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Type: Journal article
Title: On the inverse problem of a vibrating membrane of arbitrary shape
Author: Ghosh, A.
Mazumdar, J.
Elhay, S.
Citation: International Journal of Applied Mathematics and Statistics, 2004; 2(DO4):15-28
Publisher: CESER Publications
Issue Date: 2004
ISSN: 0973-1377
Statement of
A. Ghosh, J. Mazumdar and S. Elhay
Abstract: A study on the inverse problem of a transversely vibrating membrane of varying material properties has been carried out. Using a finite difference model the eigenvalue equation for the inverse problem of an anisotropic, nonhomogenous membrane of rectangular, circular and elliptical shape is formulated. The basic relations for reconstructing the variation of stiffness and mass of such a membrane from eigenvalues and eigenvectors are established. Reconstruction with a varying number of eigenvectors for a membrane of rectangular and elliptical shape is discussed. Also a procedure which can be used to reconstruct the membranes is proposed and an example illustrating the procedure given. © 2004, IJAMS,CESER.
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