Nonlinear vibration of functionally graded magneto-electro-elastic higher order plates reinforced by CNTs using FEM

In this article, finite-element formulation based on higher order shear deformation theory (HSDT) is proposed to evaluate the nonlinear frequency characteristics of carbon nanotube reinforced magneto-electro-elastic (CNTMEE) plates. The special emphasis has been made on investigating the effects of electro-magnetic circuits on the nonlinear coupled behaviour of CNTMEE plates, for the first time in the literature. The von-Karman type of nonlinear strain–displacement relations is assumed. The nonlinear fundamental frequencies for a given maximum transverse deflection are obtained through direct iterative method. Also, different forms of functionally graded CNT distributions are considered and compared with that of uniformly distributed CNT arrangement. Several numerical illustrations are depicted to highlight the influence of parameters such as electro-magnetic conditions, CNT volume fraction, boundary conditions, aspect ratio, length-to-thickness ratio etc. One of the major outcomes of this study is the influence of coupling fields on the nonlinear frequency response of CNTMEE plates.