Spectral optimization of inhomogeneous plates
Analysis of PDEs
2021-07-26 v1
Abstract
This article is devoted to the study of spectral optimisation for inhomogeneous plates. In particular, we optimise the first eigenvalue of a vibrating plate with respect to its thickness and/or density. Our result is threefold. First, we prove existence of an optimal thickness, using fine tools hinging on topological properties of rearrangement classes. Second, in the case of a circular plate, we provide a characterisation of this optimal thickness by means of Talenti inequalities. Finally, we prove a stability result when assuming that the thickness and the density of the plate are linearly related. This proof relies on H-convergence tools applied to biharmonic operators.
Cite
@article{arxiv.2107.11207,
title = {Spectral optimization of inhomogeneous plates},
author = {Elisa Davoli and Idriss Mazari and Ulisse Stefanelli},
journal= {arXiv preprint arXiv:2107.11207},
year = {2021}
}