| 用复模态理论讨论状态矩阵对角化问题 |
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| 引用本文： | 孙磊,冯国东. 用复模态理论讨论状态矩阵对角化问题[J]. 长春工程学院学报(自然科学版), 2008, 9(1): 84-85 |
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| 作者姓名： | 孙磊 冯国东 |
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| 作者单位： | 长春工程学院,理学院,长春,130012;深圳实验学校,深圳,518055 |
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| 摘 要： | 首先介绍了复模态理论,然后利用线性阻尼离散系统的自由振动微分方程的左右特征向量,推导出状态矩阵与振动系统的左右特征向量之间的关系。最后根据状态矩阵的左右特征向量系的正交性,对给出的状态矩阵进行对角化。从而实现振动微分方程的降阶与解耦。
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| 关 键 词： | 复模态 状态矩阵 特征向量系 状态空间 |
| 文章编号： | 1009-8984(2008)01-0084-02 |
| 修稿时间： | 2008-03-10 |
Diagonalizing of state matrix using method of complex mode |
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| SUN Lei. Diagonalizing of state matrix using method of complex mode[J]. Journal of Changchun Institute of Technology(Natural Science Edition), 2008, 9(1): 84-85 |
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| Authors: | SUN Lei |
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| Affiliation: | SUN Lei; et al.(Faculty of Science; Changchun Institute of Technology; Changchun 130012; China); |
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| Abstract: | At first,the method of complex mode is introduced in this paper.Then the connection of left and right eigenvector and state matrix is deduced by using left and right eigenvector of free vibration differential equation in linear damped discrete system.State matrix is diagonalized according to the orthonormality of left and right eigenvector series about the state matrix.Then the order of vibration differential equation is reduced,and the vibration differential equation is decoupled. |
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| Keywords: | complex mode state matrix eigenvector series state space |
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