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Sagged cable vibrations caused by support motion and possible external loading are investigated via the four-degree-of-freedom model proposed in Benedettini et al. (J Sound Vib 182(5):775–798, 1995). The model has a considerable potential in terms of forcing cases to be possibly addressed, with the physical motion of the supports naturally giving rise to a variety of external and parametric excitation terms. Dynamics of the system is studied close to the multiple internal resonance at cable crossover, which involves two in-plane and two out-of plane vibration modes. Solutions are found by the multiple time scale method. In the numerical investigation, attention is focused on the effects of planar support motion (symmetric and/or antisymmetric) at primary resonance, with the addition of planar symmetric external excitation entailing a nice cancellation phenomenon in the system response. Results are discussed also in the background of theoretical and experimental outcomes available in the literature. Comparison with a computer simulation of original equations of motion shows that analytical results are correct for moderately large oscillations, whereas a different scenario of multimodal responses may occur at higher excitation amplitudes. The nonlinear modal coupling is investigated through bifurcation scenarios and other dynamics tools, showing also transitions to complex response regimes.

Revisited modelling and multimodal nonlinear oscillations of a sagged cable under support motion