## 2 Experimental Setup and Scheme  
### Experimental Structure and Setup  
The experimental structure, illustrated in Figure 2, consisted of a base, a bracket, and a wheel. It is a component in the spacecraft and made from aluminum alloy. The primary structure mass is 11.07 kg. Figure 2a illustrates the Cartesian coordinates definition of the primary structure. The vertical direction is defined as the Z, the axis direction of the wheel is defined as the Y, and the direction perpendicular to the Z and Y directions is defined as the X. The natural frequency of the fundamental mode of the primary structure is \(f_{\text{n}}\) = 240 Hz. The fundamental mode shape is shown in Figure 2c. It was known by modal identification that the corresponding mode was first-order bending mode of the primary structure, and the main response is in the Y direction. According to [22; 23; 24], for achieving high damping, the damper should be installed on a large displacement position to acquire the vigorous impact of particles. The multi-unit particle damper was installed on the top of the bracket and the particle cavities connected to the bracket by an adapter, as shown in Figure 3.  
The multi-unit particle damper was made of aluminum alloy plates consisting of three rectangular containers, in which the walls in the Y direction can be removed to add particles. The cavity types  
Figure 3: Connection scheme of particle cavities with the primary structure. (**a**) bracket structure; (**b**) test model. Figure 2: Test structure (**a**) coordinate definition and component name; (**b**) structure size; (**c**) fundamental mode shape of the primary system. and internal dimensions used in this study are listed in Table 1. All cavities are equally divided into 3 sub-cavities along the X direction, as shown in Figure 3. The serial number of the cavity indicates that the number of layers along the Y and Z directions is different: The A-cavity has no layering in the Z direction, and the Z-direction height of the cavity is 64 mm. The B-cavity is divided into 2 layers in the Z direction, and the height of each sub-chamber is 31 mm (the partition thickness is 2 mm). The C-cavity is divided into 5 layers in the Z direction, and the Z-direction height of each sub-chamber is 11.2 mm. According to whether it is layered in the Y direction (the main response direction of the bracket), the above-mentioned cavity of each type is further divided into two types. The suffix number \"1\" indicates that the Y direction is not layered, that means the Y-direction dimension of a single sub-cavity is 28 mm. And the suffix number \"2\" indicates that the Y-direction is divided into two layers, and the single sub-cavity Y-direction dimension is 14 mm. The horizontal direction of the cross-sectional view in Table 1 is the Y direction, and the vertical direction is the Z direction. The modal analysis of the A1 cavity can be achieved under the condition that the bottom mounting hole is fixed, the first-order modal frequency is 1993, 6 Hz, and the main vibration direction is Y-direction. This means that the damper cavity stiffness is large enough to have a negligible effect on the first-order bending frequency of the primary structure. Figure 4 shows a schematic diagram of the experimental apparatus. The multi-unit particle damper was first fixed on a steel pedestal and then firmly connected to the shaker platform. This test system included an LS232-GT500M 2t-level shaker, several m + p Vibpilot-8 controllers and B and W piezoelectric acceleration sensors. The sampling frequency was set to 5.12 kHz. The motion of the primary structure and the base was measured with six accelerometers.