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Modelling of Thin Elastic Plates with Small Piezoelectric Inclusions and Distributed Electronic Circuits. Models for Inclusions that Are Small with Respect to the Thickness of the Plate

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Abstract

This paper is devoted to the modelling of thin elastic plates with small, periodically distributed, piezoelectric inclusions, in view of active controlled structure design. The initial equations are those of linear elasticity coupled with the electrostatic equation. Different kinds of boundary conditions on the upper faces of inclusions are considered, corresponding to different ways of control: Dirichlet, Neumann, local or nonlocal mixed conditions. We compute effective models when the thickness a of the plate, the characteristic dimension ε of the inclusions, and ε / a tend together to zero. Other situations will be considered in two forthcoming papers.

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Authors and Affiliations

  1. Laboratoire de Mathématiques de Besançon UMR 6623, Équipe de Calcul Scientifique, Université de Franche-Comté, 16 Route de Gray, F-25030 Besançon, Cédex, France E-mail

    Éric Canon & Michel Lenczner

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  1. Éric Canon
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  2. Michel Lenczner
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Canon, É., Lenczner, M. Modelling of Thin Elastic Plates with Small Piezoelectric Inclusions and Distributed Electronic Circuits. Models for Inclusions that Are Small with Respect to the Thickness of the Plate. Journal of Elasticity 55, 111–141 (1999). https://doi.org/10.1023/A:1007609122248

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