| 王波平,张君茹.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[J].计算力学学报,2021,38(4):556~564 |
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| 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 |
| 投稿时间：2021-07-05 修订日期：2021-07-23 |
| DOI：10.7511/jslx20210705418 |
| 中文关键词: MATLAB程序 时域和频域响应 多自由度系统 振型叠加法 |
| 英文关键词:Matlab programs time and frequency response multi-degree of freedom system(MDOF) mode superposition methods |
| 基金项目:工业装备结构分析国家重点实验室开放课题（GZ18103）. |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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