阻尼矩阵对角化的评述
首发时间:2010-12-16
摘要:振动的阻尼既是理论分析的难点,也是实验和测试的难点。容易处理的模型是能有实模态的阻尼,最简单就是比例阻尼。本报告首先介绍了比例阻尼,包括定义、物理意义和确定方法。第二,回顾了阻尼矩阵可对角化的充要条件及其证明。第三、总结了工程上采用近似对角处理化的依据。最后给出了由模态阻尼矩阵计算物理系统阻尼矩阵的公式。
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Remarks on Diagonalizing the Damping Matrix
Abstract:Abstract The damping in vibration is difficult for both theoretical analysis and experimental identification. The tractable model from an engineering view is the proportional damping. In this report, the proportional damping's definition, physical meaning and determination method are introduced at first. Then, the sufficient and necessary conditions that a damping matrix is diagonalizable are presented and proved. Thirdly, the approximate diagonalization and its underlying reasons are described. Finally, the formula from the diagonal modal damping matrix to that in physical space is presented.
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