This article is devoted to the study of spectral optimization for inhomogeneous plates. In particular, we consider the optimization of the first eigenvalue of a vibrating plate with respect to its thickness and/or density. We prove the existence of an optimal thickness, using fine tools hinging on topological properties of rearrangement classes. In the case of a circular plate, we provide a characterization of this optimal thickness by means of Talenti inequalities. Moreover, 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 the biharmonic operator.
Spectral optimization of inhomogeneous plates
U Stefanelli
2023
Abstract
This article is devoted to the study of spectral optimization for inhomogeneous plates. In particular, we consider the optimization of the first eigenvalue of a vibrating plate with respect to its thickness and/or density. We prove the existence of an optimal thickness, using fine tools hinging on topological properties of rearrangement classes. In the case of a circular plate, we provide a characterization of this optimal thickness by means of Talenti inequalities. Moreover, 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 the biharmonic operator.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.