Nonlinear dynamic analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium

• Nonlinear dynamic analysis of stiffened FGM cylindrical shells under elastic foundation is studied.
• Approximate three-term solution is chosen.
• Smeared stiffeners technique and Galerkin method are applied.
• Dynamic behavior of external pressure is analyzed.
• Effects of stiffeners, foundation on nonlinear dynamic behavior of shells are shown.

A semi-analytical approach eccentrically stiffened functionally graded circular cylindrical shells surrounded by an elastic medium subjected to external pressure is presented The elastic medium is assumed as two-parameter elastic foundation model proposed by Pasternak. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman–Donnell sense, the smeared stiffeners technique and Galerkin method, this paper deals the nonlinear dynamic problem. The approximate three-term solution of deflection shape is chosen and the frequency–amplitude relation of nonlinear vibration is obtained in explicit form. The nonlinear dynamic responses are analyzed by using fourth order Runge–Kutta method and the nonlinear dynamic buckling behavior of stiffened functionally graded shells is investigated according to Budiansky–Roth criterion. Results are given to evaluate effects of stiffener, elastic foundation and input factors on the frequency–amplitude curves, natural frequencies, nonlinear responses and nonlinear dynamic buckling loads of functionally graded cylindrical shells.