# Reducing Railway Track Vibrations by Applying Particle-Damping Systems
## 1 Introduction
They have measured vibrations in buildings located near surface trains and subways and found that the trains excited the surrounding buildings at certain frequencies; human comfort is strongly compromised, and this issue could be addressed in the project of new buildings. Regarding the same topic, [PERSON] et al. [11] have studied the effect of these vibrations in tall buildings, and have observed that vibrations were amplified in certain cases, depending on which floor the measurements were performed, and could surpass the comfort levels determined by some standards and associations, like the FTA (Federal Transit Administration, Washington, DC, USA) [12]. For freight trains, when considering fuel efficiency, typical optimal speeds are around 50 km/h [13]; however, optimal values may vary according to the engine type, load, terrain, railway type, and other factors. In this speed range, the noise (and vibration levels) is dominated by the rolling phenomenon (wheel-steel rail system) [14]. While for lower speeds, the total noise's main component is associated with the traction noises [15], the train's aerodynamics dominates the noise generation at high speeds [16] (above approximately 250 km/h). Consequently, if the main objective is to reduce noise and vibration for freight trains (or other types of trains with similar average speeds), focusing on the wheel and the train track is essential. For the present work, the attenuation of the steel rail vibrations will be the main target. The vibration generated by freight trains is linked with several health conditions associated with sleep disturbance [17]. Part of the traditional railroad building components, like wooden sleepers and ballast, helps with vibration attenuation; however, they are often not enough. Passive dampers are solutions used to reduce the vibration levels. They are known to be simple and robust [18]. They are constructed using mechanical devices, and they are designed to dissipate a fraction of the system's kinetic energy [19]. Typical passive dampers are built using viscoelastic materials, tuned mass dampers (TMD), and moving particles (particle dampers) [20]. Tuned dampers were studied for applications in steel rails, like in the work proposed by [PERSON] et al. [21], where by using a tuned mass inside a viscoelastic material, they observed increases in damping performance of up to five times (when measuring the damping coefficient). Another application for TMD, focusing on high-speed railway bridges, was developed by [PERSON] et al. [22]. By designing and applying a group of tuned mass dampers, the authors were able to reduce the maximum acceleration of the bridge structure by as much as 50%. The authors have observed that better performance was achieved when the vibration was dominated by the structure's natural frequencies (resonance) and the train excited those frequencies (for example, by running at specific speeds that led to these excitation frequencies). Concerning particle dampers, the working principle can be summarised as transferring kinetic energy from the structure to the particles; afterwards, part of this energy is dissipated due to collisions and friction within the particles and between the particles and the structure (or the recipient wall) [23]. Some key parameters strongly affect the efficiency of particle dampers, namely: particle size, packing ratio, position, particle overlap and excitation frequency, amplitude and orientation, for example [24]. Depending on these characteristics, the particle motion can be characterised as follows: fluid-like movement, where particles act like a liquid; collect-and-collide, where particles move similarly to a single block, colliding with the reservoir walls; and decoupled, where particles' movement displays a high level of independence from one another [25]. A very comprehensive study was performed by [PERSON] et al. [26] regarding particle size and their damping efficiency.