Nonlinear dynamic analysis of spiral stiffened functionally graded cylindrical shells with damping and nonlinear elastic foundation under axial compression

The semi-analytical method to study the nonlinear dynamic behavior of simply supported spiral stiffened functionally graded (FG) cylindrical shells subjected to an axial compression is presented. The FG shell is surrounded by damping and linear/nonlinear elastic foundation. The proposed linear model is based on the two-parameter elastic foundation (Winkler and Pasternak). A three-parameter elastic foundation with hardening/softening cubic nonlinearity is used for nonlinear model. The material properties of the shell and stiffeners are assumed to be FG. Based on the classical plate theory of shells and von Kármán nonlinear equations, smeared stiffeners technique and Galerkin method, this paper solves the nonlinear vibration problem. The fourth order Runge-Kutta method is used to find the nonlinear dynamic responses. Results are given to consider effects of spiral stiffeners with various angles, elastic foundation and damping coefficients on the nonlinear dynamic response of spiral stiffened simply supported FG cylindrical shells.