SPECTRAL OPTIMIZATION OF INHOMOGENEOUS PLATES

被引：0
|
作者：
Davoli, E. [1 ]
Mazari, I. [2 ]
Stefanelli, U. [3 ,4 ,5 ]
机构：
[1] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria
[2] Univ PSL, Univ Paris Dauphine, CNRS, CEREMADE,UMR 7534, Pl Marechal Lattre Tassigny, F-75775 Paris 16, France
[3] Univ Vienna, Fac Math, Oskar Morgenstern Pl, A-1090 Vienna, Austria
[4] Univ Vienna, Vienna Res Platform Accelerating Photoreact Discov, Wahringerstr 17, A-1090 Vienna, Austria
[5] Ist Matemat Applicata & Tecnol Informatiche&Magene, Via Ferrata 1, I-27100 Pavia, Italy
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2023年 / 61卷 / 02期
基金：
奥地利科学基金会;
关键词：
spectral optimization; two-phase problems; inhomogeneous plates; H-convergence; rearrangement inequalities;
D O I：
10.1137/21M1435203
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
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页码：852 / 871
页数：20
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