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The nonlinear vibration, including primary resonance (PR) of porous FG sandwich (PFGS) cylindrical shells with a viscoelastic core is investigated in this research. The structure considered is on a nonlinear viscoelastic foundation composing of two Pasternak and Winkler foundations augmented with a nonlinear cubic stiffness by Kelvin–Voigt viscoelastic model. Two types of PFGS cylindrical shells are considered and viscoelastic core is made of Kelvin–Voigt type material. Utilizing Donnell’s shell theory, von-Kármán equation and the Galerkin’s method, a discretized governing equation is derived and verified. The multiple scales method is applied to investigate the nonlinear PR of the shells.

Nonlinear dynamic responses of porous FG sandwich cylindrical shells with a viscoelastic core resting on a nonlinear viscoelastic foundation