## 2 Pounding Tuned Mass Damper (PTMD) and Energy Dissipating Material  
The earliest PTMD was proposed by [PERSON] et al. [36], on the basis of the TMD device, which consisted of a secondary mass and a swing arm and two delimiters covered with viscoelastic materials. Figure 2a shows the schematic of the double-sided PTMD. The double-sided PTMD has two vibration control mechanisms: when the excitation is small, the tuned mass will vibrate within the two delimiters as a traditional TMD; when the excitation exceeds a certain level, the tuned mass will collide with the viscoelastic material on the surface of the delimiter, dissipating the kinetic energy of the system. Thesetwo vibration control mechanisms can enhance the vibration control effectiveness and robustness of the damper [38; 42; 43].  
In 2017, [PERSON] et al. [37] innovatively proposed the single-sided PTMD, which contained only one delimiter, as shown in Figure 2b. When the secondary mass was in the initial equilibrium state, it was in contact with the delimiter. Thus, the mass could only move in one direction relative to the delimiter. Due to the collision of the mass with the delimiter, the corresponding frequency of the system would become twice the original frequency, as shown in Equation (1),  
\[f_{PTMD}=2f_{TMD}=\frac{\sqrt{k/m}}{\pi} \tag{1}\]  
where \(f_{PTMD}\) and \(f_{TMD}\) are the frequencies of the single-sided PTMD and conventional TMD, respectively, and \(k\) and \(m\) are the stiffness and mass of the damper. A notable advantage of the single-sided PTMD is that the gap between the mass and the delimiter is no longer a design parameter and the collision occurs at a position that could dissipate the maximum kinetic energy. The effectiveness of single-sided PTMD has been demonstrated by theoretical analysis and experimental studies [37; 62].  
Due to the simultaneous viscous and elastic characteristics, VE materials are popular in vibration mitigation and energy dissipation [63; 64; 65]. Both in the PTMD studies of [PERSON] [36] and [PERSON] [37], VE materials were used as energy dissipating material. The performance in previous experiments proves that VE materials are suitable as an energy dissipating material for PTMD [45; 66; 67].  
Shape memory alloys (SMAs) were discovered relatively recently [68; 69; 70], and uniquely possess both a shape memory effect (SME) and superelasticity, both of which give SMAs a highly hysteretic stress-strain relationship [71; 72]. The significant hysteresis in the stress-strain relationship of SMAs makes them an ideal candidate for implementation in passive vibration control [73; 74; 75; 76]. Applications include control of stay cables [77; 78], isolation bearings [79; 80; 81; 82; 83; 84], and frame braces [85; 86]. Due to its high damping capacity, SMA is an ideal energy dissipating material in passive control. In theory, it is feasible to use SMA as bounding energy dissipating material for PTMD.  
In this paper, the SMA is chosen as energy dissipating material for single-sided PTMD to improve its vibration control performance. To better understand the effectiveness of SMAs in energy dissipation, the vibration control effects of single-sided SMA-PTMDs are studied, and the results are compared with TMD and VE-PTMDs tested in a previous study conducted by the authors [45]. The PTMDs are employed to suppress the same suspended piping system under the same excitation conditions. In order to improve the readability and continuity of the article, the piping system and the experimental setup are presented again in this paper.