改进多尺度法求解圆形极板机电耦合系统强非线性振动的研究

摘要

The authors of this paper study the strong nonlinearity of circular plate electromechani-cal coupling system,construct a dynamic equation of the system based on the theory of elastic mechanics,then convert it to the nonlinear vibration equation using the Galerkin method,i.e Duffing-Mathieu equation with two external excitation frequencies,apply the idea of parameter transformation to the multiple-scale methoel to obtain the amplitude-frequency response of the paramet-ric forced combination resonance and analyze the influence of different parameters on the resonance.%研究圆形极板机电耦合系统的强非线性问题。按照弹性力学理论建立圆形极板机电耦合系统的动力学方程，并利用Galerkin方法将其转化为非线性振动方程，即杜芬-马修方程，有两个外激频率。将参数变换的思想应用到多尺度法中求得系统的参强联合共振的幅频响应曲线，分析了不同的参数对共振的影响。