The non-linear vibrations of rotating functionally graded cylindrical shells

This paper reports the result of an investigate on the non-linear vibrations of rotating functionally graded cylindrical shell in thermal environment, based on Hamilton's principle, von Karman non-linear theory and the first-order shear deformation theory. The formulation includes the initial hoop tension, the centrifugal and Coriolis forces due to rotation of the shell. The effects of in-plane and rotary inertia are taken into account in the equations of motion. Galerkin's method is utilised to convert the governing partial differential equations to non-linear ordinary differential equations. A reduction in the model is presented to investigate non-linear dynamics, including primary resonance responses, quasi-periodic and chaotic responses to harmonic transverse external forces. The modal coefficients of quadratic and cubic nonlinearities are calculated by Galerkin integration and superimposed on the linear part of equation to establish the non-linear reduction equation. To validate the approach proposed in this paper, a series of comparison are performed and the investigations demonstrate good reliability and low computational cost of the present approach.