A lever-type time-delayed feedback nonlinear energy sink for vibration suppression of stay cables under multiple excitations

To reduce stay-cable vibration caused by a uniform transverse load, support-end motion and their combined action, this study proposes a lever-type time-delayed nonlinear energy sink (TDNES) that integrates a lever mechanism, an NES and delayed velocity feedback. The lever simultaneously modifies the absorber-base motion and the equivalent control force applied to the cable, while the feedback gain and delay provide adjustable control parameters. A coupled dynamic model is established, and Galerkin truncation is used to derive reduced equations for the uniform-load, end-load and dual-load cases. The delayed system is linearized, and its characteristic equation is used to determine the Hopf stability boundary. The harmonic balance method and direct time integration are employed to calculate the frequency and steady-state responses. Parameter-plane, reduction-efficiency and energy analyses are conducted to examine the effects of the lever coefficient, feedback gain and delay and to compare parameter selection under the three excitation routes. Initial-condition scans further assess the low-response initial perturbation tolerance of the proposed TDNES. The results also show that the cable response under dual excitation varies with the relative input phase.