Internal Resonances in an Imperfect Circular Cylindrical Panel

Abstract

The aim of the present work is to investigate the influence of initial geometric imperfections on a slender cylindrical panel nonlinear response, considering the presence of internal resonances. Nonlinear Donnell shallow shell theory is used to obtain the nonlinear equations of motion. To obtain a consistent modal solution, the transversal displacement field is obtained from a perturbation technique which takes into account the phenomena of modal coupling and interaction in simply supported cylindrical panels. Then, the standard Galerkin method is applied to reduce the problem to a system of differential equations in time domain to obtain the backbone curves, which is solved by using the shooting method. The resonance curves are obtained by continuation methods displaying a complex bifurcation scenario. The influence of the shape and amplitude of the geometrical imperfection on the resonance curves is investigated.