Non-linear dynamic instability analysis of laminated composite cylindrical shells subjected to periodic axial loads

The dynamic instability of thin laminated composite cylindrical shells subjected to harmonic axial loading is investigated in the present work based on nonlinear analysis. The equations of motion are developed using Donnell’s shallow-shell theory and with von Karman-type of nonlinearity. The nonlinear large deflection shallow-shell equation of motions are solved by using Galerkin’s technique that leads to a system of nonlinear Mathieu–Hill equations. Both stable and unstable solutions amplitude of the steady-state vibrations are obtained by applying the Bolotin’s method. The nonlinear dynamic stability characteristics of both symmetric and antisymmetric cross-ply laminates with different lamination schemes are examined. A detailed parametric study is conducted to examine and compare the effects of the magnitude of both tensile and compressive axial loads, aspect ratios of the shell including length-to-radius and thickness-to-radius ratios, and different circumferential wave numbers as well on the parametric resonance particularly the steady-state vibrations amplitude. The present results show good agreement with that available in the literature.