Nonlinear oscillations of cables under harmonic loading by analytical and finite element models

In cables, near resonance time-varying loading causes large amplitude oscillations mainly involving the resonant mode. A relevant contribution of higher modes may arise as a result of nonlinear coupling phenomena. In this work, analytical and finiteelementmodels are used to study the modal interactions in both planar and spatial responses to harmonic in-plane and out-of-plane loads. The aim of the investigation is to compare the two approaches by examining the effectiveness of the analyticalmodel in describing the response with few degrees of freedom and the ability of the nonlinearfiniteelement procedure adopted to capture the complex features of cable dynamics, albeit limited to stable oscillation branches. The analyses first explore a moderately taut cable and are then extended to the behavior of a slacker cable, in order to validate the simplifying kinematic assumptions introduced in the analyticalmodels by comparing the obtained results with those furnished by the richer finiteelementmodels.