Volumetric Displacement in Large Deflection of Symmetrically Layered Piezoelectric Plate under Pretension

Abstract

Abstract The volumetric displacement of a simply supported and symmetrically layered piezoelectric circular plate under lateral load and pretension in large deflection is studied. The approach extends von Karman’s large deflection theory to a layered case and accounts for the associated piezoelectric force terms. The nonlinear governing equations based on the equilibrium were derived, but the arising nonlinear terms in governing equations were dropped, to have an analytical investigation. The solutions were found to be expressible with modified Bessel or standard Bessel functions, depending on whether it is a mechanical-load dominating or piezoelectric-load dominating condition. The previously derived expressions for lateral slopes and deflections are further manipulated to derive the analytical expressions for the volumetric displacements, following strictly the related recurrence relations. The presented approaches are implemented with typical silicon-based layer materials used in a sensing or actuating device. Various dimensions, especially the relative thickness of the piezoelectric layer, as well as different applied voltages and pretensions are considered to have an extensive parametric study. The results indicate that, piezoelectric effect is only apparent in a low pretension condition. Upon reaching a moderate pretension, the pretension effect may always be dominant over the effects of varying the applied voltage and relative thickness.