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Non-linear free vibration analysis of laminated non-homogeneous orthotropic cylindrical shells

Abstract The free vibrations of laminated non-homogeneous orthotropic thin cylindrical shells are studied, with geometric non-linearity taken into account. The basic relations and equations of motion, based on the Donnel-Mushtari shell equations considering finite deformations and the Airy stress function, are obtained for laminated thin cylindrical shells, the elasticity modulus and density of which vary piecewise continuously in the through-thickness direction. Applying the Galerkin method to the foregoing equations, a non-linear time dependent differential equation is obtained for the displacement amplitude. The frequency is obtained from this equation as a function of the shell displacement amplitude and then compared with the results in the literature. Finally, the effect of non-linearity, non-homogeneity and the number and ordering of layers on the frequency is found for different mode numbers, presented graphically and compared with other work.