Identification of Bending Modes of Vibration in Rails by a Laser Doppler Vibrometer on a Moving Platform


This paper introduces a method to identify the bending modes of vibration of railway tracks by using a laser Doppler vibrometer (LDV) mounted on a moving platform. Two sets of experiments were conducted at Transportation Technology Center Inc. (TTCI) in Pueblo Colorado, in order to validate the proposed method. First, the bending vibration modes were identified using the signals collected from a rail span (rail section between two consecutive sleepers) by accelerometers under moving car excitation. Then, vibration measurements from rail spans were obtained by using an LDV mounted on the moving railcar. All tests were carried out at four different rail car speeds: 8 km/h (5 mph), 16 km/h (10 mph), 35 km/h (22 mph), and 45 km/h (28 mph). To find LDV signal segments corresponding to rail spans, a novel approach based on the sleeper passing frequency is introduced. Comparison of the results from both sets of tests demonstrated good agreement for all speeds.

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  1. 1.

    Kostovasilis D (2017) Analytical modeling of the vibration of railway track. University of Southampton, Dissertation

    Google Scholar 

  2. 2.

    Nordborg A (2002) Wheel/rail noise generation due to nonlinear effects and parametric excitation. J Acoust Soc Am 111:1772–1781.

    Article  Google Scholar 

  3. 3.

    Thompson DJ (1993) Wheel-rail noise generation, part II: wheel vibration. J Sound Vib 161:401–419.

    Article  Google Scholar 

  4. 4.

    Thompson DJ (1993) Wheel-rail noise generation, part III: Rail vibration. J Sound Vib 161:421–446.

    Article  Google Scholar 

  5. 5.

    Yu H, Cai C, Yuan Y, Jia M (2017) Analytical solutions for Euler-Bernoulli beam on Pasternak foundation subjected to arbitrary dynamic loads. Int J Numer Anal Methods Geomech 41:1125–1137.

    CAS  Article  Google Scholar 

  6. 6.

    Ding L, Wu L, Zhu HP (2017) Propagation and localization of wave in multi-span Timoshenko beams on elastic foundations under moving harmonic loads. Int J Numer Anal Methods Geomech 41:1687–1710.

    Article  Google Scholar 

  7. 7.

    R. RJ, W. TM (1999) Finite element analysis of an elastic beam structure subjected to a moving distributed mass train. Mech Syst Signal Process 13:31–51.

  8. 8.

    Toscano Corrêa R, Pinto da Costa A, Simões FMF (2018) Finite element modeling of a rail resting on a Winkler-Coulomb foundation and subjected to a moving concentrated load. Int J Mech Sci 140:432–445.

    Article  Google Scholar 

  9. 9.

    Mallik AK, Chandra S, Singh AB (2006) Steady-state response of an elastically supported infinite beam to a moving load. J Sound Vib 291:1148–1169.

    Article  Google Scholar 

  10. 10.

    Wu TX, Thompson DJ (2004) On the parametric excitation of the wheel/track system. J Sound Vib 278:725–747.

    Article  Google Scholar 

  11. 11.

    Wu TX, Thompson DJ (2001) Vibration analysis of railway track with multiple wheels on the rail. J Sound Vib 239:69–97.

    Article  Google Scholar 

  12. 12.

    Sheng X, Li MH (2007) Propagation constants of railway tracks as a periodic structure. J Sound Vib 299:1114–1123.

    Article  Google Scholar 

  13. 13.

    Oregui M, Lo Z, Dollevoet RP, Moraal J (2011) A 3D finite element modeling of hammer test for track parameter identification. Proceedings of the international conference on structural engineering dynamics. Tavire, Portugal

    Google Scholar 

  14. 14.

    Kaewunruen S, Remennikov AM (2007) Field trials for dynamic characteristics of railway track and its components using impact excitation technique. NDT E Int 40:510–519.

    Article  Google Scholar 

  15. 15.

    Lam HF, Alabi SA, Yang JH (2017) Identification of rail-sleeper-ballast system through time-domain Markov chain Monte Carlo-based Bayesian approach. Eng Struct 140:421–436.

    Article  Google Scholar 

  16. 16.

    Oregui M, Li Z, Dollevoet R (2015) An investigation into the modeling of railway fastening. Int J Mech Sci 92:1–11.

    Article  Google Scholar 

  17. 17.

    Oregui M, Li Z, Dollevoet R (2015) Identification of characteristic frequencies of damaged railway tracks using field hammer test measurements. Mech Syst Signal Process 54:224–242.

    Article  Google Scholar 

  18. 18.

    Castellini P, Martarelli M (2006) Tomasini EPÃ. Laser Doppler Vibrometry : Development of advanced solutions answering to technology ’ s needs 20:1265–1285.

    Article  Google Scholar 

  19. 19.

    Rothberg SJ, Allen MS, Castellini P et al (2017) An international review of laser Doppler vibrometry : making light work of vibration measurement. Opt Lasers Eng 99:11–22.

    Article  Google Scholar 

  20. 20.

    Yang S, Allen MS (2012) Output-only modal analysis using continuous-scan laser Doppler Vibrometry and application to a 20kW wind turbine. Mech Syst Signal Process 31:228–245.

    CAS  Article  Google Scholar 

  21. 21.

    Martarelli M, Ewins DJ (2006) Continuous scanning laser Doppler vibrometry and speckle noise occurrence. Mech Syst Signal Process 20:2277–2289.

    Article  Google Scholar 

  22. 22.

    Stanbridge AB, Khan AZ, Ewins DJ (2000) Modal testing using impact excitation and a scanning LDV. Shock Vib 7:91–100.

    Article  Google Scholar 

  23. 23.

    Wu X, Cai W, Chi M et al (2015) Investigation of the effects of sleeper-passing impacts on the high-speed train. Veh Syst Dyn 53:1902–1917.

    Article  Google Scholar 

  24. 24.

    Schlichtharle D (2011) Digital filters: basics and design. Frankfurt/Main, Germany

    Book  Google Scholar 

  25. 25.

    Brincker R, Zhang L, Andersen P (2001) Modal identification of output-only systems using frequency domain decomposition. Smart Mater Struct 10:441–445.

    Article  Google Scholar 

  26. 26.

    Martin P, Rothberg S (2009) Introducing speckle noise maps for laser Vibrometry. Opt Lasers Eng 47:431–442.

    Article  Google Scholar 

  27. 27.

    Rothberg SJ, Halkon BJ (2004) Laser vibrometry meets laser speckle. Sixth Int Conf Vib Meas by Laser Tech Adv Appl 5503:280.

    Article  Google Scholar 

  28. 28.

    Matsumoto A, Sato Y, Ohno H et al (2008) A new measuring method of wheel-rail contact forces and related considerations. Wear 265:1518–1525.

    CAS  Article  Google Scholar 

  29. 29.

    Tomcyzk; K, Layer E (2015) Signal transforms in dynamic measurement. Springer International Publishing

  30. 30.

    De Man AP (2000) Pin-pin resonance as a reference in determining ballasted railway track vibration behavior. Heron 45:35–51

    Google Scholar 

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This work has been supported under the grant DTFR53-17-C-00024 awarded by the Federal Railroad Administration of the U.S. Department of Transportation. The authors are grateful to Robert Wilson, program manager of the FRA, for his technical guidance and valuable comments during all phases of this research, to Vikrant Palan of Polytec, and to Brian Lindeman of TTCI for providing technical and logistic support during field tests.

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Correspondence to S. Salamone.

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Kaynardag, K., Battaglia, G., Ebrahimkhanlou, A. et al. Identification of Bending Modes of Vibration in Rails by a Laser Doppler Vibrometer on a Moving Platform. Exp Tech 45, 13–24 (2021).

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  • Moving laser Doppler vibrometer
  • Rail
  • System identification
  • Vibration modes
  • Sleeper passing frequency