Analytical Study of Piezoelectric Effect on Curvature and Mechanical Sensitivity in Large Deflection of Pre-Stressed Layered Plate Including a Piezoelectric Layer

Abstract

This study explores the curvature and mechanical sensitivity of a pre-stressed layered plate embedded with a piezoelectric layer in large deflection. Piezoelectric effect was included in deriving the nonlinear governing equations but the arising nonlinear terms are neglected, yielding a standard Bessel equation or a modified Bessel equation for the lateral slope. Analytical solutions are developed and further manipulated to obtain lateral curvature and mechanical sensitivity. The results for a nearly monolithic plate under low pretension and low voltage applied across the piezoelectric layer agree well with those of CPT for a single-layered plate under pure mechanical loading. For typical symmetric 3-layered piezoelectric plates, the solutions show that, piezoelectric effect is apparent only up to a moderate initial tension. Beyond a moderate threshold value, the pretension turns to be dominant, resulting in nearly zero curvature and uniform mechanical sensitivity throughout the entire plate.