Exact three-dimensional interface stress and electrode-effect analysis of multilayer piezoelectric transducers under torsion

In this paper, exact three-dimensional analysis for torsion of multilayer piezoelectric transducers is presented to highlight the remarkable effects of electrode and size effects on interface stresses and deformation. A generalized formulation is introduced for torsion of an arbitrarily layered cross section. In order to reach an advanced and better device, multilayer piezoelectric materials with different properties are formulated while axis of torsion and the polarization axes of each layer make different orientations with respect to each other. An exact formulation for n-layer piezoelectric device with rectangular cross section is presented to compensate considerable deviation of previous studies’ results from exact solution due to the assumption of linear distribution for the electric potential. In order to improve the performance of the transducers, being utilized in industry, several case studies are presented in order to investigate the influence of different parameters, e.g. thickness and material properties of electrodes over shear and peel stresses. Besides, a correction factor is introduced to completely compensate the effect of ignoring electrodes.