Isogeometric free vibration of functionally graded porous magneto-electro-elastic plate reinforced with graphene platelets resting on an elastic foundation

Abstract

This article investigates the free vibration behavior of functionally graded porous reinforced with graphene platelets magneto-electro-elastic (FGP-GPL-MEE) plates. The FGP-GPL-MEE plate is supported by the Winkler-Pasternak foundation and subjected to the initial external electric voltage and magnetic loads. The governing equations for FGP-GPL-MEE plates are derived from the combination of Hamilton's principle and the refined plate theory (RPT) with four variables. The FGP-GPL-MEE plate is formed by combining three porosity distributions of functionally graded materials and three patterns of graphene platelets dispersion distributed along the plate thickness. Using the modified Halpin-Tsai model, effective material properties of the FGP-GPL-MEE plate are estimated. Isogeometric approach (IGA) is used to discretize the plate geometry and extract mode shapes and natural frequencies. The effects of various parameters such as porosity distributions, porosity coefficient, GPLs distributions and magnetic and electric potentials on the natural frequencies of the FGP-GPL-MEE plate are performed. The results indicate that the GPLs reinforcement can be significantly enhanced the natural frequencies of the FGP-GPL-MEE plate. Moreover, the free vibration behavior is significantly influenced by porosity, as well as magnetic and electric fields. The results of this study provide valuable insights into the vibrational characteristics of FGP-GPL-MEE plates.