# Theoretical Design of a Novel Vibration Energy Absorbing Mechanism for Cables
## 1 Introduction
A later study by [PERSON] [12] optimized the modal damping values of the lowest five modes of vibration. [PERSON] [13] experimentally studied the total pressures of viscous dampers as a function of time after excitation by a mass impact. This work showed that viscous dampers show better damping performance against large dynamic vibrations, but they are not sensitive enough to small amplitude vibrations. [PERSON] and [PERSON] et al. [14] confirmed these results through numerical simulations. Viscous dampers are susceptible to reduction in load capacity due to load misalignment. In order to explore this further, [PERSON] et al. [15] performed a buckling analysis on hydraulic cylinders, while [PERSON] et al. [16] proposed an oil damper with variable stiffness (ODVS). In their designs, the orifice size of the variable overflow valve can be changed to achieve a variable damping ratio according to different hydraulic loads. Viscous dampers are also susceptible to leakage due to thermal deformation and aging of the seal ring due to frequent reciprocating movements that are mostly associated with low amplitude vibrations. To overcome the problem of leakage, [PERSON] et al. [17] proposed the design of a third-generation hydraulic cylinder with a special lip shape at the piston periphery that varies the clearance between the piston and the cylinder according to the change in hydraulic pressure. A common method for evaluating the isolation performance of dampers is to calculate their transmissibility. [PERSON] et al. [18] established a mathematical model for calculating the damped power transmissibility of a vibration isolation system. [PERSON] et al. [19] analyzed a single degree of freedom (SDOF) displacement vibration isolation system (DVIS) and a forced vibration isolation system (FVIS) with a nonlinear viscous damper; simulations of system transmissibility were obtained. It has been noted that the non-linear viscous damper can significantly improve the damping performance across a wide range of frequencies. However, the problem of wear has not yet been solved due to frequent reciprocating movements. Magneto-rheological (MR) fluid is a force transmission fluid that can be precisely controlled while using a magnetic field. Therefore, it is widely used in controllable damping systems. [PERSON] et al. [20] proposed a tuned mass damper magneto-rheological (TMD-MR) design, which showed good damping performance in all modes during experimental verification. [PERSON] et al. [21] incorporated an elastic metal bellows in the spring-MR damper, which significantly improved the vibration absorption over the entire frequency range. MR dampers require the employment of an active feedback control system in order to operate properly. The controller senses the input vibration parameters and accordingly modulates the electrical signal that influences the MR fluid characteristics. This requires the use of complex electronic equipment and a constant supply of electrical power. These requirements increase the system complexity and costs related to installation, operation, and maintenance. They may also increase the chances of system failure due to a variety of causes including electrical failure. Friction dampers use friction to dissipate vibration energy. Using a mathematical model, [PERSON] et al. [22] analyzed the damping performance of two friction dampers on a stay cable and proposed the best design and installation method for friction dampers. However, friction dampers have some limitations, such as their inability to dampen low amplitude vibrations and the use of consumable friction materials that need to be replaced regularly, which serves to increase the system's operating and maintenance costs. With the development of industrial technology, the requirements for high vibration isolation performance are also increasing [23; 24; 25]. It is apparent from the preceding discussion that there is a need for the development of a vibration damping system.