改进多尺度法求解环形极板机电耦合强非线性系统主共振的研究

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (19) : 208-212.

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杨志安1 ，李熙 2，孟佳佳3

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The study of modified method of multiple scales for primary resonance of annular plate electromechanical coupling strong nonlinear system

Yang Zhi’an1, Li Xi 2, Meng Jiajia2

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摘要

研究环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环形极板机电耦合系统的动力学方程，利用Galerkin方法将其转化为非线性振动方程。转化后的振动方程是杜芬-马修方程，有两个外激频率。应用多尺度法求得系统的主共振的幅频响应曲线，分析了不同的系统参数对共振的影响。

Abstract

In order to study primary resonance of annular plate electromechanical coupling strong nonlinear system by applying elastic theory, the nonlinear dynamical equation of the system is established. Nonlinear oscillation equation is obtained based on the Galerkin’s method. It is Duffing-Mathieu equation with two external excitation frequencies. By means of modified method of multiple scales the approximation solutions of primary resonance of the system are acquired. Numerical analysis of the influence of different parameter is carried out.

关键词

环形极板机电耦合系统 / 改进多尺度法 / 强非线性 / 简谐激励 / 主共振

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杨志安1,李熙 2，孟佳佳3. 改进多尺度法求解环形极板机电耦合强非线性系统主共振的研究[J]. 振动与冲击, 2015, 34(19): 208-212

Yang Zhi’an1, Li Xi 2, Meng Jiajia2. The study of modified method of multiple scales for primary resonance of annular plate electromechanical coupling strong nonlinear system[J]. Journal of Vibration and Shock, 2015, 34(19): 208-212

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