非均匀圆膜轴对称振动的离散模型的振动反问题

王其申;汪 杨;何敏;钱华峰;刘全金

振动与冲击 ›› 2011, Vol. 30 ›› Issue (8) : 258-263.

PDF(993 KB)
PDF(993 KB)
振动与冲击 ›› 2011, Vol. 30 ›› Issue (8) : 258-263.
论文

非均匀圆膜轴对称振动的离散模型的振动反问题

  • 王其申1; 汪 杨2; 何敏1; 钱华峰2; 刘全金1

作者信息 +

Inverse problem of discrete model of the inhomogeneous circular membrane in axial symmetry vibration

  • wang Qi-shen1; Wang Yang 2; He Min1; Qian Hua-feng2 ; Liu Quan-jin 1
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摘要

本文研究圆膜的振动反问题。首先,采用二阶中心差分格式,导出了圆膜做轴对称振动的差分离散模型. 阐明了这一离散模型属于雅可比正系统,进而获得了该系统的振动定性性质. 在此基础上,本文提出了周边固定或周边弹性支承膜的离散系统的模态反问题以及周边固定和周边弹性支承膜的离散系统的频率反问题. 借助Jacobi矩阵反问题的已有成果,成功地求解了上述两个新的反问题. 最后给出了反问题的三个计算实例,验证了反问题的提法和解法的正确性.

Abstract

We researched the inverse problems in vibration of a membrane in this paper. First, using the second-order center difference scheme, the difference discrete model of the axial symmetry vibration of the circular membrane with arbitrary supports is established. Second, we pointed to this model belonged to the positive Jacobi system and obtained some qualitative properties of the axial symmetry vibration of the system. Furthermore, the inverse frequency problem and inverse mode problem of the circular membrane with the fixed and/or the spring supported boundary are raised. These new inverse problems are solved successfully with the aid of the results on the inverse problems of the Jacobi matrix. Finally, we gave three examples of the numerical computation. The coreectness of the formulation and solving method of the inverse problems are verified.

关键词

圆膜 / 轴对称振动 / 差分离散模型 / 定性性质 / 反问题

Key words

Circular membrane / Axial symmetry vibration / Difference discrete models / Qualitative property / Inverse problem

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王其申;汪 杨;何敏;钱华峰;刘全金. 非均匀圆膜轴对称振动的离散模型的振动反问题[J]. 振动与冲击, 2011, 30(8): 258-263
wang Qi-shen;Wang Yang;He Min;Qian Hua-feng;Liu Quan-jin . Inverse problem of discrete model of the inhomogeneous circular membrane in axial symmetry vibration[J]. Journal of Vibration and Shock, 2011, 30(8): 258-263

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