Nonlinear free vibrations of spinning functionally graded graphene reinforced cylindrical shells

The graphene nanoplatelet (GPL) is a two-dimensional single layer of carbon atoms with extraordinary mechanical, thermal and electrical properties, and can provide excellent reinforcement effects on the matrix when it disperses at a low concentration. Mechanical behaviors of graphene reinforced nanocomposites structures have attracted tremendous interests due to their potential applications in engineering fields. Nonlinear free vibration behaviors of novel functionally graded nanocomposite spinning cylindrical shells reinforced with GPLs are studied where the weight fraction of GPLs varies through the thickness direction. Three different GPL distribution patterns are considered. The modified Halpin-Tsai micromechanical model and the extend rule of mixture are employed to determine effective values of position-dependent elastic moduli, mass density and Poisson's ratio. Based on the Donnell's nonlinear shell theory, the nonlinear partial differential equations of motion for the cylindrical shell are formulated by using the Hamilton's principle with the effects of centrifugal and Coriolis forces as well as the spin-induced initial hoop tension taken into account. A set of nonlinear ordinary differential equations are derived by employing the Galerkin approach. Parametric studies of weight fractions, geometrical sizes and distribution patterns of GPLs, spinning speeds and travelling wave numbers on the linear and nonlinear natural frequencies for the nanocomposite cylindrical shell are conducted. Results show that the effective stiffness of the cylindrical shell can be significantly increased by adding small amounts of graphene into the metal matrix. GPLs with a larger surface area but less single graphene layers are preferred nanofillers as they offer the best structural performance of the nanocomposite cylindrical shell