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Volume 15, Issue 3
Finite Element Approximation of Eigenvalue Problem for a Coupled Vibration Between Acoustic Field and Plate

L. Deng & T. Kako

J. Comp. Math., 15 (1997), pp. 265-278.

Published online: 1997-06

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  • Abstract

We formulate a coupled vibration between plate and acoustic field in mathematically rigorous fashion. It leads to a non-standard eigenvalue problem. A finite element approximation is considered in an abstract way, and the approximate eigenvalue problem is written in an operator form by means of some Ritz projections. The order of convergence is proved based on the result of Babuška and Osborn. Some numerical examples are shown for the problem for which the exact analytical solutions are calculated. The results show that the convergence order is consistent with the one by the numerical analysis. 

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@Article{JCM-15-265, author = {L. Deng and T. Kako}, title = {Finite Element Approximation of Eigenvalue Problem for a Coupled Vibration Between Acoustic Field and Plate}, journal = {Journal of Computational Mathematics}, year = {1997}, volume = {15}, number = {3}, pages = {265--278}, abstract = {

We formulate a coupled vibration between plate and acoustic field in mathematically rigorous fashion. It leads to a non-standard eigenvalue problem. A finite element approximation is considered in an abstract way, and the approximate eigenvalue problem is written in an operator form by means of some Ritz projections. The order of convergence is proved based on the result of Babuška and Osborn. Some numerical examples are shown for the problem for which the exact analytical solutions are calculated. The results show that the convergence order is consistent with the one by the numerical analysis. 

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9204.html} }
TY - JOUR T1 - Finite Element Approximation of Eigenvalue Problem for a Coupled Vibration Between Acoustic Field and Plate AU - L. Deng & T. Kako JO - Journal of Computational Mathematics VL - 3 SP - 265 EP - 278 PY - 1997 DA - 1997/06 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9204.html KW - AB -

We formulate a coupled vibration between plate and acoustic field in mathematically rigorous fashion. It leads to a non-standard eigenvalue problem. A finite element approximation is considered in an abstract way, and the approximate eigenvalue problem is written in an operator form by means of some Ritz projections. The order of convergence is proved based on the result of Babuška and Osborn. Some numerical examples are shown for the problem for which the exact analytical solutions are calculated. The results show that the convergence order is consistent with the one by the numerical analysis. 

L. Deng and T. Kako. (1997). Finite Element Approximation of Eigenvalue Problem for a Coupled Vibration Between Acoustic Field and Plate. Journal of Computational Mathematics. 15 (3). 265-278. doi:
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