指导意义.

Impact and periodical solutions on nonlinear vibration of circular composite plate with distortion

In order to solve the nonlinear oscillation large deflection equation of circular sandwich plate with loading,an assumption and variational method based on space mode are used to obtain control equation with time mode.Using Galerkin’s method,a nonlinear dynamic equation of circular sandwich plate under static deflection and dynamic deflection coupling action is derived,therefore,the expression with time mode is obtained.Also,the periodical solutions of nonlinear vibration are obtained by using Lindstedt-Poincare perturbation methods and the curve of amplitude-frequency is plotted.When there is a large lateral vibration in the circular sandwich plate,due to existing distortion,there will be some additional dynamic deflection coupling with distortion.Therefore,the distortion will affect the kinetic characteristic of circular sandwich plate.This study has some reference values and guiding importance to the nonlinear oscillation problems.