LAUSR

Abstract This study investigated the nonlinear dynamic and vibration of the S-FGM shallow spherical shells with ceramic-metal-ceramic layers (in two cases: non-axisymmetric and axisymmetric shells) on an elastic foundations (EF) with different types of boundary conditions in thermal environment. Material compositions of the shell are graded in the thickness direction according to a sigmoid law distribution in terms of the volume fractions of the constituents. The governing equations are derived by using the classical shell theory and Pasternak's two parameters EF. The motion equations of dynamic analysis are determined due to Galerkin method and the obtained equation is numerically solved by using Runge–Kutta method. The approximate solutions are assumed to satisfy the different types of boundary conditions. The criterion suggested by Budiansky–Roth is applied to determine the dynamic critical buckling load and the nonlinear dynamic response is found by numerical form. In numerical results, the effects of geometrical parameters, material properties, the EF, boundary conditions, mechanical loads and temperature on the nonlinear dynamic and vibration stability of the shells are investigated.