Homogenization of a model describing vibration of nonlinear thin plates excited by piezopatches

A model describing vibration of nonlinear von Karman 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.