# Theoretical Design of a Novel Vibration Energy Absorbing Mechanism for Cables
## 5 Conclusions  
This study has proposed a novel damper design for cable stayed bridges that can respond to different vibration amplitudes that are caused by different environmental phenomena. It is a hybrid system that combines non-linear stiffness vibration isolation modules and hydraulic viscous damper modules. The VEAM proposes a novel way to utilize the minimum working force of the hydraulic cylinders, which is an unavoidable characteristic that can be leveraged to combine the two modules together to form a hybrid system that is able to automatically switch the module in operation based on the input vibration amplitude. This paper presented the mechanism design and theoretical model of the VEAM. Multiple numerical case studies were performed in order to observe the influence of various factors on the vibration isolation and damping performance of the entire system. The key findings of this research are as follows:  
1. VEAM mechanism, through the combined action of hydraulic cylinder bearings, ball joints, and springs, can maintain the alignment of PMs at all times, and will not cause vibration force transmission instability due to tangential shift. 2. The external hydraulic circuit connecting the opposing damper pairs can maintain motion synchrony to avoid the jumping phenomenon, thus preventing system damage. This method can also easily make adjustments of the orifice regulating valves to achieve a variable damping ratio. Through the Simscape simulation of the entire VEAM subsystem, the design theory of the automatic switching mechanism was tested. The results showed that, when the whole system is working, due to the non-linear stiffness, chaotic output is observed in the high frequency bandwidth. The implications of this behavior need to be verified in future experiments with the real system. 3. We can use strong repulsive magnets to ensure the maintenance of a safe distance between the PM pairs. The use of magnets with stronger linear stiffness will reduce the transmissibility of the nonlinear stiffness module in the low frequency region, but it will increase the transmissibility in the high frequency region. However, magnets with stronger nonlinear stiffness can effectively  
Figure 14: Transmissibility of the hydraulic viscous damper module of VEAM with varying k\({}_{\text{s}}\). reduce the peak of transmissibility. In the design stage, according to the needs of the actual situation, the selection of PMs of appropriate magnetic strength can ensure a high performing safe design, while also ensuring a safe distance. However, during prototype manufacturing, we found that, due to space constraints, it is difficult to only use the magnetic force between the two PMs to actuate the hydraulic cylinder. Accordingly, it may be necessary to use crash pads between the magnets to achieve rigid transmission of force. The magnetic resistance of the surrounding environment and design involving stronger PMs will be considered in future studies. 4. In the low-frequency region, the greater the spring linear stiffness, the lower will be the transmissibility of both the non-linear stiffness vibration isolation module and the hydraulic damper module, i.e., there will be better vibration isolation performance. However, in the high-frequency region, the stiffness of the spring will affect the vibration isolation performance when only the nonlinear stiffness vibration isolator is in operation. Therefore, the common effect of both modules must be considered when selecting the spring stiffness. 5. The structural damping of the spring will undoubtedly provide good isolation performance when the non-linear stiffness module is working. However, the viscous damping of the hydraulic cylinder is different. Excessive viscous damping will affect the vibration isolation performance of the VEAM and increase the possibility of structural damage.