2008/06/05 by G. T. Lei, Lei, G. T.
Computer Science · Engineering · Mathematics · #35G15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in engineering #math.AP #msc:35G15
paper · pdf · doi:10.48550/arxiv.0806.0879
The paper has been withdrawn by the author due to the improper submission
openalex publication_date 2008/06/05 · arxiv created 2011/04/18 · arxiv updated 2011/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 identities, we first obtain the uniqueness criteria for the solutions of the bi-Laplacian eigenvalue problems, and then prove that each eigenvalue of the problem with simply-supported boundary condition increases strictly with Poisson's ratio, thereby showing that each natural frequency of a simply-supported vibrating plate increases strictly with Poisson's ratio. In addition, we obtain boundary integral representations for the strain energies of the vibrating plates under the three boundary conditions.