Three-dimensional electromechanical responses of a parallel piezoelectric bimorph

This paper proposes a three-dimensional study for parallel piezoelectric bimorphs, which are used commonly as sensors and actuators. Firstly, a general analysis is performed based on the state space formulation combined with an asymptotic expansion technique. By properly truncating the expansions, a analytical expressions for the three-dimensional distributions of electric and mechanical fields in the bimorph is obtained in terms of the displacements on the mid-plane. These displacements are governed by two-dimensional equations formally similar to those in the classical plate theory. Thus, a three-dimensional solution to the bimorph generates directly, provided the two-dimensional equations are solved. As an example, a piezoelectric cantilever bender with a clamped edge is considered, and detailed numerical results are illustrated.

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