Nonlinear Vibrations of Circular Cylindrical Shells with Different Boundary Conditions

Abstract

Large-amplitude (geometrically nonlinear) vibrations of circular cylindrical shells with different boundary conditions and subjected to radial harmonic excitation in the spectral neighborhood of the lowest resonances are investigated. In particular, simply supported shells with allowed and constrained axial displacements at the edges are studied; in both cases, the radial and circumferential displacements at the shell edges are constrained. Elastic rotational constraints are assumed; they allow simulating any condition from simply supported to perfectly clamped, by varying the stiffness of this elastic constraint. Two different nonlinear, thin shell theories, namely Donnell's and Novozhilov's theories, are used to calculate the elastic strain energy. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite shells. Geometric imperfections are taken into account. Comparison of calculations to experimental and numerical results available in the literature is performed. Both empty and fluid-filled shells are investigated by using a potential fluid model. The nonlinear equations of motion are studied by using a code based on arclength continuation method that allows bifurcation analysis.