# Reducing Railway Track Vibrations by Applying Particle-Damping Systems
## 2 Materials and Methods  
The present section will provide details regarding experimental analysis. Next, the details concerning data processing will be presented. The experimental procedure consists of a rail, which will be loaded by an excitation system (for the present case, a speaker, amplifier, and signal generator). Additionally, particles from several materials will be confined in a reservoir, whose main function is to act as particle dampers. Known excitation amplitudes and forces will be applied, and the system response will be measured. As previously discussed, the main goal of an efficient particle damper system is to attenuate the vibrations at the train rail, and the system's behaviour will be analysed for several different configurations of particle dampers regarding materials, mass, and filling ratio. The testing setup is presented in Figure 1, where Figure 1a,b present an overview of the testing rig, and Figure 1c shows a schematic view of the experimental apparatus. The testing setup can be summarised by:  
* Steel rail: It is the principal component of the testing apparatus to which almost all other devices are connected. The steel rail is two metres long, being a profile of an ASCE (American Society of Civil Engineers) 60 light rail, with a total mass of 60 kg. The rail was positioned sideways, and excited vertically (the original direction concerning lateral vibrations of the mounted rail). The rail is suspended by supports in two locations (discussed in the following topic) and excited at the central portion of its length. The steel rail was tested sideways (when compared to its position during use). * Supports and ropes: In order to minimise the impact of the fixturing system on the dynamic behaviour of the system, the steel rail was suspended by a pair of racks and ropes. The suspension region was located at the two vibration nodes of the 1 st bending mode (slender beam), corresponding to a distance of 22.4% of the total length of the rail, measuring from the closest free edge. * Speaker: This component was used to provide external excitation to the steel rail. A 6-inch speaker was used, with a power of 90 W RMS (Root Mean Square). The working range of the presented speaker extends from 50 Hz to 5 kHz. The speaker was driven by a signal generator and a 100 W amplifier. The speaker was attached to an inertia block. The entire weight of the rail is maintained by supports, and the rail is positioned to just stay over the speakers (with no force when at rest). The excitation force orientation is parallel to the gravity
* Force transducer and central accelerometer: An impedance head was used to measure the excitation force and acceleration. This measurement device was located between the speaker and the web of the steel rail, placed in the mid-section of its length. * Accelerometer (edge location): This sensor was used to measure the steel rail's response under different excitations and with different damping systems, and it was placed 30 mm away from one of the rail ends. More details regarding the measuring system (impedance head and accelerometer) will be provided below. * Particle reservoir: It is presented in Figure 1d. It consists of a steel box with an adjustable cover, having external dimensions of \(550\times 55\times 75\) mm. Only one reservoir was used for the present study, located on the web. The reservoir was attached to the rail using a structural adhesive, epoxy. Additionally, its height (75 mm) can be adjusted by two pairs of nuts. This is important since the filling ratio of the particle reservoir can be changed independently of the particle's total mass. An internal volume of approximately 2 litres is obtained when the cover is positioned at the utmost configuration. The reservoir is attached to the middle section (half length). Regarding the measuring system, Table 1 presents more details about both the impedance head (force and acceleration sensors) and the accelerometer (located near the rail edge).