Study on Vibration of Damped Linear Systems with Multiple Eigenvalues
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摘要: 本文在復模態理論基礎上引入系統傳遞函數矩陣及其留數矩陣的概念,推證了傳遞函數矩陣展式,通過展式導出系統振動響應的實數表達式可用于計算具有重特征值的阻尼線性系統振動響應,從而解決了涉及重特征值的振動求解問題,文中對特征值、特征向量及留數矩陣做了探討,并給出了算例.Abstract: In this paper, the transfer function method in complex modal theory has been studied.The transfer function matrix and its residual matrices of a damped linear system are introduced. The expansion formula of the transfer function matrix is derived and proved, with which the real expressions are developed for vibration response of a damped linear system with multiple degrees of freedom. The expressions presented in the paper can be used to compute the vibration response of a damped linear system in which one or more multiple eigenvalues may exist, so the problem dealing with multiple eigenvalues is solved about the solution of the vibration response of a damped linear system. Finally one example is shown.
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Key words:
- vibration /
- multiple eigenvalues /
- residual matrix /
- Laplace trnsform
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