Behavior of an elastic plate having a small vibrating rigid support. Asymptotic study of the impedance matrix. (Comportement d’une plaque élastique dont une petite région est rigide et animée d’un mouvement vibratoire. Étude asymptotique de la matrice d’impédance.) (French) Zbl 0834.73041

Summary: This paper consideres a Love-Kirchhoff plate \({\mathcal P}\) which is fixed to a vibrating rigid support along a domain \(\omega _e\). The size of \(\omega _e\) is small so that we set diam \(\omega _e\) = \(\epsilon\) diam \({\mathcal P}\). We study the behaviour of the impedance matrix when \(\epsilon\) vanishes. We give the asymptotic expansion of the solutions of the outer problem together with the fundamental solution of the biharmonic problem and its derivatives. Then we set the inner problem after a dilatation of the domain and we write also asymptotic expansions of its solutions. Finally, in the case of a given rigid motion of \(\omega _e\), we match the outer and inner expansions, and we obtain rational equivalents in \(\ln \varepsilon\) for impedance terms.


74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
35C20 Asymptotic expansions of solutions to PDEs
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