Integral identities for Bi-Laplacian problems and their application to vibrating plates
| Autor: | Guang-Tsai Lei, Guang-Wen (George) Pan |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Bi-Laplacian eigenvalue problems
General Mathematics Mathematical analysis Simply-supported boundary conditions Boundary (topology) Poisson's ratio Mathematics::Spectral Theory Poisson distribution Dirichlet boundary conditions 35J40 Rellich's identity Dirichlet distribution Pohozaev's identity symbols.namesake Dirichlet boundary condition Vibrating plates Rayleigh's conjecture symbols Boundary value problem Laplace operator Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Hokkaido Math. J. 42, no. 3 (2013), 425-443 |
| ISSN: | 0385-4035 |
| DOI: | 10.14492/hokmj/1384273391 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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