## 5 Test Validation
### FRF Test of Pipeline  
The pipeline test bench, as depicted in Figure 16a, is fabricated with an outer diameter of 80 mm, a wall thickness of 3 mm, and a length of 1500 mm, constructed from aluminum and possessing a total mass of 2950 g.  
Acceleration sensors are positioned at 450 mm from each end of the pipeline (marked as points A1 and A2), while a shaker is mounted at the midpoint of the pipeline (marked as point A3) through an elastic cord. The elastic cord is secured to the portal frame, which in turn is firmly anchored to the ground by means of pressing blocks. The shaker is connected to a force sensor through a screw stem, and the force sensor is fixed to the pipeline. Install one CMS at 300 mm, 600 mm, 900 mm, and 1200 mm along the pipeline, respectively. Figure 16b shows the sample of the CMS. Figure 16c shows the large added mass; the medium and small added masses have similar structures but different sizes, corresponding to the resonant units of different sizes.  
The basic mass and added mass of each resonant unit are shown in Table 3, with the values derived from our prior research endeavors. We have demonstrated on a shorter pipeline that the frequency mistuning strength of the resonant units is appropriate under this mass configuration [34]. The mass of the resonant unit for each CMS is about 368.5 g, and the mass of the framework is about 165 g. The total mass of the pipeline and the four frameworks is calculated to be 3610 g, with the total mass of all resonant units constituting 40.8% of this value.  
When installing the CMS on the pipeline, additional impedance is introduced, which leads to a decrease in the FRF of the pipeline. Therefore, by measuring the FRF of the  
Figure 16: Pipeline test bench and CMS sample. (**a**) Pipeline test bench. (**b**) CMS sample. (**c**) Large added mass.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Resonant Unit** & **Basic Mass (g)** & **Added Mass (g)** \\ \hline Large & 12.2 & 2.0 (3); 4.0 (3); 6.0 (2); 8.0 (2) \\ Medium & 9.7 & 0.6 (3); 1.8 (3); 3.0 (2); 4.2 (2) \\ Small & 7.4 & 0 (4); 0.88 (3); 1.76 (3) \\ \hline \hline \end{tabular} The number of the resonant units at a given added mass is in italics.  
\end{table}
Table 3: Mass setting of the resonant units.  
pipeline to reflect the impedance of the CMS, the vibration reduction capability of the CMS can be effectively characterized. The FRF test is carried out using an impact hammer, which offers the advantages of simple operation, ease of testing, and flexible excitation position. The frequency analysis range is set to 10-400 Hz, with a frequency resolution of 0.5 Hz. The FRF of the pipeline at points A1 and A2 under vertical impact excitation at point A3 is shown in Figure 17.  
It can be seen that the pipeline exhibits a peak at approximately 82 Hz, which corresponds to the vertical bending mode peak. When the CMS is attached, the frequency response characteristics of the original pipeline are altered, resulting in the mode peak shifting toward a lower frequency. We can also see that the FRF of the pipeline is significantly reduced in the frequency range of 65.0-123.5 Hz upon installation of the CMS compared with the bare pipe. The CMS demonstrates a substantial impedance effect, confirming its potential for low-frequency broadband vibration reduction.