Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties

In this article, the nonlinear free vibration behavior of functionally graded (FG) spherical shell panel is examined under nonlinear temperature field. The functionally graded material (FGM) constituents are assumed to be the function of temperature and the thermal conductivity. The effective properties of the FGM are obtained using the Voigt micromechanical model through power-law distribution. The mathematical model of the shell panel is developed using Green–Lagrange nonlinear kinematics in the framework of the higher order shear deformation theory. The desired governing of the FG shell panel under thermal environment is obtained using the classical Hamilton's principle. The domain is discretized with the help of the finite element steps and the responses are computed using the direct method. The convergence behavior of the present nonlinear numerical model has been checked and compared with the previous reported results. Numerous examples have been demonstrated for the FG spherical panel to show the influence of different geometrical and material parameters and support conditions on the linear and nonlinear frequency parameters.