Matlab编程实现求解基于振型叠加法的多自由度动力学系统的时域和频域响应  

Short Matlab programs for time and frequency response of MDOF system by mode superposition methods

作　　者：王波平 张君茹 WANG Bo-ping;ZHANG Jun-ru(Department of Mechanical and Aerospace Engineering,University of Texas at Arlington,Arlington 76019,USA;State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]美国德克萨斯大学机械与航空工程系,美国阿灵顿76019 [2]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《计算力学学报》2021年第4期556-564,共9页Chinese Journal of Computational Mechanics

基　　金：工业装备结构分析国家重点实验室开放课题(GZ18103).

摘　　要：给出了求解多自由度动力学系统响应的Matlab程序,这些程序基于振型叠加法可用于求解由质量矩阵M和刚度矩阵K以及常见阻尼矩阵描述的线性离散系统的时域和频域解。对于无阻尼系统,用户可以选择数值解或符号解析解(以时间或频率表示),并利用复模态叠加法计算了阻尼系统的数值解。总结了模态叠加方法下动力学响应的求解,并在简短的Matlab程序中实现。以三自由度系统和悬臂梁模型为例说明了程序的应用。这些程序也可用于工程应用中,通过对商用有限元软件包产生的质量和刚度进行后处理,产生感兴趣的时域和频域响应。Matlab programs for vibration responses analysis are presented in this paper.These programs can be used for time and frequency domain solution of linear discrete systems described by mass,stiffness matrices M and K and general viscous damping matrix.Mode superposition formulations are used to compute the solutions.For undamped systems,the user can select either numerical or symbolic solutions(in terms of time or frequency).Numerical solutions are computed for damped system via superposition of complex modes.Mode superposition methods are summarized and implemented in several short Matlab programs.Various cases of a three degrees-of-freedom system and a cantilever beam model are used to illustrate the application of the programs.These programs can also be used in industrial application by post-processing mass and stiffness matrixes generated by commercial finite element package to produce time or frequency response of interest.

关 键 词：MATLAB程序 时域和频域响应 多自由度系统 振型叠加法 

分 类 号：O313[理学—一般力学与力学基础] TP31[理学—力学]