Skip to main content
SpringerLink
Log in

Modelling and analysis of vehicle-structure-road coupled interaction considering structural flexibility, vehicle parameters and road roughness

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

To determine the dynamic forces acting on vehicle components a vehicle-structure-road interaction is considered. Coupled interaction was modelled using a flexible bridge-like thin beam structure with four and six Degree of freedom (DOF) half car models. In addition to the flexible structure, the road conditions were added to the model as random and non-random surface irregularities. A coupled equation of motion of the whole system was derived using Lagrange equations, and converted to a first-order state-space equation and then solved using the fourth-order Runge-Kutta method. Besides the dynamic forces, the effects of the vehicle speed, bridge flexibility, tire stiffness, random or non-random road irregularities on the passenger comfort are widely investigated. The results obtained were compared by several early VBI (Vehicle-bridge-interaction) studies in the literature and proved accurate with a 5 % difference.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. Fryba, Vibration solids and structures under moving loads, Thomas Telford House(1999).

    Book  MATH  Google Scholar 

  2. C. I. Bajer and B. Dyniewicz, Numerical analysis of vibrations of structures under moving inertial load, Springer, New York(2012) Doi:10.1007/978-3-642-29548-5.

    Book  MATH  Google Scholar 

  3. S. K. C. P. C. Sujatha and S. Krishnapillai, Non-uniform Euler-Bernoulli beams under a single moving oscillator: An approximate analytical solution in time domain, J. of Mechanical Science and Technology, 30 (2016) 4479–4487, Doi:10.1007/s12206-016-0704-6.

    Article  Google Scholar 

  4. B. Dyniewicz and C. I. Bajer, New consistent numerical modelling of a travelling accelerating concentrated mass, World J. Mech., 2 (2012) 281–287, Doi:10.4236/wjm.2012. 26034.

    Article  Google Scholar 

  5. S. Timoshenko, Vibration problems in engineering, second, Van Nostrand, New York(1929) Doi:10.1016/S0016-0032(29)91051-6.

    MATH  Google Scholar 

  6. H. P. Lee, Transverse vibration of a Timoshenko beam acted on by an accelerating mass, Appl. Acoust., 47 (1996) 319–330, Doi:10.1016/0003-682X(95)00067-J.

    Article  Google Scholar 

  7. G. Michaltsos, Dynamic behaviour of a single-span beam subjected to loads moving with variable speeds, J. Sound Vib., 258 (2002) 359–372, Doi:10.1006/jsvi.5141.

    Article  Google Scholar 

  8. Y. Wang, The transient dynamics of a moving accelerating / decelerating mass traveling on a periodic-array nonhomogeneous composite beam, Eur. J. Mech. A/Solids, 28 (2009) 827–840, Doi:10.1016/j.euromechsol.2009.03.005.

    Article  MATH  Google Scholar 

  9. M. Dehestani, M. Mofid and A. Vafai, Investigation of critical influential speed for moving mass problems on beams, Appl. Math. Model, 33 (2009) 3885–3895, Doi:10. 1016/j.apm.2009.01.003.

    Article  MathSciNet  MATH  Google Scholar 

  10. I. Esen, A new FEM procedure for transverse and longitudinal vibration analysis of thin rectangular plates subjected to a variable velocity moving load along an arbitrary trajectory, Lat. Am. J. Solids Struct., 12 (2015) 808–830.

    Article  Google Scholar 

  11. I. Esen, Dynamic response of a beam due to an accelerating moving mass using moving finite element approximation, Math. Comput. Appl., 16 (2011) 171–182.

    MathSciNet  Google Scholar 

  12. V. Kahya, Dynamic analysis of laminated composite beams under moving loads using finite element method, Nucl. Eng. Des., 243 (2012) 41–48, Doi:10.1016/j.nucengdes.2011.12. 015.

    Article  Google Scholar 

  13. I. Esen and M. A. Koç, Dynamics of 35 mm anti-aircraft cannon barrel durig firing, Int. Symp. Comput. Sci. Eng., Aydin (2013) 252–257.

    Google Scholar 

  14. I. Esen and M. A. Koç, Optimization of a passive vibration absorber for a barrel using the genetic algorithm, Expert Syst. Appl., 42 (2015) 894–905, Doi:10.1016/j.eswa.2014.08.038.

    Article  Google Scholar 

  15. M. Fafard, M. Bennur and M. Savard, A general multi-axle vehicle model to study the bridge-vehicle interaction, Eng. Comput., 14 (1997) 491–508, Doi:10.1108/02644409710170339.

    Article  MATH  Google Scholar 

  16. Y. B. Yang, J. D. Yau and Y. S. Wu, Vehicle-bridge interaction dynamics with applications to high-speed railways, World Scientific Publishing Co. Pte. Ltd., Danvers(2004).

    Book  Google Scholar 

  17. Y. A. Dugush and M. Eisenberger, Vibrations of nonuniform continuous beams under moving loads, J. of Sound Vib., 254 (2002) 911–926, Doi:10.1006/jsvi.2001.4135.

    Article  Google Scholar 

  18. K. Wang, H. Xia, M. Xu and W. Guo, Dynamic analysis of train-bridge interaction system with flexible car-body, J. of Mechanical Science and Technology, 29 (2015) 3571–3580, Doi:10.1007/s12206-015-0801-y.

    Article  Google Scholar 

  19. Y. Wang and W. Qu, Numerical study on moving train parameter identification system through a simply supported bridge, J. of Mechanical Science and Technology, 26 (2012) 2641–2648, Doi:10.1007/s12206-012-0720-0.

    Article  Google Scholar 

  20. G. Michaltsos, D. Sophianopoulos and A. N. Kounadis, The effect of a moving mass and other parameters on the dynamic response of a simply supported beam, J. Sound Vib., 191 (1996) 357–362, Doi:10.1006/jsvi.1996.0127.

    Article  MATH  Google Scholar 

  21. K. Youcef, T. Sabiha, D. El Mostafa, D. Ali and M. Bachir, Dynamic analysis of train-bridge system and riding comfort of trains, J. of Mechanical Science and Technology, 27 (2013) 951–962, Doi:10.1007/s12206-013-0206-8.

    Article  Google Scholar 

  22. Y. B. Yang, M. C. Cheng and K. C. Chang, Frequency variation in vehicle-bridge interaction systems, Int. J. Struct. Stab. Dyn., 13 (2013) 1350019, Doi:10.1142/S02194554135 00193.

    Article  MathSciNet  MATH  Google Scholar 

  23. H. Azimi, K. Galal and O. A. Pekau, A numerical element for vehicle-bridge interaction analysis of vehicles experiencing sudden deceleration, Eng. Struct., 49 (2013) 792–805, Doi:10.1016/j.engstruct.2012.12.031.

    Article  Google Scholar 

  24. P. Lou and F. T. K. Au, Finite element formulae for internal forces of Bernoulli-Euler beams under moving vehicles, J. Sound Vib., 332 (2013) 1533–1552, Doi:10.1016/ j.jsv.2012.11.011.

    Article  Google Scholar 

  25. H. Shi and P. Wu, Flexible vibration analysis for car body of high-speed EMU, J. of Mechanical Science and Technology, 30 (2016) 55–66, Doi:10.1007/s12206-015-1207-6.

    Article  Google Scholar 

  26. J. Wyss, D. Su and Y. Fujino, Prediction of vehicle-induced local responses and application to a skewed girder bridge, Engineering Structures, 33 (2011) 1088–1097, Doi:10.1016/j.engstruct.2010.12.020.

    Article  Google Scholar 

  27. B. Liu, Y. Wang, P. Hu and Q. Yuan, Impact coefficient and reliability of mid-span continuous beam bridge under action of extra heavy vehicle with low speed, J. Cent. South Univ., 22 (2015) 1510–1520, Doi:10.1007/s11771-015-2668-6.

    Article  Google Scholar 

  28. E. Esmailzadeh and N. Jalili, Vehicle-passenger-structure interaction of uniform bridges traversed by moving vehicles, J. Sound Vib., 260 (2003) 611–635, Doi:10.1016/S0022-460X(02)00960-4.

    Article  Google Scholar 

  29. P. Lou, A vehicle-track-bridge interaction element considering vehicle’s pitching effect, Finite Elem. Anal. Des., 41 (2005) 397–427, Doi:10.1016/j.finel.2004.07.004.

    Article  Google Scholar 

  30. M. S. Kim, G. Y. Kim, H. T. Kim and J. S. Koo, Theoretical cross-wind speed against rail vehicle derailment considering the cross-running wind of trains and the dynamic wheel-rail effects, J. of Mechanical Science and Technology, 30 (2016) 3487–3498, Doi:10.1007/s12206-016-0708-2.

    Article  Google Scholar 

  31. A. K. Belyaev, H. Irschik and M. Krommer, Mechanics and model-based control of advanced engineering systems(2014) Doi:10.1007/978-3-7091-1571-8.

    Book  MATH  Google Scholar 

  32. P. E. Uys, P. S. Els and M. Thoresson, Suspension settings for optimal ride comfort of off-road vehicles travelling on roads with different roughness and speeds, J. Terramechanics, 44 (2007) 163–175, Doi:10.1016/j.jterra. 2006.05.002.

    Article  Google Scholar 

  33. A. Shirahatt, P. Panzade and M. M. Kulkarni, Optimal design of passenger car suspension for ride and road, J. Brazilian Soc. Mech. Sci. Enginering (2008) 66–76.

    Google Scholar 

  34. L. Frýba, A rough assessment of railway bridges for high speed trains, Eng. Struct., 23 (2001) 548–556, Doi:10.1016/ S0141-0296(00)00057-2.

    Article  Google Scholar 

  35. Y. B. Yang and Y. S. Wu, A versatile element for analyzing vehicle-bridge interaction response, Eng. Struct., 23 (2001) 452–469, Doi:10.1016/S0141-0296(00)00065-1.

    Article  Google Scholar 

  36. P. Lou and F. T. K. Au, Finite element formulae for internal forces of Bernoulli-Euler beams under moving vehicles, J. Sound Vib., 332 (2013) 1533–1552, Doi:10.1016/ j.jsv.2012.11.011.

    Article  Google Scholar 

  37. N. Zhang, H. Xia and G. de Roeck, Dynamic analysis of a train-bridge system under multi-support seismic excitations, J. of Mechanical Science and Technology, 24 (2010) 2181–2188, Doi:10.1007/s12206-010-0812-7.

    Article  Google Scholar 

  38. M.-K. Song, H.-C. Noh and C.-K. Choi, A new threedimensional finite element analysis model of high-speed train-bridge interactions, Eng. Struct., 25 (2003) 1611–1626, Doi:10.1016/S0141-0296(03)00133-0.

    Article  Google Scholar 

  39. Y. S. Cheng, F. T. K. Au and Y. K. Cheung, Vibration of railway bridges under a moving train by using bridge-trackvehicle element, Eng. Struct., 23 (2001) 1597–1606, Doi:http://dx.doi.org/10.1016/S0141-0296(01)00058-X.

    Article  Google Scholar 

  40. S. H. Ju and H. T. Lin, A finite element model of vehiclebridge interaction considering braking and acceleration, J. Sound Vib., 303 (2007) 46–57, Doi:10.1016/j.jsv.2006.11. 034.

    Article  Google Scholar 

  41. H. Yang, Z. Chen, S. Li, H. Zhang and J. Fan, An integrated coupling element for vehicle-rail-bridge interaction system with a non-uniform continuous bridge, Acta Mech. Solida Sin., 28 (2015) 313–330, Doi:10.1016/ S0894-9166(15)30018-5.

    Article  Google Scholar 

  42. J. Yang and R. Duan, Modelling and simulation of a bridge interacting with a moving vehicle system, Blekinge Institute of Technology(2013).

    Google Scholar 

  43. I. Esen, Hareketli Yükler Altindaki Köprülü Kren Kirislerinin Dinamik (Mukavemet) Analizi, Istanbul Technical University(2009).

    Google Scholar 

  44. E. L. Wilson, Static and dynamic analysis of structures, Computers and Structures Inc., Berkeley(2002).

    Google Scholar 

  45. U. Lee, Separation between the flexible structure and the moving mass sliding on it, J. Sound Vib., 209 (1998) 867–877.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Sakarya University, Sakarya, 54187, Turkey

    Mehmet Akif Koç

  2. Department of Mechanical Engineering, Karabuk University, Karabuk, 78050, Turkey

    İsmail Esen

Authors
  1. Mehmet Akif Koç
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. İsmail Esen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mehmet Akif Koç.

Additional information

Recommended by Associate Editor Junhong Park

Mehmet Akif Koc received the M.S. in Mechanical Engineering from Karabuk University, Karabuk, Turkey, in 2013. He is a Research Assistant in Mechanical Engineering, Sakarya University, Sakarya. His current research interests include vehicle bridge interaction analysis and its control using artificial intelligence techniques.

Ismail Esen graduated from ITU Mechanical Engineering in 1991, earned the M.S. in 1994 and in 2009 completed his doctorate at the same univesrsity. Between 1992 and 2009 he worked as a Professional Engineer in the industry. He has been working at Karabuk University.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koç, M.A., Esen, İ. Modelling and analysis of vehicle-structure-road coupled interaction considering structural flexibility, vehicle parameters and road roughness. J Mech Sci Technol 31, 2057–2074 (2017). https://doi.org/10.1007/s12206-017-0403-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-017-0403-y

Keywords

Search

Navigation