Nonlinear Axisymmetric Vibration of Sandwich FGM Shallow Spherical Caps with Lightweight Porous Core

This paper presents the axisymmetric vibration responses of sandwich Functionally graded material (FGM) shallow spherical caps with lightweight porous core subjected to uniformly external loads and shell-foundation Pasternak interaction. Based on the first-order shear deformation theory (FSDT) with von Karman geometrical nonlinearity, the governing equations are established. By using the Galerkin method and the Runge–Kutta method, the fundamental frequencies and the nonlinear dynamic responses of the shell are obtained. The effects of porosity coefficient, geometrical parameters, and foundation are considered.