Piezoelectric d ₁₅ shear-response-based torsion actuation mechanism: An exact 3D Saint-Venant type solution

This paper is concerned with the detailed analysis of the behavior of a piezoceramic bi-morph torsion actuator using the d 15-effect. The bi-morph actuator is made of two oppositely polarized adjacent piezoceramic prismatic beams. The mathematical analysis is based on the Saint-Venant torsion theory; a formulation of the electromechanically coupled problem in terms of a stress function and of the electric potential is derived, which represents an exact solution of a specific three-dimensional problem; in particular, for the case when the axial stress and the axial component of the electric displacement vector are independent of the axial coordinate. The resulting boundary-value problem in the cross-section is solved using the method of finite differences. Solutions for the actuated rate of twist are presented and compared to three-dimensional electromechanically coupled finite element solutions using ABAQUS® for the case of a cantilevered bi-morph actuator. A very good agreement is found.