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

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (8) : 258-263.

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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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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.

Key words

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

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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