# Theoretical Design of a Novel Vibration Energy Absorbing Mechanism for Cables
## Mechanism of the VEAM  
Figure 1 presents the 3D model of VEAM. The cable passing through the center is supported on six sides by the developed multi-physic dampers, which are in turn connected to the bridge deck. Traditional viscous damper systems usually adopt a three damper arrangement [16]. In contrast, the VEAM adopts an arrangement of three opposing pairs of dampers resulting in a six-directional cable support system. This has been done to better counter the randomness of stay cable vibration. Figure 2a shows the internal configuration of the VEAM. Because the system is symmetrically constructed using six identical modules, we will only use one of those modules to illustrate the design principles. The complete system is fitted to the cable via a central hex piece that is divided into two parts which are assembled using long through bolts. The six damper assemblies are attached to this hex piece, one on each side. The damper assemblies consist mainly of a ball-joint connected to the hex piece, a PM based non-linear stiffness isolator, a viscous damper, and a rotary mount to allow the rotation of the damper assembly about an axis perpendicular to the damper's axis of travel. The vibration of the stay cable moves the magnets, which dampen it due to non-linear stiffness. The vibration force is transmitted to the viscous damper through repulsion between the PMs placed with like poles facing each other. If the force magnitude is greater than the minimum force required to actuate the viscous damper, then the damper starts moving and dissipates the vibration energy through viscous drag. Figure 1: Three-dimensional (3D) model of the vibration energy absorbing mechanism (VEAM). Figure 2: Internal configuration of 1/6 piece of VEAM. The thrust force applied to the piston should be aligned with the cylinder axis and should have no radial component in order to keep the viscous damper moving smoothly with minimal amount of wear. In the proposed system, the source of this thrust force is the PM based isolator attached to the end of the hydraulic piston. Thus, the necessary conditions for the smooth operation of the hydraulic cylinder can only be guaranteed if the force applied to the PM assembly has no radial component. However, in reality, the direction of vibration is not always aligned with the center axis of the damper assembly. Therefore, a compliant attachment between the damper assembly and the cable is required to ensure that only axial forces are transmitted to the damper assembly. In the proposed design, a ball joint is added between the hex and the PM side of the damper assembly in order to allow for the cable fixing hex to change angles with respect to the damper assembly. This joint, as shown in Figure 2b, consists of a ball at the center with four retaining springs around it to prevent excessive movement and damage to the joint. At the other end of the damper assembly, the cylinder of the viscous damper is connected to the system frame using a ball bearing based rotary joint shown in Figure 2c that allows for rotation of the damper assembly around an axis perpendicular to the cylinder axis. The addition of these two joints ensures that the two PMs are always coaxial and only axial loads are applied to the viscous damper. Furthermore, to provide structural damping while keeping the PMs in parallel [49; 50], the design also includes a spring connecting the hex side PM and the viscous damper cylinder. It can be seen from Figure 3a that when the hex moves due to cable movement, the six damper assemblies rotate to different angles to compensate for this displacement. However, the PMs and viscous damper always remain aligned with each other. The rotation angle of each damper assembly can be derived while using the geometric relationship between the key elements. Figure 3b shows the simplified schematic diagram of this scenario.