Free Vibration of the Magneto-Electro-Elastic Plates Resting on Elastic Foundation Using the Refined Plate Theory with Two Variables

Abstract

The objective of this article is to investigate the free vibration analyses of the functionally graded magneto-electro-elastic (FG MEE) plates supported by an elastic foundation using the refined plate theory (RPT) with two variables. The elastic foundation is modeled utilizing the Winkler-Pasternak theory. The power-law model is employed to characterize the graded material properties of the FG MEE plates. According to the RPT and Hamilton's principle, the governing equations of the FG MEE plate are derived. The displacement fields and electric and magnetic potentials are approximated using the Non-Uniform Rational B-Splines (NURBS) basic functions of the isogeometric approach (IGA). The proposed model’s advantages and accuracy are demonstrated by comparing the obtained results with those reported in the existing literature. The study comprehensively examines and discusses the impact of several parameters, including the power index, initial external magnetic potential and electric voltage, and the geometry, on the vibration frequency of the FG MEE plates. The numerical findings indicate that an increase in the power index leads to a decrease in the frequency of the FG MEE plates. Besides, the stiffness of FG MEE plates decreases with an increase in the initial external electric voltage, whereas it increases with an increase in the initial external magnetic potential. This article presents valuable perspectives on examining vibration analysis of the FG MEE plates, which can inform the design of innovative materials and structures with customized properties.