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

L. Deng & T. Kako

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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 Babu$\v{s}$ka and Osborn. Some numerical example is shown for the problem for which the exact analytical solutions are calculated. The results shows that the convergence order is consistent with the one by the numerical analysis.

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@Article{JCM-15-265, author = {}, 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 Babu$\v{s}$ka and Osborn. Some numerical example is shown for the problem for which the exact analytical solutions are calculated. The results shows 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 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 Babu$\v{s}$ka and Osborn. Some numerical example is shown for the problem for which the exact analytical solutions are calculated. The results shows that the convergence order is consistent with the one by the numerical analysis.
L. Deng & T. Kako. (1970). 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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