基于逆阵更新方法的局部非线性结构频响分析

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.

Frequency response analysis for local nonlinear structures using an inverse matrix updating method

This paper introduces a new method for the frequency response analysis of the structures with nonlinear links. When the local nonlinear structures, especially for the large scale structures, is excited by the harmonic external forces, the describing functions are used to express the nonlinear internal forces. And then the frequency 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 Inverse Matrix Updating (IMU) Method is proposed to transform the high rank inversion problem into low rank inversion 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.