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  

Improved multi-scale method for primary resonance of an annular plate electromechanical coupled strong nonlinear system

作　　者：杨志安[1] 李熙[2] 孟佳佳[3] 

机构地区：[1]唐山学院唐山市结构与振动工程重点实验室,河北唐山063000 [2]天津大学机械工程学院,天津300072 [3]河北联合大学机械工程学院,河北唐山063009

出　　处：《振动与冲击》2015年第19期208-212,共5页Journal of Vibration and Shock

基　　金：河北省自然科学基金(A2009000997)

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。In order to study primary resonance of an annular plate electromechanical coupled strong nonlinear system,the nonlinear dynamic equation of the system was established by applying the elastic theory. The nonlinear oscillation equation was obtained based on Galerkin＇s method. It was a Duffing-Mathieu equation with two external excitation frequencies. The approximation solutions to the primary resonance of the system were gained with the improved multi-scale method. The influences of different system parameters on the primary resonance of the system were analyzed in detail.

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 

分 类 号：O322[理学—一般力学与力学基础]