Piezoelectric Transverse Shear Actuation and Sensing of Plates,Part 1: A Three-Dimensional Mixed State Space Formulation

Abstract

This paper, in two parts, presents in this first part an exact three-dimensional solution of transverse shear actuation and sensing of simply-supported piezoelectric laminated plates. For this, the piezoelectric laminae are considered initially polarized along their first materialaxis (x₁) and subjected to through-thickness electric field. Hence, transverse shear strains can be induced or measured under electric or mechanical loading, respectively. The formulation is based on a new mixed state space approach that retains the standard state mechanical displacement and transverse stress variables augmented with the electric potential and transverse displacement. The latter are condensed analytically at the piezoelectric lamina transfer matrix level. Thus, the solution of the assembled system is reduced to that of only a third-order one. Both open- and closed-circuit electric boundary conditions are considered for sensing and actuation problems, respectively. Corresponding computational procedures are also detailed. In part two of the paper, the present approach is applied to transverse actuation and sensing of sandwich plates. Parametric studies are also conducted for physical understanding of these mechanisms. Presented analytical results are useful for future reference and comparison with other approximate laminate electromechanics.