Analysis of nonlinear vibration of magneto-electro-elastic plate on elastic foundation based on high-order shear deformation

Abstract

Considering the condition of the elastic foundation and obeying Reddy's third-order shear deformation theory, the nonlinear forced vibration behavior of the magneto-electro- elastic composite materials (MEE) plate is studied. Combined with von Karman's nonlinear principle and Hamilton's principle for model derivation, the nonlinear partial differential equations of the MEE plate are obtained, and then the equations obtained are dimensionless. Based on the mechanical model of the nonlinear forced vibration of the MEE plate and the Galerkin method, the nonlinear high-order partial differential equations are reduced the two-degree-of-freedom nonlinear ordinary differential equations and the model is analyzed by the multi-scale method. In the numerical calculation, the influence of the geometrical parameters, loads, damping, magnetic and electric field strength of the MEE plate on the nonlinear amplitude-frequency response curve (AFRC) of the MEE plate is discussed.