## 4 Experimental Setup  
In the previous study by the authors [45], the TMD and VE-PTMDs were tested for the vibration control of the same piping system. For comparison, in this experiment, the mass and the swing arms of PTMD are identical to the previous study [45], except that the VE material is replaced by an SMA sponge. Figure 4 shows these two different energy dissipating materials. The shape memory alloy wire is manipulated into a cuboid shaped sponge and used as an energy dissipating layer. Its dimensions are 48 mm, 20 mm, and 10 mm, respectively. The mass used in the TMD and PTMDs is a 0.403 kg cylindrical steel block, and the corresponding mass ratio is 4.33%. The mass ratio is a key parameter of TMD, and is often designed to be in the range of 1-5%. To determine an appropriate mass ratio for TMD, the feasibility of the actual engineering application and the required vibration control effect should be taken into consideration. To achieve the bounding between the mass of the PTMD system and the pipe, a fixture tightly sleeved around the pipe is precisely machined, and the PTMD is mounted on the fixture, which is installed at the middle of the pipe, as shown in Figure 5a. Spring steel type and pendulum type are both tested, as shown in Figure 5b,c. In single-sided PTMD, the collision occurs at the equilibrium position and the frequency is doubled after the collision [37]. Thus, the frequency of the swing arm-mass system of the PTMD should be half of the piping system's frequency (2.55 Hz), which is 1.28 Hz. When  
Figure 3: Piping system model and its finite element model: (**a**) Suspended piping system; (**b**) first vibration mode shape; (**c**) second vibration mode shape. pounding occurs, the swing arm-mass system will vibrate at 2.55 Hz and will thus be tuned to the frequency of the piping system. The natural frequency of the swing arm-mass system is tuned to 1.28 Hz through trial and error adjustments to the length of the swing arm. Results show that the target frequency is achieved when the length of the spring steel and the length of the nylon rope are 170 mm and 128 mm, respectively. The detailed parameters of the PTMDs are listed in Table 1.  
During the experiment, a laser displacement sensor (MX1A-A, IDEC Sensors, Tokyo, Japan) with a range of \(\pm\)40 mm is installed at a separate table not coupled to the piping system to record the \begin{table}
\begin{tabular}{c c c c} \hline \hline  & Frequency of the spring steel–mass system & 1.28 Hz \\ PTMD (Spring steel type) & Component & Description & Value \\  & Spring steel & Material & Spring steel \\  & & Dimensions (mm) & 170 \(\times\) 6.5 \(\times\) 0.4 \\ \hline  & Frequency of the pendulum–mass system & 1.28 Hz \\ PTMD (Pendulum type) & Component & Description & Value \\  & Nylon rope & Material & Nylon \\  & & Length (mm) & 128 \\ \hline  & & Material & Steel \\  & & Weight (kg) & 0.403 \\  & Energy dissipating material & SMA & 48 \(\times\) 20 \(\times\) 10 (mm) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of PTMDs (bounding tuned mass dampers). Figure 4: Energy dissipating materials used in PTMD: (**a**) Viscoelastic (VE) material; (**b**) shape memory alloy (SMA) material in the form of sponge. Figure 5: (**a**) Control device installed at the piping system; (**b**) spring steel type SMA–PTMD; (**c**) pendulum type SMA–PTMD. displacement response of the piping system. The sampling frequency of the laser sensor is set to 200 Hz. In the forced vibration experiment, a high-power DC motor (DC-158A, AVIC, Beijing, China) with a rotating arm is used as the excitation source. A bungee cable is used to connect the pipe and the rotating arm. In order to ensure excitation in the horizontal direction only, a pulley is installed to turn the bungee cable by 90 degrees. A wide range of excitation frequencies can be achieved by changing the motor's angular speed. Figure 6a,b show the experimental setup of the forced excitation system and the data acquisition system, respectively.