# Experimental Study on Vibration Control of
## 5 Experiment of Piping System Vibration Control
### Control Performance of Forced Vibration  
In the forced vibration experiment, different frequencies of excitations are realized by changing the rotation speed of the motor. The displacement responses of the piping system under four working conditions (without control, with TMD control, with steel spring-type PTMD control, and with simple pendulum-type PTMD control) are recorded at different frequencies and plotted as a frequency-displacement curve, as shown in Figure 10.  
The black line in Figure 10 is the frequency response curve of the piping system without control. When the excitation frequency is 2.57 Hz, the maximum response displacement is 18.90 mm. When the piping system is controlled by the TMD, two peaks appear on the frequency spectra of the piping system, as shown in the figure (green line). The frequencies of the two peaks are 2.12 Hz and 3.02 Hz, and the corresponding displacements are 16.98 mm and 12.86 mm, which are 90% and 68% of the uncontrolled resonant amplitude. In the frequency range of 2.3 Hz to 2.9 Hz, the TMD can effectively reduce the displacement of the piping system by more than 80%. When the excitation frequency is close to 2.6 Hz, the pipe displacement is close to zero. The blue line describes the frequency response of the piping system with the spring steel-type PTMD control. The frequency response curve only has  
Figure 9: Experimental results of free vibration: (**a**) With spring steel-type PTMD; (**b**) With simple pendulum-type PTMD.  
one peak (2.46 Hz), which is on the left side of the uncontrolled resonance frequency. Additionally, the peak displacement is 9.72 mm, which is 51% of the uncontrolled resonant amplitude. Similar to spring steel-type PTMD, there is only one peak of the amplitude frequency curve controlled by the simple pendulum-type PTMD. The peak frequency is also 2.46 Hz, and the corresponding amplitude is 9.24 mm, which is 49% of the uncontrolled resonant amplitude. The appearance of only one peak after the addition of the PTMD was also observed in other cases [64; 68].  
At the resonance frequency (2.57 Hz) of the piping system, the control effects of the following systems are arranged in the order from largest to smallest: TMD, simple pendulum-style PTMD, spring steel-style PTMD. The corresponding displacement ratios are 3%, 42%, and 47%, respectively. Figure 11 shows the vibration responses of the piping system before and after the PTMD is released. After the release of the PTMDs, the piping system reaches a new steady state in a short time, with a displacement amplitude of about half that from before the PTMD is released. In the whole frequency domain, the rank of vibration control effectiveness under three conditions is simple pendulum-type PTMD > spring steel-type PTMD > TMD, and the corresponding displacements were reduced to 49% (Figure 12a), 51% (Figure 12b), and 90% (Figure 12c), respectively.  
Figure 11: Experiment results of forced vibration with PTMD released: **(a)** Spring steel-type PTMD; **(b)** Simple pendulum-type PTMD.  
Figure 10: Experiment results of forced vibration.