Homogenization of von Kármán Plates Excited by Piezoelectric Patches
Karl Heinz Hoffmann, Nikolai D. Botkin · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2000
A model describing vibration of nonlinear von Kármán thin plates excited by actuators made of piezoelectric ceramics is considered. The model contains strong oscillating coefficients due to the piezoelectric actuators. A procedure of homogenization based on the so-called two-scale convergence is applied to the model. This yields a nonlinear system of equations with constant coefficients. The unique solvability of the resulting system is proved. The convergence of all solutions of the original system to the solution of the resulting system as the number of piezoelectric actuators goes to infinity is proved.