Abstract
Flexural vibrations of smart beams are studied in this paper. Layers made of piezoelectric material are used to perform a distributed actuation of the beam. Special emphasis is given to the following actuator shaping problem: A spatial shape function of the distributed actuator is sought such that vibrations induced by external forces are completely annihilated. The formulation is restricted to forces with a given spatial distribution and an arbitrary time evolution of their intensity. The scope is to derive a class of easy to obtain analytic solutions of this inverse problem. Actuator equations are used in the present contribution which take into account the interaction of mechanical and electrical fields. Extending the preliminary results, the above actuator shaping problem is solved in the context of these coupled equations. Beams with different boundary conditions are considered. Shape functions responsible for nonuniqueness of the shaping problem are also considered. These nilpotent solutions may be added to the above derived solution of the actuator problem without producing any additional vibrations. The presented analytic results are validated by means of coupled finite-element calculations.
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