On the non-linear vibrations of clamped-free cylindrical shells subjected to combined loads

Resumo

In this work, the nonlinear vibrations of clamped-free cylindrical shells subjected to combined loads is
studied. Combined loads such as axial, lateral and base acceleration can generate complex vibrations in shells and
its combination is important to consider in project of these kind of structures. For this, to model the shell the Koiter

– Sanders nonlinear shell theory is considered, and the Rayleigh-Ritz method is applied to obtain a set of non-
linear dynamic equations which are solved in turn by the fourth order Runge-Kutta method. To study the nonlinear

dynamic response, an expansion with fifteen degrees of freedom in the axial, radial and lateral directions, which
represents the correct modal coupling, is considered. The nonlinear static paths, the parametric instability
boundaries, resonance curves and Poincaré maps are obtained. It is possible to observe that, depending on the
geometry ratios, the intensity of the loads, the shell will display complex nonlinear response showing softening,
chaotic or quasi-periodic oscillations.