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February 2013 Integral identities for Bi-Laplacian problems and their application to vibrating plates
Guang-Tsai LEI, Guang-Wen (George) PAN
Hokkaido Math. J. 42(3): 425-443 (February 2013). DOI: 10.14492/hokmj/1384273391

Abstract

In this paper we derive boundary integral identities for the bi-Laplacian eigenvalue problems under Dirichlet, Navier and simply-supported boundary conditions. By using these integral identities, we prove that the first eigenvalue of the eigenvalue problem under the simply-supported boundary conditions strictly increases with Poisson's ratio. In addition, we establish the boundary integral expressions for the strain energy calculation of the vibrating plates under the three types of boundary conditions.

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Guang-Tsai LEI. Guang-Wen (George) PAN. "Integral identities for Bi-Laplacian problems and their application to vibrating plates." Hokkaido Math. J. 42 (3) 425 - 443, February 2013. https://doi.org/10.14492/hokmj/1384273391

Information

Published: February 2013
First available in Project Euclid: 12 November 2013

zbMATH: 1287.35051
MathSciNet: MR3137394
Digital Object Identifier: 10.14492/hokmj/1384273391

Subjects:
Primary: 35J40

Rights: Copyright © 2013 Hokkaido University, Department of Mathematics

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Vol.42 • No. 3 • February 2013
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