NONLINEAR OSCILLATIONS OF A 4-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 whic h 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 t wo out-of-plane components, one symmetric and one antisymmetric. An or der two multiple time scales solution is obtained for the case of prim ary external resonance and three simultaneous internal resonances (cab le at crossover frequency). Possible classes of steady state (planar/n on-planar, unimodal/multimodal) regular motions of the system are iden tified, and their linearized stability analysis is performed. Some res ults are presented to highlight the role played by key perturbations o n the onset of various classes, the rich behaviour of the system and t he influence of some control parameters on the response.