Nonlinear free vibration analysis of thermally induced FG-CNTRC annular plates: Asymmetric versus axisymmetric study

Due to axisymmetric fundamental vibrational mode shape, the most studies on the large-amplitude free vibration of annular plates have been presented based on the axisymmetric formulation. However, the initial thermal loading can change the vibration behavior of annular plates. To analyze this effect, the nonlinear free vibration of carbon nanotube (CNT) reinforced composite annular plates is investigated under thermal loading based on the asymmetric formulation. The material properties of the CNT-reinforced composites are assumed to vary continuously along the thickness direction and estimated through a micromechanical model by which the temperature-dependency is taken into account. The governing equations are derived on the basis of first-order shear deformation theory, and an efficient numerical variational method is employed to solve the problem. In this regard, the quadratic form of the energy functional is directly discretized using numerical differential and integral operators, and the pseudo-arc length continuation method is then applied to find the frequency response of the structure. The numerical results of asymmetric and axisymmetric formulations are compared and it is observed that in the presence of initial thermal loading, the axisymmetric analysis leads to inaccurate results and complete asymmetric formulation should be considered.