基础激励下基于模态叠加法的谐响应分析

针对ANSYS等商业有限元软件无法进行基础激励下基于模态叠加法的谐响应分析的问题,将以绝对响应为变量的动力学方程改写为基础响应与结构相对响应之和的形式,重新推导以相对响应为变量的结构动力学方程.以组合梁结构为例进行MATLAB程序仿真,并以ANSYS的PSD分析结果验证所推导的动力学方程的正确性,说明基础激励下利用模态叠加法进行谐响应分析的可行性.

Harmonic response analysis based on mode superposition method under base excitation

As to the fact that the harmonic response analysis based on the mode superposition method when suffering base excitation can not be performed in the commercial finite element software such as ANSYS, the dynamics equation which takes absolute response as variable is expressed as the sum of base excitation and relative response of structure, and the equation of structure dynamics which takes relative response as variable is re derived. Taking the composite beam structure as an example, the simulation is performed by MATLAB program, and the PSD analysis results of ANSYS are used to verify the correctness of the derived dynamics equations, which indicates the feasibility of harmonic response analysis using mode superposition method.