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Parametrically Excited Vibration of a Timoshenko Beam on Random Viscoelastic Foundation jected to a Harmonic Moving Load

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An Erratum to this article was published on 25 January 2007

Abstract

The vibration response of a Timoshenko beam supported by a viscoelastic foundation with randomly distributed parameters along the beam length and jected to a harmonic moving load, is studied. By means of the first-order two-dimensional regular perturbation method and employing appropriate Green's functions, the dynamic response of the beam consisting of the mean and variance of the deflection and of the bending moment are obtained analytically in integral forms. Results of a field measurement for a test track are utilized to model the uncertainty of the foundation parameters. A frequency analysis is carried out and the effect of the load speed on the response is studied. It is found that the covariance functions of the stiffness and the loss factor both have the shape of an exponential function multiplied by a cosine function. Furthermore, it is shown that in each frequency response there is a peak value for the frequency, which changes inversely with the load speed. It is also found that the peak value of the mean and also standard deviation of the deflection and bending moment can be a decreasing or increasing function of the load speed depending on its frequency.

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References

  1. Fryba, L., Vibration of Solids and Structures Under Moving Loads, Thomas Telford, London, 1999.

    Google Scholar 

  2. Kargarnovin, M. H., Younesian, D., Thompson, D. J., and Jones, C. J. C., ‘Response of beams on nonlinear viscoelastic foundations to harmonic moving loads’, Computers & Structures 83(23), 2005, 1865–1877.

    Article  Google Scholar 

  3. Chen, Y.-H., Huang, Y.-H., and Shih, C.-T., ‘Response of an infinite Timoshenko beam on a viscoelastic foundation to a harmonic moving load’, Journal of Sound and Vibration 241(5), 2001, 809–824.

    Article  Google Scholar 

  4. Koh, C. G., Ong, J. S. Y, Chua, D. K. H., and Feng, J., ‘Moving element method for train-track dynamics’, International Journal for Numerical Methods in Engineering 56(11), 2003, 1549–1567.

  5. Kim, S-M., ‘Stability and dynamic response of Rayleigh beam–columns on an elastic foundation under moving loads of constant amplitude and harmonic variation’, Engineering Structures 27(6), 2005, 869–880

    Google Scholar 

  6. Fryba, L., Nakagiri, S., and Yoshikawa, N., ‘Stochastic finite elements for a beam on a random foundation with uncertain damping under a moving force’, Journal of Sound and Vibration 163(1), 1993, 31–45.

    Article  MATH  Google Scholar 

  7. Naprstk, J. and Fryba, L., ‘Interaction of a Long Beam on Stochastic Foundation With a Moving Random Load’, in Structural Dynamics: Recent Advances, The Institute of Sound and Vibration Research, Southampton, 1993.

  8. Naprstk, J. and Fryba, L., ‘Stochastic modelling of track and its substructure In: interaction of railway vehicles with the track and its substructure’, Supplement to Vehicle System Dynamics 24, 1995, 297–310.

    Google Scholar 

  9. Andersen, L. and Nielsen, R. K., ‘Vehicle moving along a beam on a random modified Kelvin foundation’, in Proceeding of 8th International Congress on Sound and Vibration ICSV8, Hong Kong, 2001.

  10. Andersen, L. and Nielsen, R. K., ‘Vibration of track caused by variation of the foundation stiffness’, Probabilistic Engineering Mechanics 18, 2003, 171–184.

    Article  Google Scholar 

  11. Oscarsson, J., ‘Dynamic train/track interaction – linear and non-linear track models with property scatter’, Ph.D Thesis, Department of Solid Mechanics, Chalmers University of Technology, Goteborg, 2001.

  12. Sheng, X., Jones C.J.C. and Thompson D.J., ‘A theoretical study on the influence of the track on train-induced ground vibration’, Journal of Sound and Vibration 272(3–5), 2004, 909–936.

    Article  Google Scholar 

  13. Sheng, X., Jones, C. J. C., and Thompson, D. J., ‘A theoretical model for ground vibration from trains generated by vertical track irregularities’, Journal of Sound and Vibration 272(3–5), 2004, 937–965.

    Article  Google Scholar 

  14. Thompson, D. J., ‘The influence of the contact zone on the excitation of wheel/rail noise’, Journal of Sound and Vibration 267(3), 2003, 523–535.

    Article  Google Scholar 

  15. Wu, T. X. and Thompson, D. J., ‘On the impact noise generation due to a wheel passing over rail joints’, Journal of Sound and Vibration 267(3), 2003, 485–496.

    Article  Google Scholar 

  16. Kargarnovin, M. H. and Younesian, D., ‘Dynamic response analysis of Timoshenko beam on viscoelastic foundation under an arbitrary distributed harmonic moving load’, in Proceeding of the 5th International Conference on Structural Dynamics, EURODYN, Munich, 2002.

  17. Kargarnovin, M. H. and Younesian, D., ‘Dynamics of Timoshenko beams on Pasternak foundation under moving load’, Mechanics Research Communication 31(6), 2004, 713–723.

    Article  MATH  Google Scholar 

  18. Nyfeh, A. H. and Mook, D., Nonlinear Oscillations, Wiley, New York, 1979.

    Google Scholar 

  19. Younesian, D., Esmailzadeh, E., and Sedaghati, R., ‘Existence of periodic solutions for the generalized form of Mathieu equation’, Nonlinear Dynamics 39, 2004, 335–348.

    Article  MathSciNet  Google Scholar 

  20. Rand, R., Guennoun, K., and Belhaq, M., ‘Resonance in the quasi-periodic Mathieu equation’, Nonlinear Dynamics 31, 2003, 367–374.

    Article  MathSciNet  MATH  Google Scholar 

  21. Guennoun, K., Houssni, M., and Belhaq, M., ‘Quasi-Periodic solutions and stability for a weakly damped nonlinear quasi-periodic Mathieu equation’, Nonlinear Dynamics 27, 2002, 211–236.

    Article  MathSciNet  MATH  Google Scholar 

  22. Solnes, J., Stochastic Processes and Random Vibration, Wiley, New York, 1997.

    Google Scholar 

  23. George, R., ‘Railway ballast quality monitoring’, Technical report, Institute of Sound and Vibration Research, University of Southampton, 2003.

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Authors and Affiliations

  1. Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran

    D. Younesian

  2. Center of Excellence in Design, Robotics and Automation, Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran

    M. H. Kargarnovin

  3. Institute of Sound and Vibration Research (ISVR), University of Southampton, Southampton, UK

    D. J. Thompson & C. J. C. Jones

Authors
  1. D. Younesian
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  2. M. H. Kargarnovin
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  3. D. J. Thompson
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  4. C. J. C. Jones
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Corresponding author

Correspondence to M. H. Kargarnovin.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s11071-006-9159-0.

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Younesian, D., Kargarnovin, M.H., Thompson, D.J. et al. Parametrically Excited Vibration of a Timoshenko Beam on Random Viscoelastic Foundation jected to a Harmonic Moving Load. Nonlinear Dyn 45, 75–93 (2006). https://doi.org/10.1007/s11071-006-1460-4

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  • DOI: https://doi.org/10.1007/s11071-006-1460-4

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