# Parametric Study on the Effect of Rail Dampers on Track Decay Rate
## 4 Conclusions  
The rail damper is a mechanical tool that is mounted on the rail to reduce the propagation of bending waves along it. Considering this, the rail damper is a means of reducing the noise produced by the rail.  
In this paper, a parametric study on the influence of the rail damper with mixed damping system upon the dynamic response of the light rail and rail damper effectiveness in terms of the receptance and TDR, respectively, was carried out. This study is based on a continuous-discrete model in which the rail is an infinite Timoshenko beam, and the elastic supports, including rail pad, sleeper, and ballast, and the rail dampers are made up of elements with concentrated parameters. The rail receptance and TDR were calculated using the frequency-domain Green's function associated with the Timoshenko differential operator. Four scenarios were taken regarding the condition of the rail pads (soft/stiff) and the ballast (tampered/settled), considering two values for the distance between the sleepers (short/long).  
The main frequencies that characterize the dynamic response of the rail, the low/high resonance, the anti-resonance and pinned-pinned resonance, and the shape of the bending waves that propagate along the rail (standing/propagative waves) have been outlined. The low/high resonance frequencies are mostly determined by the ballast/rail pad stiffness, while the pinned-pinned resonance depends on the rail features and the sleeper bay.  
TDR is higher in the case of the track featured with stiff rail pads in comparison to the track with soft rail pads.  
The rail receptance decreases around the second resonance and within the second propagative wave range when the rail is fitted with rail dampers. The difference between the receptance of the rail in the midspan and the one above sleepers around the pinned-pinned resonance is diminished by the presence of rail dampers.  
Using rail dampers with a mixed damping system, TDR can increase at middle and high frequencies, from 4 to 500 Hz up to 1250-1600 Hz, for both soft and stiff rail pads, independent of the ballast condition. TDR increasing depends on the position of the  
Figure 15: Illustrative for the influence of the sleeper bay enlargement from 0.544 m to 0.595 m (\(k_{b}\) = 40 MN/m): (**a**) between sleepers, \(k_{p}\) = 60 MN/m; (**b**) between sleepers, \(k_{p}\) = 300 MN/m; (**c**) above sleepers, \(k_{p}\) = 60 MN/m; and (**d**) above sleepers, \(k_{p}\) = 300 MN/m;, track with rail dampers and sleeper bay of 0.544 m;, track with rail dampers and sleeper bay of 0.595 m.  
excitation force, and it is higher when the force position is between sleepers. Larger sleeper bay, lower TDR for both tracks without/with rail dampers.  
Conceptualization, T.M. and D.F.; methodology, T.M. and D.F.; software, T.M., D.F. and M.-A.G.; validation, T.M.; formal analysis, T.M. and I.-I.A.; investigation, T.M. and D.F.; resources, D.F., M.-A.G. and I.-I.A.; data curation, D.F.; writing--original draft preparation, D.F.; writing--review and editing, T.M.; visualization, T.M. and D.F.; supervision, T.M.; project administration, T.M.; funding acquisition, T.M. All authors have read and agreed to the published version of the manuscript.  
The second, third, and fourth authors declare that their work was supported by a grant from the National Program for Research of the National Association of Technical Universities-GNAC ARUT 2023, contract No. 154/04.12.2023.  
Not applicable.  
The original contributions presented in this study are included within the article; further inquiries can be directed to the corresponding authors.  
The authors declare no conflicts of interest.