# Theoretical Design of a Novel Vibration Energy Absorbing Mechanism for Cables
## 1 Introduction  
Cables are widely used in construction, cable cars, traction, and other fields due to their extremely high tensile strength, long-distance capabilities, and low cost. This article will conduct research that is based on the cable-stayed bridge, which is the most representative and technically demanding application of cables, and illustrate a novel vibration energy absorbing mechanism that effectively responds to common vibration that is caused by environmental impacts with the automatic switching modes of the non-stiffness vibration isolators with the hydraulic viscous dampers. In recent years, the cable-stayed bridge design has gained popularity as the design of choice for the construction of long-span bridges. This can be attributed to its simple and beautiful design, and its ability to span longer distances at relatively low construction costs [1]. From 2016 to 2019, a total of 20 cable stayed bridges with spans over 500 m were built around the world. Currently, the longest span cable-stayed bridge in the world is the Russky Bridge built over the Eastern Bosphorous in Russia, which has a span of 1104 m. Although the span of this bridge is quite short when compared to suspension bridges, the trend in construction seems to be moving towards an increasing number andspans of cable-stayed bridges. The cable-stayed bridge is mainly composed of bridge pylons, cables, and decks. The cables connect the decks to the pylons directly, so that the pylons carry the entire load. Like all structures, cable-stayed bridges are also subjected to vibration resulting from such exogenous factors, such as wind, rain, temperature change, and the movement of pedestrians and vehicles. These vibrations are transmitted to pylons and decks by the cables [2]. If the excitation frequency is close to a natural frequency of the bridge system, resonance will occur. Resonance is regarded as one of the main causes of bridge damage leading to fatigue and shortened life [3; 4; 5; 6; 7]. Therefore, a great amount of effort has been undertaken to develop methods for avoiding/mitigating the effects of vibration on cable-stayed bridge structures. Increasing the damping between the cable and the bridge deck is one of the key methods used to improve the robustness of cable-stayed bridges by preventing the occurrence of resonance. Various types of vibration control systems are used in a wide variety of fields, such as automotive, aerospace, and structural engineering. According to their working mechanisms, vibration control systems for cable-stayed bridges can be divided into: (1) high-damping rubber (HDR) dampers, (2) viscous dampers, (3) magneto-rheological (MR) dampers, and (4) friction dampers. Rubber dampers are the oldest type of damping systems used in cable-stayed bridges. These dampers dissipate vibration energy via hysteretic losses. [PERSON] et al. [8] proposed an external high-damping rubber (HDR) damper for cable-stayed bridges and experimentally evaluated its performance against dynamic vibration. [PERSON] et al. [9; 10] formulated a complex eigen value problem in order to address the different damping effects of a single HDR damper and two attached HDR dampers under different installation conditions and material loss factors. Their work provides a strong theoretical basis for the design of HDR dampers. The damping performance of the HDR damper is highly dependent on the damping characteristics of its material, e.g., rubber. However, rubber materials have a limited energy consumption performance and they are easily affected by environmental factors, such as temperature. The viscous damper category is mainly comprised of hydraulic cylinder type dampers that dissipate the vibration energy through the friction between the hydraulic fluid and their orifice(s). The maximum damping ratio of a viscous damper has a relationship with the relative distance between the support and the damper. This was proposed by [PERSON] et al. [11], who also derived an optimal damping constant for viscous dampers with low modes of vibration.