# Parametric Study on the Effect of Rail Dampers on Track Decay Rate
## 1 Introduction  
Rail passenger and freight transport have been considered an increasingly attractive alternative in recent decades due to its low environmental impact. However, railway vehicles have multiple sources of noise, which, taken together, determine the overall sound level of railway noise. The dominant source of railway noise up to 300 km/h is the rolling of the vehicle's wheels on the rail (rolling noise), and beyond this speed limit, the aerodynamic noise becomes prevalent [1]. Much research in the field has shown that rail vibration has an important contribution to the generation of rolling noise [2; 3; 4]. Indeed, the rail behaves as a one-dimensional elastic medium through which the bending waves induced by wheel-rail vibrations caused by the defects in the railway track and the irregularities in the running surfaces are mainly propagated [5; 6; 7; 8; 9]. At the surface of the rail, the bending waves are transformed into acoustic waves, and the rail becomes an acoustic radiator. Two types of bending waves propagate through the rail: an evanescent wave (near field wave) and a propagative wave [10]. The attenuation of the evanescent wave increases with frequency, so that the vibration of the rail along it is basically due to the propagative wave in a wide frequency range. Consequently, the acoustic effectiveness of the rail depends on the distance over which the bending wave can propagate. Longer propagation distance, higher acoustic effectiveness. Track decay rate is the parameter that describes how the bending waves decrease along the track [11; 12]. The measurement unit of the track decay rate is dB/m, which means by how many decibels the vibration level of the rail decreases at each meter of track. Consequently, TDR reflects the acoustic performance of the track: higher TDR, lower noisefrom the track because the propagation distance of waves is shorter. This explains why TDR is used in the technical measurement of noise generated by railway vehicles [13]. Rail dampers can be used to limit the propagation distance of the bending waves through the rail and to reduce the rolling noise [14; 15]. Rail dampers are mechanical devices usually designed as dynamic absorbers with one or often two tuning frequencies to be effective over a wide frequency range [16; 17]. These consist of one or two steel pieces encapsulated in a massive rubber jacket and attached to both rail web faces via clamps and even glue between sleepers [18; 19; 20]. When the rail is vibrating due to the wheel/rail interaction, the rail motion is transmitted to the rail dampers via the bending waves that propagate along the track. Consequently, the steel pieces of the rail dampers are vibrating, but out of phase to each other and to the rail because of the damping. In this way, a part of the rail energy is transferred to the rail dampers, where it is dissipated due to the viscoelastic property of the rubber element, shortening the bending wave propagation distance. Rail damper performance is evaluated in terms of TDR that can be calculated using the theoretical models [11; 14; 18; 21; 22] or can be determined via laboratory or on-site experiments [18; 23; 24; 25]. The possibilities of reducing track noise with the help of rail dampers have been analyzed in many theoretical and experimental studies. [PERSON] et al. analyzed the effect of a tuned rail damper on the rail noise depending on rail temperature [18]. Also, [PERSON] et al. elaborated a method of weighting the noise reduction at different temperatures [26]. It has been shown that the rail dampers should be designed in correlation with specific environmental factors to maximize their effectiveness. [PERSON] investigated the impact of both continuous and discrete rail damper model parameters on vibration decay along the track using a continuous-discrete track model [21; 27]. Subsequently, [PERSON] and [PERSON] applied the previous track with rail dampers model to predict the rail component of rolling noise [28]. [PERSON] et al.