Axisymmetric nonlinear vibration analysis of sandwich annular plates with FG-CNTRC face sheets based on the higher-order shear deformation plate theory

In this paper, a comprehensive numerical study is presented on the large-amplitude free vibration of sandwich annular plates integrated with functionally graded carbon nanotube-reinforced composite (FG-CNTRC) face sheets resting on elastic foundation. The sandwich plate is made of a homogeneous core and two FG-CNTRC face sheets whose material properties are estimated through a micromechanical model. Since the fundamental vibrational mode shapes of annular plates are axisymmetric, the governing equations are derived assuming the axisymmetric formulation. For this purpose, the quadratic form of total potential energy of the structure is presented based on the higher-order shear deformation theory (HSDT) of plates along with von-Karman nonlinear kinematic relations. The numerical differential and integral operators are then employed to discretize the energy functional in space and time domains. Finally, using the response of linear analysis and applying the pseudo-arc length continuation method, the nonlinear frequencies are obtained. After validating the results of proposed approach, detailed numerical results are given to analyze the effects of geometrical and material parameters on the nonlinear vibration of FG-CNTRC sandwich annular plates.