The present paper is concerned with the dynamic shape control of force loaded beams by means of the converse piezoelectric effect. We consider smart beams composed of substrate layers bonded to piezoelastic actuation layers with shaped electrodes at both sides. Piezoelastic extension actuators as well as piezoelastic shear actuators are used. We study transient disturbances produced by assigned forces, and we seek for a transient piezoelastic actuation which, when superimposed upon the assigned forces, leads to zero total displacements and cross-sectional rotations of the beams under consideration. In the following, a solution of this dynamic shape-control problem is presented which is exact within the framework of the Timoshenko theory of beams. The required shape-functions of the electrodes for eliminating the dynamic deformations due to the assigned forces are shown to be the quasi-static bending moment and shear force distributions due to the same assigned forces. When the assigned forces have a fixed space-wise distribution with a time-varying intensity, this solution can be easily realized and is felt to be appealing for practical purposes. We furthermore identify nilpotent shape functions, which may be added to the former solutions of the shape control problem without violating their validity.

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