Minimization of the first eigenvalue in problems involving the bi-laplacian

By C. Anedda, F. Cuccu, G. Porru. 2008

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This paper concerns the minimization of the first eigenvalue in problems involving the bi-Laplacian under either homogeneous Navier boundary conditions or homogeneous Dirichlet boundary conditions. Physically, in case of N = 2, our equation models the vibration of a non homogeneous plate  which is either hinged or clamped along the boundary. Given several materials (with different densities) of total extension | |, we investigate the location of these materials inside  so to minimize the first mode in the vibration of the corresponding plate. Keywords: bi-Laplacian, first eigenvalue, minimization.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e9f159b1a2d2dfa67d4a2ba45c4fbfad0c9421ab