## 5 Test Validation
### Model of Pipeline-Oriented CMS  
The pipeline-oriented CMS model, as shown in Figure 15, is proposed. This structure consists of a framework, resonant units, and a mounting fixture.  
Figure 14: Numerical results of eigenvalues for different coupling strengths.  
Figure 13: Numerical results of eigenvalues for different mistuning strengths.  
The framework is a circular hierarchical honeycomb structure with three layers of circular holes processed. The inner diameters of the circular holes in each layer differ, and based on these size differences, the circular holes can be categorized into three types: large, medium, and small. The resonant unit consists of an elastic unit, a basic mass, and an added mass. The elastic element is a double-ring structure, with the inner and outer ring connected by the connecting beam serving to provide stiffness. The outer diameter of the outer ring matches the inner diameter of the circular hole, thus enabling the resonant unit to be firmly embedded in the framework. Based on the size of the elastic elements, the resonant units can also be divided into three types: large, medium, and small. The basic mass is a cylindrical structure, with the diameter of its bottom circle matching the inner diameter of the inner ring of the elastic element, thereby enabling the basic mass to be firmly embedded in the elastic element. By setting the geometric and material parameters of the elastic element and the basic mass, the resonant frequency of the resonant unit can be preliminarily determined. By attaching the added mass to the basic mass to introduce mistuning parameters, the frequency adjustment can be achieved.  
Here we will describe the core parameters of the pipeline-oriented CMS to facilitate readers' understanding. The inner diameter of the circular hole in the framework is denoted as \(R_{1}\), the outer diameter of the elastic element's outer ring as \(r_{1}\), the inner diameter of the inner ring as \(r_{2}\), and the thickness as \(H\). The length, width, and height of the connecting beam are denoted as \(h_{1},h_{2}\), and \(h_{3}\), respectively. The diameter of the bottom circle of the basic mass is denoted as \(r_{3}\), and its height is equal to the thickness of the elastic element. The values of the above parameters are shown in Table 2.  
In terms of material parameter selection, aluminum alloy is chosen for the framework, tungsten for the basic mass, iron for the additional mass, and resin for the elastic element. The Young's modulus of the resin is 2.5 GPa, and the density is 1100 kg m\({}^{-3}\). The complete geometric and material parameters can be found in our previous work [34], which also established a numerical model based on the above parameters to conduct mode analysis and verify the good vibration localization effect of the pipeline-oriented CMS.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Parameters**} & \(\mathbf{R_{1}}\) & \(\mathbf{r_{1}}\) & \(\mathbf{r_{2}}\) & \(\mathbf{r_{3}}\) & \(\mathbf{h_{1}}\) & \(\mathbf{h_{2}}\) & \(\mathbf{h_{3}}\) & \(\mathbf{H}\) \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Value (mm) \\ \end{tabular} } & Large & 8.5 & 8.5 & 4.5 & 4.5 & 2 & 2.4 & 1 & 10 \\  & Medium & 8 & 8 & 4 & 4 & 2 & 2 & 1 & 10 \\  & Small & 7.5 & 7.5 & 3.5 & 3.5 & 2 & 1.6 & 1 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The core parameters of the pipeline-oriented CMS.  
Figure 15: Structural model of the pipeline-oriented CMS.