A Reliable Plain Solution for Rectangular Plates with Piezoceramic Patches

Abstract

The present study investigates the behavior of a laminated composite plate with embedded or bonded piezoelectric materials. An exact mathematical model based on Reissner—Mindlin theory for plates (FSDT) has been developed for laminated composite plates with continuous piezoelectric layers. The flexural behavior has been solved based on Levy's method for plates. Therefore, the study has been limited to obtain exact solutions only for the cases of plates with at least two opposite simply supported edges, and only continuous piezoelectric layers. For a plate with piezoelectric patches, an approximate energy solution is presented, using Reissner—Mindlin theory, where the lateral displacement and the two bending rotations are expressed as infinite series. The point of merit for this model is its simplicity and reliability (depending on the number of terms) to solve a plate with any required boundary conditions and lay-ups. Furthermore, this model can be easily adapted to solve piezo-composite plates with an unlimited number of piezoelectric patches in arbitrary locations over the plate. A comprehensive parametric investigation has been performed to study the behavior of a plate actuated by extension or shear piezoelectric mechanisms. This investigation has been performed to yield results for plates with various boundary conditions and arbitrary patch locations.