Abstract
In this study, dynamic response of a periodic viaduct to a moving loading is investigated. Based on the impulse response function of the viaduct, the time domain response of the periodic viaduct to a moving loading is represented by a Duhamel integral. Applying the Fourier transform to the time domain response, the frequency domain response of the viaduct is obtained. By means of the Floquet transform method, the frequency domain response of the viaduct is reduced to an integral of the frequency–wavenumber domain response function over the representative span of the viaduct. The frequency–wavenumber domain response function is then derived via the transfer matrix method. Applying the inverse Fourier transform to the frequency domain response, the time domain response of the viaduct is retrieved. Based on the proposed model, numerical results about the dynamic responses of the viaduct to the moving loading with different velocities in the frequency and time domains are presented. It is found that the resonance peak of the response of the viaduct most likely occurs in the passbands of the viaduct. When the velocity of the loading is small, the time domain response of the viaduct is almost symmetrical with respect to the arrival time of the loading. However, with increasing velocity, the response of the viaduct becomes asymmetrical with respect to the arrival time. When the velocity of the loading is large enough, the shock wave-like vibration occurs in the periodic viaduct. The mechanism responsible for the shock wave-like vibration in the periodic viaduct is proposed based on the energy bands of the periodic viaduct.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Filipov, A.P.: Steady state vibrations of an infinite beam on an elastic half-space subjected a moving load. Izvestija AN SSSR OTN Mehanika i Mashinostroenie 6, 97–105 (1961)
Labra, J.J.: An axially stressed railroad track on an elastic continuum subjected to a moving load. Acta Mech. 22, 113–129 (1975)
Dieterman, H.A., Metrikine, A.V.: The equivalent stiffness of a half-space interacting with a beam. Critical velocities of a moving load along the beam. Eur. J. Mech. A/Solids 15, 67–90 (1996)
Vostroukhov, A.V., Metrikine, A.V.: Periodically supported beam on a visco-elastic layer as a model for dynamic analysis of a high-speed railway track. Int. J. Solids Struct. 40, 5723–5752 (2003)
Dieterman, H.A., Metrikine, A.V.: Steady-state displacements of an elastic half- space due to a uniformly moving constant load. Eur. J. Mech. A/Solids 16, 295–306 (1997)
Cheng, C.C., Kuo, C.P., Yang, J.W.: Wavenumber-harmonic analysis of a periodically supported beam under the action of a convected loading. J. Vib. Acoust. 122, 272–280 (2000)
Sheng, X., Jones, C.J.C., Thompson, D.J.: Responses of infinite periodic structures to moving or stationary harmonic loads. J. Sound Vib. 282, 125–149 (2005)
Chebli, H., Othman, R., Clouteau, D.: Response of periodic structures due to moving loads. Comptes Rendus Mécanique 334, 347–352 (2006)
Chebli, H., Clouteau, D., Schmitt, L.: Dynamic response of high-speed ballasted railway tracks: 3D periodic model and in situ measurements. Soil Dyn. Earthq. Eng. 28, 118–131 (2008)
Ju, S.H.: Finite element analyses of wave propagations due to a high-speed train across bridges. Int. J. Numer. Methods Eng. 54, 1391–1408 (2002)
Wu, Y.S., Yang, Y.B.: Semi-analytical approach for analyzing ground vibrations caused by trains moving over elevated bridges with pile foundations. In: Bull, J.W. (ed.) Linear and Non-linear Numerical Analysis of Foundations, pp. 231–280. CRC Press, Boca Raton (2009)
Wu, Y.S., Yang, Y.B.: A semi-analytical approach for analyzing ground vibrations caused by trains moving over elevated bridges. Soil Dyn. Earthq. Eng. 24, 949–962 (2004)
Kittel, C., McEuen, P.: Introduction to Solid State Physics. pp. 409–539. Wiley, New York (1996)
Clouteau, D., Elhabre, M.L., Aubry, D.: Periodic BEM and FEM-BEM coupling. Comput. Mech. 25, 567–577 (2000)
Oppenheim, A.V., Willsky, A.S., Nawab, S.H.: Signals and Systems. Prentice Hall, Englewood Cliffs (1983)
Paz, M.: Structural Dynamics: Theory and Computation. Kluwer, Norwell, Massachusetts (1997)
Papoulis, A.: The Fourier Integral and Its Applications. McGraw Hill Book Company, New York (1962)
Graff, K.F.: Wave Motion in Elastic Solids. Clarendon Press, Oxford (1975)
Carcione, J.J.M.: Wave Fields in Real Media-Wave Propagation in Anisotropic, Anelastic and Porous Media. Elsevier, Oxford (2007)
Lu, J.F., Yuan, H.Y.: The sequence Fourier transform method for the analysis of a periodic viaduct subjected to non-uniform seismic waves. Acta Mech. 224, 2143–2168 (2013)
Mead, D.J.: Free wave propagation in periodically supported, infinite beams. J. Sound Vib. 11, 181–197 (1970)
Mead, D.J.: A general theory of harmonic wave propagation in linear periodic systems with multiple coupling. J. Sound Vib. 27, 235–260 (1973)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lu, JF., Zhong, L. & Zhang, R. Dynamic response of a periodic viaduct to a moving point loading. Arch Appl Mech 85, 149–169 (2015). https://doi.org/10.1007/s00419-014-0907-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-014-0907-1