Free vibration of flexible cables

The free undamped vibrations of cables undergoing stretching, bending and twisting are investigated. To this end, a geometrically exact model of elastic cables accounting for bending and torsional stiffness is employed. The cable kinematics retain the full geometric nonlinearities. Starting from a prestressed catenary configuration, the nonlinear equations of motion are linearized about the initial equilibrium. In particular, two initial equilibrium states (shallow and taut) are considered while varying the cable elastic axial stiffness. The influence of the bending flexibility on the cable frequencies is assessed by direct comparisons with the frequencies predicted by classical cable theories of purely extensible cables.