Nonlinear vibration of FGM moderately thick toroidal shell segment within the framework of Reddy’s third order-shear deformation shell theory

Nonlinear vibration and dynamic response of functionally graded moderately thick toroidal shell segments resting on Pasternak type elastic foundation are investigated in this paper. Functionally graded materials are made from ceramic and metal, and the volume fraction of constituents are assumed to vary through the thickness direction according to a power law function. Reddy’s third order shear deformation, von Karman nonlinearity, Airy stress function method and analytical solutions are used to derive the governing equations. Galerkin method is used to convert the governing equation into nonlinear differential equation, then the explicit expressions of natural frequencies and nonlinear frequency–amplitude relations are obtained. Using Runge–Kutta method, the nonlinear differential equation of motion is solved, and then nonlinear vibration and dynamic response of shells are analyzed. The effects of temperature, material and geometrical properties, and foundation parameters on nonlinear vibration and dynamic characteristics are investigated and discussed in detail.