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April  1996, 2(2): 281-293. doi: 10.3934/dcds.1996.2.281

Control of plate vibrations by means of piezoelectric actuators

Marius Tucsnak 1,

1. 

Centre de Mathématiques Appliqués (CMAP), Ecole Polytechnique, 91128 Palaiseau and Université de Versailles, France

Received  July 1995 Revised  October 1995 Published  February 1996

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.
Keywords: piezoelectric actuator, strong stabilization, plate equation, approximate controllability..
Mathematics Subject Classification: 35B37, 93C2.
Citation: Marius Tucsnak. Control of plate vibrations by means of piezoelectric actuators. Discrete and Continuous Dynamical Systems, 1996, 2 (2) : 281-293. doi: 10.3934/dcds.1996.2.281
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