# Theoretical Design of a Novel Vibration Energy Absorbing Mechanism for Cables
## 1 Introduction
Moreover, a vibration damping system is needed that can handle both high and low amplitude vibrations without requiring complex hardware, continuous power supply, and frequent maintenance. One approach that offers promise is non-linear damping technology that has attracted a great amount of attention from researchers in recent years [26; 27; 28]. The existing literature shows that the natural frequency of an isolation system can be decreased by introducing a non-linear stiffness [29; 30; 31]. This means that the introduction of non-linear stiffness is an effective method for broadening the isolation bandwidth of a damping system. [PERSON] et al. [32] proposed a quasi-zero-stiffness (QZS) vibration isolation system with non-linear stiffness consisting of a positive stiffness spring and two negative stiffness springs. The high-static-low-dynamic-stiffness (HSLDS) vibration isolation characteristic of their system was confirmed by calculating its transmissibility. Numerous innovative QZS designs have been proposed and applied in various fields due to the desirable performance of QZS vibration isolation [33; 34; 35; 36]. Permanent magnets (PM), when placed in an opposing repulsive manner, can generate a non-linear stiffness. This characteristic of PMs has resulted in their wide usage in the design of QZS vibration isolators in recent years. A large number of studies have shown that vibration isolators that are composed of PMs have better vibration isolation performance than linear vibration isolators [37; 38; 39]. [PERSON] et al. [40; 41] proposed the design of a vari-stiffness nonlinear isolator (VSNI) and a bi-state nonlinear vibration isolator (BS-NVI). In their designs, the nonlinear stiffness is controlled through the manipulation of the magnetic fields. This means that the isolation performance of the system is controlled by changing the distance and included angle between the PMs. Thus, the transmissibility models established were verified through experiments. [PERSON] et al., through field observations and wind tunnel tests, conducted in-depth evaluation and analysis of the influence of rain and wind induced vibrations on a cable bridge [42; 43; 44; 45; 46]. [PERSON] et al. [47] and [PERSON] et al. [48] used wind tunnel tests and digital imaging techniques to study the dynamic characteristics of cable-stayed bridges. These studies confirmed that the amplitude of rain, wind, and traffic induced vibrations at the installation position of the damping system is usually very small. Large amplitude vibrations only occur under special circumstances and are, thus, less frequent. Hence, cable-stayed bridges can greatly benefit from the design of a vibration damping system that does not require external power supply and can handle small amplitude vibrations with minimal wear while also being able to cater to larger amplitude vibrations. Consequently, this paper proposes a hybrid damping system design that combines a PM based non-linear stiffness vibration isolator and a hydraulic viscous damper. In the proposed design, when the amplitude of vibration in the cable is less than a preset threshold value, the non-linear stiffness isolator damps the vibration transmitted to the deck and the viscous damper is not actuated. This will help to increase the overall system life, as it protects the viscous damper from thermal deformation and excessive wear of the seal ring due to its high frequency reciprocating motion that is associated with low amplitude vibrations. When the vibration amplitude becomes greater than the threshold value, the PMs travel until there is a minimum relative distance between them and then the viscous dampers are actuated to further dissipate the vibration energy. Thus, the presented system, which we have called a vibration energy absorbing mechanism (VEAM), is developed to meet three objectives: (1) reduce the wear due to inefficient working conditions of the viscous dampers used in the system.