基于逆阵更新方法的局部非线性结构频响分析  

FREQUENCY RESPONSE ANALYSIS FOR LOCAL NONLINEAR STRUCTURES USING AN INVERSE MATRIX UPDATING METHOD

作　　者：云永旺[1] 王珺[1] 陈力奋[1] 唐国安[1] 

机构地区：[1]复旦大学力学与工程科学系,上海200433

出　　处：《动力学与控制学报》2015年第3期177-183,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11172067)~~

摘　　要：针对含有非线性连接的大型局部非线性结构,采用描述函数表示其所连接的非线性内力,将非线性结构频响表示为拟线性动柔度矩阵(Quasilinear Receptance Matrix),提出一种逆阵更新(Inverse Matrix Updating Method,IMU)方法,将求解系统动柔度(频响特性)的高阶矩阵求逆转化为低阶矩阵的求逆,从而获得大型局部非线性结构主频响应的快速计算方法.仿真结果表明,本文的分析方法具有较好的稳定性,并能大幅提高大型局部非线性结构主频响应的计算效率.This paper introduces a new method for the frequency response analysis of the structures with nonlin- ear links. When the local nonlinear structures, especially for the large-scale structures, is excited by the harmon- ic external forces, the describing functions are used to express the nonlinear internal forces. And then the fre- quency response of the nonlinear system can be expressed by a Quasilinear Receptance Matrix （ compared with the Receptance Matrix in the linear system）. As the Quasilinear Receptance Matrix is an inverse matrix, an In- verse Matrix Updating （IMU） Method is proposed to transform the high-rank inversion problem into low-rank in- version problem. This method makes it much faster to get the frequency responses of the local nonlinear system for large-scale structures. Single degree of freedom （SDOF） system and Multi-degree of freedom （MDOF） system case studies show that the IMU Method can greatly improve the computational efficiency, and has high calculation stability.

关 键 词：局部非线性 逆阵更新 频率响应 动柔度 

分 类 号：V414[航空宇航科学与技术—航空宇航推进理论与工程]