Control of plate vibrations by means of piezoelectric actuators

Marius Tucsnak

doi:10.3934/dcds.1996.2.281

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1996, Volume 2, Issue 2: 281-293. Doi: 10.3934/dcds.1996.2.281

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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

Received: June 30, 1995

Revised: September 30, 1995

Published: March 1996

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Abstract

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.

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Mathematics Subject Classification: 35B37, 93C20.

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