欢迎光临《计算力学学报》官方网站！ 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

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 作者 单位 邮编 张君茹 工程力学系 116024 王波平 机械与航空航天学院 76019

本文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、刚度矩阵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。本文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。

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.
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