A unified analysis of negative stiffness dampers and inerter-based absorbers for multimode cable vibration control

This paper performs a unified analysis of multimode damping effects of negative stiffness and inerter mechanisms when combined with a viscous damper for cable vibration control. They are referred to as negative stiffness dampers (NSDs) and inerter-based vibration absorbers (IVAs), respectively. Multimode control of cable vibrations is of practical importance because wind-rain induced cable vibrations typically have frequencies in the range of 1 Hz to 3 Hz which covers a number of modes of long cables. The NSD and IVAs have been extensively studied for enhancing damping of a particular cable mode while multimode cable vibration control using such devices is still absent in the literature. Therefore, this study begins with a discussion of an ideal NSD for multimode cable vibration control. Dynamic properties of a typical NSD and four typical IVAs with respect to vibration frequency are then examined with reference to the ideal NSD. Subsequently, multimode damping effects of all the devices when attached to a cable respectively are investigated in details using an analytical method. Their performances and tuning conditions are discussed in depth. Analytical results show that theoretically an NSD improves damping for each cable mode equally and hence it can achieve multimode damping enhancement per design requirement. To balance damping effects for multiple cable modes, an upper bound of damping enhancement exists when using an IVA. Particularly, an IVA with an inerter and a viscous damper with intrinsic stiffness in series (so-called tuned inerter damper) has the best performance among the investigated IVAs. The characteristic frequency of this type of IVA needs to be close to the lowest frequency of target cable modes and a relatively large inertance is needed. The analytical results are then exemplified by a case study for damper design of a real cable of 454.1 m long. The analytical findings have further been verified by numerical analyses on multimode responses of the cable with the investigated devices respectively.