Homogenization of an equation describing linear thin plates excited by piezopatches
Nikolai D. Botkin · 1999
: In this paper we consider the problem of homogenization of equations describing linear thin plates excited by actuators made of piezoelectric ceramics (see e.g. [1]). It is assumed that the number of actuators goes to infinity whereas their dimension tends to zero. The procedure of homogenization is based on the theory of two-scale convergence studied in [2]. The specific of the problem considered is the time dependence and the appearance of the forth spatial derivatives in the equation. A result of [3] about two-scale convergence of the second derivatives of subsequences of sequences bounded in L 2 (0; T ; H 2 0 (S)) enables us to handle this case. The paper is illustrated by computer simulations that demonstrate a good approximation of solutions of the original equation by solutions of the homogenized equation if the number of piezoelectric patches is sufficiently large. KEY WORDS: Linear thin plates, Piezoelectric actuators, Homogenization, Twoscale convergence. AMS (MOS) subjec...