# Numerical and Experimental Investigations of Particle Dampers Attached to a Pipeline System
## 5 Conclusions  
Particle damping technology was introduced into a pipeline system. The energy dissipation mechanism of particle damping was analyzed via numerical calculations and experimental testing. The particle damper for pipeline systems was designed, and the effects of the damper material and structure, external excitation, and other parameters on the energy dissipation characteristics of particle damping were revealed. The vibration suppression test of the designed particle damper in a pipeline system was performed. The main conclusions of this paper are as follows:  
1. The total energy dissipated in the particle system shows a trend of increasing and then decreasing with an increasing filling rate. The highest total energy dissipated by the particle system was achieved when the filling rate was 60%. When the damper space is a constant value, the number of particles and energy dissipated in the particle system decreases with increasing particle size. The total energy dissipated by the particle system increases with increasing particle density.
2. The total energy dissipated by the particle system increases with increasing particle density, increasing particle-particle and particle-container wall friction coefficients, and decreasing recovery coefficients. The total energy dissipated in the particle system shows a tendency to increase and then decrease with increasing numbers of damper cavities, and the highest total energy dissipated in the particle system was achieved with a four-cavity structure.
3. The total energy dissipated by the particle system increases with increasing excitation frequency, amplitude displacement, and number of the damper structure. The frequency domain amplitude of the aluminum alloy damper pipeline decreased by 9.97% and 19.61% for the four-cavity and six-cavity damper configurations, respectively, compared with that of the ABS. This indicates that the damping effect of aluminum alloy particle damper cavities is better than that of ABS dampers.
4. For both ABS and aluminum alloy damper structures, the frequency domain amplitudes of the four-cavity damper were smaller than that of the six-cavity ones. This  
Figure 21: Vibration response of a six-cavity particle damper made of two different materials.  
indicates that four-cavity particle dampers have a better damping effect on pipeline systems. Under basic harmonic excitation, the damping effects of the two materials and two-cavity structures have the same pattern when attached to the pipeline.  
Methodology, R.M. and F.S., Software, T.Y., Validation, J.W., Formal analysis, J.J., Investigation, R.M., Data curation, F.S., Writing--original draft, R.M., Writing--review and editing, J.J., Project administration, M.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Provincial Natural Science Foundation of China, grant number ZR2020 ME121.  
Not applicable.  
The data used to support the findings of this study are available from the corresponding author upon request. The data are not publicly available due to privacy.  
The authors declare no conflict of interest.