Parametric Vibration Suppression Study Of An Inclined Cable Based On Nonlinear Energy Sink

As the main force member of cable-stayed bridges,cable-stayed bridges are characterized by high flexibility and low damping,which are highly susceptible to large vibrations caused by external disturbances,which causing structural damage.In many researches,nonlinear energy sink(NES)has been proved to have broadband damping effect,which has obvious advantages over viscous dampers and tuned mass damper(TMD)in the field of multimode damping.There are few applications about NES on inclined cable,and mainly focused on the study of the suppression of forced vibration.Therefore,it is necessary to explore the possibility of parametric vibration suppression of NES on inclined cable.This paper analyzes the parametric vibration characteristics of in-plane and out-plane cable without and with NES,and the vibration characteristics of cable subjected to multi-frequency excitation.The main contents of this paper are:(1)The cable-NES equations of motion were established and the effects of the cable/NES parameters on the multimode state of the inclined cable were analyzed.Firstly,the in-plane nonlinear equations of motion of an inclined cable under axial harmonic excitation(parametric excitation)are derived on the basis of Hamilton’s principle.The ordinary differential equations(ODEs)of the system are derived by the Galerkin method and solved by the 4th order RungeKutta method.Then,the effects of the NES on the fundamental frequency of the cable,the effects of Galerkin truncation on the results and the effect of inclined cable/NES parameters on parametric vibrations.(2)By optimizing the parameters of NES,the effect of optimized NES on the multimodal vibration of the inclined cable is analyzed.The corresponding results are also compared with the non-control system and the inclined cable with TMD,and the results demonstrate the superior vibration damping performance of NES;Compared with the optimized TMD,the vibration suppression effect of the optimized NES on the cable is better in terms of multimodal,and the amplitude robustness of NES is also significantly better than that of TMD;Through time-frequency analysis,revealing that the energy transfer between the stay cable and the absorber is mainly dominated by 1:1resonance capture,further demonstrating that NES has a stronger energy dissipation ability than TMD.(3)The vibration characteristics of the inclined cable subjected to axial multi-frequency excitation and the suppression effect after attaching dampers were studied.The in-plane nonlinear equations of motion of an inclined cable under multi-frequency axial harmonic excitation are derived on the basis of Hamilton’s principle.A new optimization of NES is carried out,and the results show that NES also has significant suppression effect on inclined cable vibration under multi-frequency excitation.(4)The vibration characteristics of in-plane and out-plane inclined cable when NES/ring NES is installed(not installed)are investigated.The in-plane and out-plane nonlinear equations of motion of the inclined cable under parametric excitation are derived by Hamilton’s principle,the incentive conditions of out-plane vibration are analyzed by numerical methods.Since the in-plane NES cannot control the out-of-plane vibration of the cable,the ring NES is used to control the spatial vibration of the cable,and the results show the superiority of the ring NES in suppressing the in-plane and out-of-plane vibration of the cable.