# Reducing Railway Track Vibrations by Applying Particle-Damping Systems
## 2 Materials and Methods
The impedance head's main function is to measure the input signals (force and acceleration) at the central portion of the rail. On the other hand, the edge accelerometer is responsible for measuring the output signal. The main objective of the damping system is to minimise the excitation response of the rail. Therefore, the most efficient system will be considered the one capable of better reducing the vibration (output signal) over a wide range of frequencies and amplitudes. The experimental procedure consists of exciting the central section of the steel rail web with a known frequency and amplitude. For the present analysis, a sinusoidal wave sweep was used, where the frequency was modulated. Three frequency ranges and three excitation amplitudes were used, and they are presented in Table 2, resulting in a total of nine tests per condition. For simplicity, the amplitudes were often referred to as Amp1, Amp2, and Amp3, being the 1 st on the smallest amplitude (4 m/s\({}^{2}\)), while the last corresponds to the highest excitation amplitude (12 m/s\({}^{2}\)). Each sweep test was 20 s long, starting at the lower frequency up to the higher one. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multicolumn{1}{c}{**Sensor**} & \multicolumn{1}{c}{**Sensitivity**} & \multicolumn{1}{c}{**Measuring Range**} \\ \hline Dytran 5860B—impedance & accelerometer & 10.43 mV/(m/s\({}^{2}\)) & 1.0 to 8000 Hz \\ \cline{2-4} head, Chatsworth, CA, USA & force transducer & 23.18 mV/N & 1.0 to 8000 Hz \\ \hline Bruel and Kjaer 4508 b, Naerum, Denmark & accelerometer & 9.73 mV/(m/s\({}^{2}\)) & 0.3 to 8000 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measuring system information. Figure 1: Steel rail and particle reservoir testing setup: (**a**) Testing setup overview, top view; (**b**) Testing setup overview, front view; (**c**) Schematic view, front view; (**d**) Reservoir. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Start Excitation Frequency** & **End Excitation Frequency** & **Excitation Acceleration** \\
**(Hz)** & **(Hz)** & **Amplitude (m/s\({}^{2}\))** \\ \hline
50 & 800 & 4, 8 and 12 \\
800 & 2000 & 4, 8 and 12 \\
2000 & 4000 & 4, 8 and 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Loading amplitudes and excitation frequencies. Regarding the damping systems, four different damping particles were used, namely: polymer clay (FIMO(r)), lead spheres, magnetite powder, and natural rubber (segments of rubber bands). An overview of the particles can be seen in Figure 2. These materials were chosen in order to encompass a wide range of elasticity modulus (\"hard\" or \"soft\" materials) and bulk densities as well, which will be discussed next. Table 3 presents the average particle dimensions and bulk densities. Materials were tested in their \"as supplied\" shapes and sizes, like powder for magnetite and spheres for lead. Moreover, in order to compare the efficiency of each particle type with the same total mass, natural rubber was used as the reference mass, as it was the material with the lowest bulk density. Therefore, the reference mass for comparison was considered to be the maximum natural rubber mass (entire reservoir filled with these particles), resulting in a total particle mass of 1.1 kg. As stated earlier, all particle materials were tested under several different conditions, one of which was the same total mass (1.1 kg). All materials were tested with the maximum possible mass (entire reservoir, filled to 100%), except for the lead. Due to its high density, it was not possible to test the lead in that condition, as it would require more than 12 kg of lead spheres. Consequently, a total mass of 7 kg was used for lead. Moreover, tests were conducted for two different filling ratios, 100% and 80%. This was performed in order to analyse the effect of the free space on the particle dampers' efficiency. Additionally, a test with an empty reservoir was also performed and used as the reference (no particle damping). The combinations for testing conditions are summarised in Table 4 for all materials.