Nonlinear Vibration Analysis of Laminated Magneto-Electro-Elastic Rectangular Plate Based on Third-Order Shear Deformation Theory

摘要

Nonlinear vibration of magneto-electro-elastic rectangular thick plate is studied based on the third-order shear deformation theory. The plate is symmetrically laminated and simply supported along all of its edges. The magneto-electric boundary condition on upper and bottom surfaces of the plate is considered to be closed-circuit. Gauss's laws for electrostatics and magnetostatics are used to model the electric and magnetic behavior of the plate. After deriving the nonlinear partial differential equations of motion, Galerkin method is applied to transform these equations into a single ordinary differential equation. This equation is solved analytically by using Lindstedt-Poincare and multiple time scales methods. Several examples are provided to investigate the effects of different parameters on the nonlinear vibration of these plates.