Exact 3D Saint Venant type solutions for piezoelectric d 15 shear-mode bi-morph and sandwich torsion actuation and sensing problems

This paper is concerned with the analysis of two types of piezoelectric torsion transducers using the d ₁₅-effect of mono-morph piezoelectric materials. The first problem is concerned with a bi-morph transducer made of two identical mono-morph straight rods, which are perfectly bonded to each other along their width; the polarization direction is parallel, but opposite in sign, such that the piezoelectric material parameter d ₁₅ has an opposite sign as well. The second problem sandwiches the bi-morph transducer between two identical elastic face layers. In both cases, the resulting transducer represents a torsion transducer. Therefore, we analyze the electromechanically coupled problem in the framework of Saint Venant’s torsion theory for straight rods taking into account the electrical problem as well. The results of our approach are compared to electromechanically coupled three-dimensional finite element computation and a very good agreement for the mechanical as well as the electrical entities is achieved, in particular for the rate-of-twist, the axial warping function, and the sensed voltage.