多自由度非线性系统的同伦分析方法  

Homotopy Analysis Method for Multi-degree of Freedom Nonlinear Systems

作　　者：钱有华[1,2] 张伟[2] 

机构地区：[1]浙江师范大学数理信息学院,浙江金华321004 [2]北京工业大学机电学院,北京100124

出　　处：《力学季刊》2009年第1期144-148,共5页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金项目(10732020);浙江省高校青年教师资助计划项目

摘　　要：大部分工程实际问题可以用多自由度非线性系统来描述,这些系统的数学模型是许多个耦合的两阶常微分方程。一般地,要精确求解这些方程非常困难,因此可以考虑它们的解析近似解。同伦分析方法是解非线性系统响应的有用工具,本文将它应用于多自由度非线性系统的求解中。利用求两自由度耦合van del Pol振子周期解的实例,展示了同伦分析方法的有效性和巨大潜力。同时,把得到的解析近似解与系统的Runge-Kutta数值解作了比较,结果表明同伦分析方法是求解多自由度非线性系统的有效方法。Most of practical engineering problems can be described by multi-degree of freedom nonlinear systems. The mathematical model of such systems is given by many second order coupled differential equations. In general, it is extremely difficult to find their exact solutions. Therefore, the efforts have been mainly concentrated on approximate analytical solutions. The homotopy analysis method is the useful analytic tool for solving nonlinear systems. The method was applied to obtain the analytical approximation solution for multi-degree of freedom system. The periodic solutions for the coupled van del Pol oscillators of two degree of freedom were applied to illustrate the validity and great potential of the method. Comparisons were made between results of present method and Runge-Kutta method. The results demonstrate that the homotopy analysis method is an attractive and effective technique for nonlinear multi-degree of freedom systems.

关 键 词：同伦分析法 非线性系统 多自由度 

分 类 号：O322[理学—一般力学与力学基础] O175.14[理学—力学]