# Impact Fatigue of Viscoelastic Materials Subjected to Pounding
## 1 Introduction  
The tuned mass damper (TMD) is a classical vibration control technique. Its concept dates back to 1909, when [PERSON] proposed a vibration control device called a dynamic vibration absorber [1]. Due to its simplicity and effectiveness, the TMD technology has been widely used in vibration mitigation for many types of structures. However, the vibration reduction efficiency will deteriorate if its frequency shifts away from the target value. To compensate for this de-tuning effect, many active and semi-active solutions were proposed. Semi-active vibration absorbers, which enabled real-time tuning of the frequency and the damping, were proposed by [PERSON] and his collaborators [2; 3; 4]. [PERSON] et al. [5] replaced the linear spring in a traditional TMD with a spring made of shape memory alloy (SMA). The simulation results demonstrated significant improvements of the SMA-TMD in the control efficiency at a much reduced mass ratio compared with a linear TMD. Although TMDs incorporated with smart materials can achieve improved control effectiveness and robustness, this combined system requires reliable instant feedback, which will increase the cost of the vibration control system. The pounding tuned mass damper (PTMD) employs the energy dissipation scheme through impacts, which dramatically improves its vibration reduction capacity. The schematics of the TMD and the PTMD are compared in Figure 1. As shown in the figure,the essential difference between the PTMD and the regular TMD is a delimiter, which is covered by viscoelastic materials. When there is only a slight vibration of the primary structure, the tuned mass will vibrate freely between the two delimiters, and the PTMD will act as a traditional TMD. When the motion of the primary structure exceeds a certain level, the tuned mass will pound on the delimiter as an impact damper. Energy can be dissipated through the collision [6,7]. In other words, the viscoelastic delimiter introduced the energy dissipation mechanism for impacts to the PTMD. Therefore, the PTMD is more effective than the regular TMD in vibration reduction [8,9]. Another benefit of the viscoelastic delimiter is that it can enhance the robustness of the PTMD. According to the literature [9,10], in the off-tuned case, the relative motion between the tuned mass and the delimiter is larger than that of the optimal-tuned case. Therefore, in the off-tuned case, the added mass will impact the viscoelastic material more severely, generating a larger pounding force, resulting in larger momentum exchange and energy dissipation. This can compensate for the vibration effectiveness deteriorated by the detuning effect. Even though the impacts of the viscoelastic material have improved the vibration effectiveness and robustness of the PTMD, the repeated impacts may damage the material and deteriorate its long term performance [11, 12, 13]. Moreover, the PTMD is often applied to structures located in extreme environments (e.g., subsea jumpers and offshore platforms). Therefore, it is expected to function well for two or more decades, since it is very difficult to repair or replace the PTMD. During long-term service, a PTMD may undergo many cycles of impacts. The repeated impacts may damage the viscoelastic material and degrade its vibration control effectiveness. Thus, it is necessary to conduct an impact-fatigue study of the viscoelastic material. Over the past decades, the viscoelastic material has been intensively studied [14, 15, 16]. [PERSON] et al. proposed a new experimental device to investigate the crack propagation in viscoelastic materials [17]. [PERSON] et al. investigated the contact mechanics between rough surfaces of the viscoelastic materials [18]. [PERSON] and [PERSON] proposed a methodology to numerically investigate the steady-state sliding or rolling contact of viscoelastic materials [19]. Several studies have focused on the impact fatigue property of the viscoelastic material.