具有重特征值的阻尼线性系统振动

详细信息

Study on Vibration of Damped Linear Systems with Multiple Eigenvalues

摘要: 本文在复模态理论基础上引入系统传递函数矩阵及其留数矩阵的概念,推证了传递函数矩阵展式,通过展式导出系统振动响应的实数表达式可用于计算具有重特征值的阻尼线性系统振动响应,从而解决了涉及重特征值的振动求解问题,文中对特征值、特征向量及留数矩阵做了探讨,并给出了算例.
- 振动 /
- 重特征值 /
- 留数矩阵 /
- Laplace变换
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.
- vibration /
- multiple eigenvalues /
- residual matrix /
- Laplace trnsform