Study on Vibration Suppression of an Inclined Cable with a Nonlinear Energy Sink Under the Axial Excitation

The nonlinear energy sink (NES) has been verified to have a broadband damping effect in many studies. In this paper, the in-plane vibration of an inclined cable attached with an NES is considered. First, nonlinear motion equation of the cable under an axial harmonic excitation (parametric excitation) is derived on the basis of Hamilton’s principle. The ordinary differential equations (ODEs) of the system are derived by Galerkin method and solved by fourth-order Runge–Kutta method. In this way, the suppression effects of the NES on primary resonance, 1/2-order sub-harmonic resonance and second-order super-harmonic resonance of the cable are investigated when the cable is subjected to a parametric excitation. Then, by optimizing the parameters of the NES individually, the corresponding results are compared with those of the uncontrolled system and the cable with a tuned mass damper (TMD). Meanwhile, the robustness of the NES against changes in the amplitude of axial excitation is also studied. The results demonstrate the high-efficiency vibration suppression of the NES and the vibration suppression effect of the optimized NES on the cable shows better performance in terms of multi-modality compared with the optimized TMD.