Skip to main content
SpringerLink
Log in

Nonlinear coupled longitudinal–transverse vibration analysis of a beam subjected to a moving mass traveling with variable speed

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In this paper, transverse and coupled longitudinal–transverse vibration of a beam subjected to a moving mass traveling with variable speed is considered. The speed change can be due to either an external force (traction or braking force) or the sliding friction force created immediately after the braking. The equation of motions for both cases was extracted and discretized using Galerkin decomposition method. The dynamic response of the beam and the moving mass was calculated and compared for different loading scenario. Next, coupled longitudinal–transverse vibration of a beam under the friction force was studied and the effect of friction coefficient on the dynamic response of the system was evaluated. A comparison between transverse and coupled longitudinal–transverse vibration of the beam subjected to a moving mass was also made.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Fryba, L.: Vibration of Solids and Structures Under Moving Loads. Thomas Telford, London (1972)

    Book  MATH  Google Scholar 

  2. Kocatürk, T., Şimşek, M.: Dynamic analysis of eccentrically prestressed viscoelastic Timoshenko beams under a moving harmonic load. Comput. Struct. 84, 2113–2127 (2006)

    Article  Google Scholar 

  3. Kargarnovin, M.H., Younesian, D., Thompson, D.J., Jones, C.J.C.: Response of beams on nonlinear viscoelastic foundations to harmonic moving loads. Comput. Struct. 83, 1865–1877 (2005)

    Article  Google Scholar 

  4. Nguyen, V., Duhamel, D.: Finite element procedures for nonlinear structures in moving coordinates. Part II: Infinite beam under moving harmonic loads. Comput. Struct. 86, 2056–2063 (2008)

    Article  Google Scholar 

  5. Wayou, A.N.Y., Tchoukuegno, R., Woafo, P.: Non-linear dynamics of an elastic beam under moving loads. J. Sound Vib. 273, 1101–1108 (2004)

    Article  Google Scholar 

  6. Mamandi, A., Kargarnovin, M.H., Younesian, D.: Nonlinear dynamics of an inclined beam subjected to a moving load. J. Nonlinear Dyn. 60, 277–293 (2010)

    Article  MATH  Google Scholar 

  7. Kang, B., Tan, C.A.: Nonlinear response of a beam under distributed moving contact load. Commun. Nonlinear Sci. Numer. Simul. 11, 203–232 (2006)

    Article  MATH  Google Scholar 

  8. Bajer, C.I., Dyniewicz, B.: Numerical modeling of structure vibrations under inertial moving load. Arch. Appl. Mech. 79, 499–508 (2009)

    Article  MATH  Google Scholar 

  9. Ding, H., Shi, K., Chen, L., Yang, S.: Adomian polynomials for nonlinear response of supported Timoshenko beams subjected to a moving harmonic load. Acta Mech. Solida Sin. 27(4), 385–393 (2014)

    Article  Google Scholar 

  10. Jorge, P.C., Simões, F.M.F., da Costa, A.P.: Dynamics of beams on non-uniform nonlinear foundations subjected to moving loads. Comput. Struct. 148, 26–34 (2015)

    Article  Google Scholar 

  11. Shadnam, M.R., Rofooei, F.R., Mehri, B.: Dynamics of nonlinear plates under moving loads. Mech. Res. Commun. 28(4), 453–461 (2001)

    Article  MATH  Google Scholar 

  12. Michaltsos, G., Sophianapoulos, D., Kounadis, A.N.: The effect of a moving mass and other parameters on the dynamic response of a simply supported beam. J. Sound Vib. 191(3), 357–362 (1996)

    Article  MATH  Google Scholar 

  13. Cojocaru, E.C., Irschik, H., Gattringer, H.: Dynamic response of an elastic bridge due to a moving elastic beam. Comput. Struct. 82, 931–943 (2004)

    Article  Google Scholar 

  14. Shadnam, M.R., Mofid, M., Akin, J.E.: On the dynamic response of rectangular plate with moving mass. Thin-Walled Struc. 39, 797–806 (2001)

    Article  Google Scholar 

  15. Emailzaseh, E., Ghorashi, M.: Vibration analysis of beams traversed by uniform partially distributed moving masses. J. Sound Vib. 188(1), 9–16 (1995)

    Google Scholar 

  16. Metrikine, A.V., Verichev, S.N.: Instability of vibrations of a moving two-mass oscillator on a flexibly supported Timoshenko beam. Arch. Appl. Mech. 71, 613–624 (2001)

    Article  MATH  Google Scholar 

  17. Siddiqui, S.A.Q., Golnaraghi, M.F., Heppler, G.R.: Large free vibrations of a beam carrying a moving mass. Int. J. Nonlinear Mech. 38, 1481–1493 (2003)

    Article  MATH  Google Scholar 

  18. Bilello, C., Bergman, L.A., Kuchma, D.: Experimental investigation of a small-scale bridge model under a moving mass. ASCE J. Struct. Eng. 130(5), 799–804 (2004)

    Article  Google Scholar 

  19. Michaltsos, G.T.: Dynamic behavior of a single beam subjected to loads moving with variable speeds. J. Sound Vib. 258(5), 359–372 (2002)

    Article  Google Scholar 

  20. Lee, H.P.: On the dynamic behavior of a beam with an accelerating mass. Arch. Appl. Mech. 65, 564–571 (1995)

    Article  MATH  Google Scholar 

  21. Oni, S.T., Omolofe, B.: Dynamic response of prestressed Rayleigh beam resting on elastic foundation and subjected to masses traveling at varying velocity. J. Vib. Acoust. 133, 041005 (2011)

    Article  Google Scholar 

  22. Wang, Y.M.: The dynamical analysis of a finite inextensible beam with an attached accelerating mass. Int. J. Solids Struct. 35, 831–854 (1998)

    Article  MATH  Google Scholar 

  23. Pu, J., Liu, P.: Numerical calculation of dynamic response for multi-span non-uniform beam subjected to moving mass with friction. J. Eng. 2, 367–377 (2010)

    Article  Google Scholar 

  24. Esen, I.: Dynamic response of a beam due to an accelerating moving mass using moving finite element approximation. Math. Comput. Appl. 16(1), 171–182 (2011)

    MathSciNet  Google Scholar 

  25. Abu-Hilal, M.: Vibration of beams with general boundary conditions due to a moving random load. Arch. Appl. Mech. 72, 637–650 (2003)

    Article  MATH  Google Scholar 

  26. Abu Hilal, M., Zibdeh, H.S.: Vibration analysis of beams with general boundary conditions traversed by a moving force. J. Sound Vib. 229(2), 377–388 (2000)

    Article  Google Scholar 

  27. Han, S.M., Benaroya, H.: Non-linear coupled transverse and axial vibration of a compliant structure, part 1: formulation and free vibration. J. Sound Vib. 237(5), 837–873 (2000)

    Article  Google Scholar 

  28. Mashadi, B., Crolla, D.: Vehicle Powertrain Systems. Wiley, London (2012)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111, Esfahān, Iran

    A. H. Karimi & S. Ziaei-Rad

Authors
  1. A. H. Karimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Ziaei-Rad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. H. Karimi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karimi, A.H., Ziaei-Rad, S. Nonlinear coupled longitudinal–transverse vibration analysis of a beam subjected to a moving mass traveling with variable speed. Arch Appl Mech 85, 1941–1960 (2015). https://doi.org/10.1007/s00419-015-1028-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-015-1028-1

Keywords

Search

Navigation