Dynamic stability of simply supported composite cylindrical shells under partial axial loading

• Expressions for the pre-buckling stress distributions are presented.
• Instability regions are reported for partial edge loading.
• Linear response grows exponentially but the nonlinear response is bounded in the unstable region.
• Frequency of beats is different for linear and nonlinear responses in the lower-stability region.
• The shell shows chaotic behavior for certain values of geometric and loading parameters.

The parametric vibration of a simply supported composite circular cylindrical shell under periodic partial edge loadings is discussed in this article. Donnell׳s nonlinear shallow shell theory considering first order shear deformation theory is used to model the shell. The applied partial edge loading is represented in terms of a Fourier series and stress distributions within the cylindrical shell are determined by prebuckling analysis. The governing equations of the dynamic instability of shells are derived in terms of displacements (u−v−w  ) and rotations(φx,φθ)(φx,φθ). Employing the Galerkin and Bolotin methods the dynamic instability regions are computed. Using the expression for the stress function derived in this paper, the pre-buckling stresses in the cylindrical shell due to partial loading can be calculated explicitly. Numerical results are presented to show the influence of radius-to-thickness ratio, different partial edge loading distributions and shear deformation on the dynamic instability regions. The linear and nonlinear responses in the stable and unstable regions are presented to bring out the characteristic features of the dynamic instability regions, such as the existence of beats, its dependence on forcing frequency and effect of nonlinearity on the response. The effect of dynamic load amplitude on the nonlinear response is also studied. It is found that for higher values of dynamic loading, the shell exhibits chaotic behavior.