Hokkaido Mathematical Journal
- Hokkaido Math. J.
- Volume 42, Number 3 (2013), 425-443.
Integral identities for Bi-Laplacian problems and their application to vibrating plates
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.
Hokkaido Math. J., Volume 42, Number 3 (2013), 425-443.
First available in Project Euclid: 12 November 2013
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J40: Boundary value problems for higher-order elliptic equations
Bi-Laplacian eigenvalue problems Dirichlet boundary conditions Simply-supported boundary conditions Rellich's identity Pohozaev's identity Vibrating plates Poisson's ratio Rayleigh's conjecture
LEI, Guang-Tsai; PAN, Guang-Wen (George). Integral identities for Bi-Laplacian problems and their application to vibrating plates. Hokkaido Math. J. 42 (2013), no. 3, 425--443. doi:10.14492/hokmj/1384273391. https://projecteuclid.org/euclid.hokmj/1384273391