Mathematical analysis of piezoelectric sandwich torsion transducers based on the d₃₆-effect

In the present article, we analyze a d₃₆-effect piezoelectric torsion transducer following the Saint-Venant torsion theory taking the electrical field into account. A representation of the stress function, the electric potential, and the warping function are derived and solved with finite differences. Then, the one-dimensional governing equations at the structural beam level, including the constitutive relations as well as the balance equations for the dynamics of the transducer, are presented. The axial moment and the total charge are computed as functions of the rate of twist and the applied potential difference. As an example, a cantilevered transducer is studied.