The negative stiffness electromagnetic tuned inerter damper for damping enhancement of stay cables

Long stay cables may be subject to vortex-and rain-wind-induced vibrations. To suppress the two types of vibrations simultaneously, integrating the advantages of negative stiffness and inerter-based damper, a new negative stiffness electromagnetic tuned inerter damper (NSETID) is proposed in this study. The equivalent mechanical model of the NSETID is presented according to its working principle. On this basis, non-dimensional analytical equations of the cable with NSETID are developed. Subsequently, the optimum parameters of the NSETID are identified by optimizing the damping ratio of the tuned cable mode. The effects of the cable sag and flexural stiffness on the control performance and optimum parameters of the NSETID are also taken into consideration. In addition, the benefits and damping enhancement of the NSETID for mitigating single-mode and multi-mode cable vibrations are illustrated by comparing with tuned inerter damper (TID), negative stiffness damper (NSD), and negative stiffness inerter damper (NSID). Finally, the damping enhancement mechanism of the NSETID for cable multi-mode is explored through its stiffness and damping properties. The results highlight the superior damping enhancement capabilities of the NSETID in mitigating single-mode and multi-mode cable vibrations. The better control performance of the NSETID can be attributed not only to its negative stiffness behavior but also to the adaptability of its equivalent damping and negative stiffness coefficients to the cable mode order.