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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2023

Spectral Optimization of Inhomogeneous Plates

Résumé

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.
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Dates et versions

hal-04320016 , version 1 (03-12-2023)

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E. Davoli, Idriss Mazari, U. Stefanelli. Spectral Optimization of Inhomogeneous Plates. SIAM Journal on Control and Optimization, 2023, 61 (2), pp.852-871. ⟨10.1137/21M1435203⟩. ⟨hal-04320016⟩
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