Analytical Solutions of Laminated Plates with Oblique Piezoelectric Patches

Abstract

This work presents a detailed model of symmetric laminated plates with oblique piezoelectric patches. The model is developed to predict the static behavior of laminated plates subjected to bending moments induced by piezoelectric strains. The model considers plates of orthotropic layers and obeys the classical plate theory. The piezoelectric patches are symmetrically bonded at off-axis orientation on the plate upper and lower surfaces. Furthermore, the patches may have straight and curved boundaries. The action of the active patches is represented by the singularity functions. Analytical solutions of specially orthotropic plates, i.e., plates for which bending-twisting coefficients D16 and D26 are zero, with simply supported boundary conditions are developed. The solutions rely on the Navier’s approach. Numerical examples of plates with oblique PZT patches that have straight and curved boundaries are presented. These examples demonstrated that the use of oblique patches could provide control authority that is difficult to be provided by the traditional orientation. The results of the present study can be directly used to perform various analysis of shape control of laminated plates. Analytical solutions of plates with two opposite edges simply supported and the remaining two edges having any possible combination of boundary conditions are natural extension of the present study. Keywords: Smart structures, Laminates, Plates, Piezoelectric actuators, Oblique patches, Shape control, Analytical solutions