Characterization of Vibrating Plates by Bi-Laplacian Eigenvalue Problems
نویسنده
چکیده
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 first obtain uniqueness criteria for the solutions of the bi-Laplacian eigenvalue problems, and then prove that each eigenvalue of the problem with simply-supported boundary conditions increases strictly with Poisson’s ratio, thereby showing that each natural frequency of a simply-supported 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.
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