Non-linear planar dynamics of suspended cables investigated by the continuation technique

In this paper, the continuation technique is used to investigate the non-linear response of a suspended cable under harmonic excitation. Taking into account the geometric non-linearity of the suspended cable as well as the assumption of quasi-static stretching, a mathematical model of the suspended cable is formulated. The periodic solution for the suspended cable is obtained by means of the shooting method, and the continuation technique is used to trace the frequency-response curves of the suspended cable, while the non-periodic motions are studied through direct simulations. Moreover, the results obtained by this method and the numerical integration are compared in detail. Finally, the effects of the amplitude of the harmonic excitation on the periodic motion of the suspended cable are investigated.