Vibration suppression of a cable under harmonic excitation by a nonlinear energy sink

Abstract

The application research of nonlinear energy sink (NES) on vibration suppression in many fields is a hot topic. In this paper, the vibration suppression mechanism of a nonlinear energy sink on a cable under a harmonic load is studied novely. First, the dynamic model of the cable-NES system under harmonic excitation is established. The partial differential Equations (PDEs) of motion governing the in-plane vibration of the cable-NES system are derived by Hamilton’s principle. Then, by considering the coupling effect among the first three in-plane modes of the cable, the ordinary differential equations (ODEs) of the coupled system are obtained applying Galerkin integral. The incremental harmonic balance (IHB) method is used to solve the nonlinear ordinary differential equations. Meanwhile, the stability of the solution is determined using Floquet theory. Finally, the primary resonances of the first and third in-plane modes of the cable are explored respectively, and the vibration mitigation performance of the NES and the wavelet transform of the cable displacement response are analyzed. The research results show that the NES has a significant effect on the dynamic behavior and vibration mitigation of the cable, especially, when the NES parameters are the same, the vibration mitigation effect of the NES on the primary resonance of the 3rd mode of the cable is better than that of the 1st mode.