Free Vibration Analysis of Functionally Graded Magneto-electro-elastic Plates Resting on Elastic Foundations with Considering Interfacial Imperfections

In this study, a three-dimensional (3D) Peano series solution is presented for the dynamic analysis of functionally graded (FG). Layered magneto-electro-elastic (MEE) plates resting on elastic foundations with considering imperfect interfacial bonding and the interfacial imperfection is modeled using a generalized spring layer method. Regardless of the number of layers, the equations of motion, Gauss’ equations (for electrostatics and magnetostatics), and the boundary and interface conditions are satisfied exactly. In this method, no assumptions on deformations, stresses, magnetic and electric fields along the thickness direction are introduced. Finally, the governing partial differential equations are solved using state-space method. The proposed formulation is validated through comparison with other available results. Effects of a two-parameter elastic foundation, gradient index, bonding imperfection, applied mechanical and electrical loads on the dynamic response of the functionally graded magneto-electro-elastic (FGMEE) plate are discussed The obtained exact solution can be used to assess the accuracy of the theorems for layered FGMEE plates and validating finite element codes.