Shape control of hybrid functionally graded plate through smart application of piezoelectric material using simple plate theory

Abstract

The present study takes its inspiration from notable work in the literature related to the flexural analysis of functionally graded material (FGM) plate along with a smart application of piezoelectric material but maintains its novelty in terms of simple approach, an analytical solution with a wide scope of application. Coupling the plate element with piezoelectric smart material can control deflection, vibration thereby increasing the safety, stability, and life of these elements. Plates made up of functionally graded material further enhances the applicability as two different materials are fused. Analysis of such a system is challenging especially for a closed form mathematical solution along with complex boundary conditions. In the present study, it is proposed to develop a simple analytical model for bending analysis of FGM plate coupled with piezoelectric layers. Polynomial based shear deformation function taken from literature is applied to develop a simple mathematical model. A complete flexural analysis is performed for FGM plate to validate the governing simple mathematical model. Through the smart application of piezoelectric material, the deflection of the FGM plate is controlled in as closed loop feedback system. Analytical solution valid over the entire plate domain is obtained incorporating fixed and simple support types of boundary conditions. The initial part of the study details complete mathematical formulation for the plate under consideration, followed by numerical validation in which results of the present model are compared with notable studies in the literature. Lastly, the smart application through shape control of the FGM plate is demonstrated graphically and numerically. The development and application of the discussed mathematical model presented in this study are complete in all aspects of its mathematical form, solution, and numerical validation.