# Reducing Railway Track Vibrations by Applying Particle-Damping Systems
## 3 Results
### Summary  
The present section will provide a summary of the results. As discussed before, three frequency ranges were used. For each frequency range, average values regarding peak values will be presented for each material. Two comparisons will be performed, one presenting the same total particle mass for all four materials, while the remaining case will showcase the best configuration for each material. Although some mass configurations performed better than others in specific frequency ranges and amplitudes, the overall best will be used. Figure 9 presents the summary results for the same total mass comparison, 1.1 kg, across the three frequency ranges and amplitudes. All cases were analysed with an 80% filling ratio, except for the rubber band, which was tested at 100% (once the reservoir was completely full). Figure 9a presents the results for the lowest excitation amplitude. Regarding the lowest frequency range, 50 to 800 Hz, the FIMO presents the highest attenuation, while lead shows the worst results. On the other hand, for intermediate and higher frequencies, lead presents the best behaviour, attenuating the vibrations' average amplitudes by approximately 6.0 and 2.5 times for the intermediate and highest frequencies, respectively. Figure 9b,c presents the results for the intermediate and highest excitation amplitudes. It can be observed that the overall damping behaviour of lead particles has improved, even for the lowest frequency (where lead presented the worst results for the lowest excitation amplitude). One hypothesis is that, when the excitation amplitude is very small, not enough energy is provided to generate significant movement of the lead particles (which are the heaviest among the analysed ones). Moreover, regarding the lowest frequency range, FIMO presented the best behaviour for all three analysed excitation amplitudes. Additionally, rubber bands present good results for low excitation amplitudes and frequencies, probably  
Figure 8: Effect of excitation amplitude on vibration response, comparison of the lowest and highest excitation amplitudes, frequency-domain analysis: (**a**) Lead particles; (**b**) FIMO particles. associated with their low particle mass (which requires less energy to move and results in more frequent collisions with other particles). Regarding the comparison presenting the best results for each configuration, Figure 10 shows a summary of these data. The lowest excitation amplitude is presented in Figure 10a. This time, lead presents the best results for all analysed frequencies. It is important to emphasise that this mass configuration of lead had 7.0 kg of particles, nearly six times more than FIMO and a rubber band. By using lead particles, attenuation factors of 3, 20 and 2.5 times were obtained for the lowest, intermediate, and highest frequencies, respectively. Magnetite also presented good results. Once again, magnetite was the second heaviest configuration, with a particle mass of 3.6 kg. Next, FIMO presented good attenuation factors, especially for the lowest and intermediate frequency ranges. Figure 9: Equal mass comparison for all materials: (**a**) Lowest excitation amplitude; (**b**) Intermediate excitation amplitude; (**c**) Highest excitation amplitude. Figure 10b,c presents the results regarding intermediate and highest excitation amplitudes. Once again, the best results were obtained using lead particles (heaviest particles and total particle mass), followed by magnetite configuration. In some cases, attenuation factors of approximately 10 were obtained, like in the case of intermediate frequencies and highest amplitudes. As was observed before, FIMO and rubber band particles presented low attenuation for the highest excitation frequencies. Figure 11a-c displays the analysis regarding the impact of filling ratio. As discussed before, the same particle mass of 1.1 kg was used for all cases, and filling ratios of 100% and 80% were analysed.