A semi-analytical approach for instability analysis of composite cylindrical shells subjected to harmonic axial loading

Abstract

In this article, nonlinear vibration and dynamic stability analyses of simply supported laminated composite circular cylindrical shells subjected to periodic edge loading are carried out. A third-order shear deformation shell theory that considers all the nonlinear terms in all five kinematic parameters and rotary inertia is used to develop the present mathematical model so that the model is also valid for thick cylindrical shells. Hamilton’s principle, an energy-based approach, is used to obtain the governing partial differential equations (PDEs) of motion of the cylindrical shell. Further, these equations are reduced into ordinary differential equations by employing Galerkin’s method. The incremental harmonic balance (IHB) method in conjunction with the pseudo-arc-length method is used to obtain the frequency-amplitude response of the system. For obtaining the zone of instability regions, Bolotin’s method is adopted. For more practical significance, analysis of results is also extended by considering damping into account for the composite cylindrical shells. Time history response and phase portrait are plotted by adopting Newmark-beta method. The effects of the static load factor, dynamic load factor, modal damping coefficient, and stacking sequence on nonlinear vibration, instability regions and time history responses are also examined.