Parametric analysis of large amplitude free vibrations of a suspended cable

Partial differential equations of motion suitable to study moderately large free oscillations of an clastic suspended cable arc obtained. An integral procedure is used to eliminate the spatial dependence and to reduce the problem to one ordinary differential equation which shows quadratic and cubic nonlincarities. The frequency-amplitude relationship for symmetric and antisymmetric vibration modes is studied and a numerical investigation is performed to describe the nonlinear phenomenon in a large range of values of the cable sag-to-span ratio. Softening and hardening behaviour is evidenced dependent on both the cable properties and the amplitude of oscillation