含参数多自由度非线性系统的降维方法研究  

DIMENSION REDUCTION OF NONLINEAR MUTI-DEGREE-OF-FREEDOM SYSTEM WITH MULTIPLE PARAMETERS

作　　者：宫晓春[1] 曹登庆[1] 

机构地区：[1]哈尔滨工业大学航天学院,哈尔滨150001

出　　处：《动力学与控制学报》2009年第2期129-135,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(10772056;10632040);黑龙江省自然科学基金重点项目(ZJG0704)~~

摘　　要：研究一类具有一定结构特点的含参数多自由度非线性系统,以固定界面动态子结构方法为基础,借助于灵敏度分析的基本思路,提出一种实用的降维方法首先根据实际系统的结构特点将其划分为若干子系统,使其中部分子系统是线性的,其余子系统是非线性的基于灵敏度分析的相关理论导出线性部分子系统的频率、模态对于参数的依赖关系,采用固定界面模态综合法将线性部分子系统的截断模态与非线性子系统进行综合,最终得到具有较低维数的含参数非线性动力系统结合具体算例,将降维前后的非线性动力系统随参数值变化时的对应的幅频特性曲线进行了比较算例表明,采用这里提出的降维方法所得到的低维系统可以较为准确地反映原系统的动力学特性。The problem of dimension reduction of high-dimensional nonlinear systems with multiple parameters was addressed in terms of structural characteristics of the system. The dimension reduction approach based on the fixed interface component mode synthesis of substructures was employed to analyze the system, and then an order reduction for the entire nonlinear system was proposed along with the process of sensitivity analysis. First the system was divided into a number of subsystems according to the characteristics of practical structure,some of which are linear subsystem, and the remains are nonlinear. Then the frequencies and modes related to parameters of the linear subsystems were derived from the sensitivity analysis theory. Finally lower dimension nonlinear dynamic systems with multiple parameters were obtained by synthesizing the nonlinear subsystems and the modes truncated from the linear subsystems in terms of the fixed interface mode synthesis. Numerical example was given to illustrate the effect of the proposed approach.

关 键 词：参数系统 非线性振动 模态综合法 灵敏度分析 降维方法 

分 类 号：O322[理学—一般力学与力学基础]