Nonlinear vibration of functionally graded sandwich shallow spherical caps resting on elastic foundations by using first-order shear deformation theory in thermal environment

A semi-analytical approach to investigate the nonlinear vibration axisymmetric analysis of functionally graded sandwich shallow spherical caps under external pressure resting on elastic foundation in thermal environment is presented. The governing equations are derived by using the first-order shear deformation theory taking into account von Karman geometrical nonlinearity and Pasternak’s two-parameter elastic foundation. The motion equations are determined by Galerkin method and the obtained equation is numerically solved by using Runge–Kutta method. Results of nonlinear dynamic responses show the effects of foundation, material, geometric parameters, and temperature change on the nonlinear vibration of shells.