Control of Plate Vibrations by Means of Piezoelectric Actuators

We consider initial and boundary value problems modelling the vibrations of a plate with piezoelectric actuator. The simplest model leads to the Bernoulli-Euler plate equation with right hand side given by a distribution concentrated in an interior curve multiplied by a real valued time function representing the voltage applied to the actuator. We prove that, generically with respect to the curve, the plate vibrations can be strongly stabilized and approximatively controlled by means of the voltage applied to the actuator. 1. Introduction In this paper we will study control of vibrations for a structure composed of an elastic plate and of a piezoelectric actuator bonded to the plate. The control function is the voltage applied to the actuator. The usual model leads to the Bernoulli-Euler plate equation with right hand side given by a distribution concentrated in an interior curve multiplied by a real valued time function representing the voltage applied to the actuator (cf. 2], 3], 8], 11]).