Nonlinear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions

A four-degree-of-freedom model able to capture the main phenomena which are likely to occur in the non-planar finite dynamics of an elastic suspended cable subjected to external forcings and support motions is developed from the continuum equations. It contains two in-plane and two out-of-plane components, one symmetric and one antisymmetric. An order two multiple time scales solution is obtained for the case of primary external resonance and three simultaneous internal resonances cable at crossover frequency.[ Possible classes of steady state "planar/non-planar, unimodal/multimodal) regular motions of the system are identified and their linearized stability analysis is performed[ Some results are presented to highlight the role played by key perturbations on the onset of various classes, the rich behaviour of the system and the influence of some control parameters on the response