Two-degrees-of-freedom nonlinear free vibration analysis of magneto-electro-elastic plate based on high order shear deformation theory

Abstract

This article tries to investigate the nonlinear free vibration (NFV) response of magneto-electro-elastic (MEE) composite plates considering von Karman’s nonlinear strain–displacement theory under the high order shear deformation theory (HSDT). The governing equations are derived via Hamilton’s principle. The nonlinear motion equations are dimensionless and solved by the Galerkin method and harmonic balance method. Thereout, the nonlinear relationship curves of the dimensionless frequency ratio and free vibration amplitude of MEE plate under two degrees of freedom are given respectively. According to the parametric method, the effects of the aspect ratio, span-thickness ratio, and magnetic and electric potential on the NFV behavior of MEE plates are analyzed. The differences in nonlinear free vibration of the MEE plate under different degrees of freedom are discussed. This paper also verifies the reliability of the method and results by comparing them with the published literature.