# Experimental Study on Vibration Control of
## 4 Experimental Setup  
In the experiment, a TMD and a PTMD were employed separately to control the vibration of the piping system. In order to compare the effectiveness of two dampers, the mass ratio, which is an important factor in damper design, remained the same in TMD and PTMD. It is well-known that a larger mass ratio will lead to a better control effect; however, having a large mass is unfavorable for engineering applications. Thus, it is essential to select an appropriate mass ratio, whose used range in practice is from 1% to 5%. In the experiment, the same mass block (0.403 kg) was used for TMD and PTMDs, and the corresponding mass ratio is 4.33%. In this experiment, the control fixture was placed in the middle of the pipe (Figure 5a) due to two main factors. First, by placing the control fixture in the middle of the pipe, the torsion caused by eccentricity will be reduced. The reduced torsion will improve the control efficiency of the PTMDs. Secondly, the PTMDs were leveled with the pipe, thus freeing up space above and below the pipe. The extra space may help avoid making modifications to existing suspension systems and thus facilitate the retrofitting of existing piping systems. The TMD, which was tested separately, is composed of mass and spring steel, as shown in Figure 5b. The PTMD consists of mass, a swing arm, and energy dissipation material. Two types of PTMDs were designed: one used a spring steel and the other used a simple pendulum, as shown in Figure 5c,d. Due to its stable mechanical properties and outstanding fatigue resistance, the spring steel was chosen as the swing arm of the TMD and also for one of the PTMDs. Additionally, using a simple pendulum as the swing arm of the PTMD has the advantages of simple structure and easy adjustment of the frequency. In order to understand the dynamic characteristics of the TMD and the PTMD, free vibration tests were conducted on the spring steel-mass systems. The result shows that the frequency of TMD and PTMD was 2.55 Hz and 1.28 Hz, and the corresponding damping ratios (only of the spring steel and mass) were 0.06% and 0.04%, respectively. From previous studies, when the single-sided PTMD is working, the mass will pound the energy-dissipating material and then rebound, and the PTMD's working frequency will be twice the free vibration frequency. In other words, since the structure's free vibration frequency is 2.55 Hz, the PTMD frequency should be tuned to 1.28 Hz. Thus, the free vibration frequency of the single-sided PTMD is designed to be close to half the frequency of the piping system. In the experiment, viscoelastic material (3M Inc., Maplewood, MN, USA, as shown in Figure 5c) was used to dissipate energy, and its thickness was 6 mm. The detailed parameters of the TMD and PTMDs are shown in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Component** & **Description** & **Value** \\ \hline \multirow{4}{*}{1} & & \multicolumn{2}{c}{Material} & Steel \\  & & Outer diameter (mm) & 115 \\  & & Wall thickness (mm) & 2.1 \\  & & Length (mm) & 1133 \\  & & Weight (kg) & 6.68 \\ \hline
2 & Fixtures & Weight (kg) & 2.62 \\ \hline \multirow{3}{*}{3} & \multirow{3}{*}{Bar} & Material & Steel \\  & & Diameter of thread (mm) & 6.35 \\  & & Length (mm) & 195 \\ \hline \multirow{4}{*}{4} & \multirow{3}{*}{Beam} & Material & Aluminum \\  & & Length (mm) & 1220 \\ \cline{1-1}  & & Width (mm) & 80 \\ \cline{1-1}  & & Height (mm) & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimension of the piping system. The experimental setup is shown in Figure 6a,b. A laser displacement detection sensor (MX1A-A, IDEC Sensors, Tokyo, Japan) with a maximum range of \(\pm 40\) mm was used to measure the lateral horizontal displacement of the suspended piping system. The pipe displacement was generated by a wheel chair motor (DG-158A, AVIC, Beijing, China) driven by a power supply (CSI3020 SW, CircuitSpecialists, Tempe, AZ, USA).