Skip to main content
SpringerLink
Log in

Equivalent stiffness of the saturated poro-elastic half space interacting with an infinite beam to harmonic moving loads

  • Published:
Journal of Shanghai Jiaotong University (Science) Aims and scope Submit manuscript

Abstract

The expression of the equivalent stiffness of the saturated poro-elastic half space interacting with an infinite beam to harmonic moving loads is obtained via the Fourier transformation method in the frequency wave number domain. Based on the obtained equivalent stiffness, the frequency wave number domain solution of the beam-half-space system is obtained by the compatibility condition between the beam and the half space. Critical velocity of harmonic moving loads along an infinite Euler-Bernoulli elastic beam is determined. The time domain solutions for the beam and the saturated poro-elastic half space are derived by means of the inverse Fourier transformation method. Also, the influences of the load speed, frequency and material parameters of the poro-elastic half space on the responses of the beam are investigated. Numerical results show that the frequency corresponding to the maximum deflection and bending moment increases with increasing load speed. Moreover, it can be seen that at higher frequencies, the dynamic response is independent of the load speed. The present results also show that for a beam overlying a saturated poro-elastic half space, there still exist critical velocities even when the load velocity is larger than the shear wave speed of the medium.

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. Metrikine A V, Dieterman H A. Three-dimensional vibrations of a beam on and elastic half-space: Resonance interaction of vertical longitudinal and lateral beam waves [J]. Journal of Applied Mathematics and Mechanics, 1997, 64(4): 951–956.

    MATH  Google Scholar 

  2. Lipen A B, Chigarev A V. The displacements in an elastic half-space when a load moves along a beam lying on its surface [J]. Journal of Applied Mathematics and Mechanics, 1998, 62(5): 791–796.

    Article  Google Scholar 

  3. Sheng X, Jones C J C, Petyt M. Ground vibration generated by a harmonic load acting on a railway track [J]. Journal of Sound and Vibration, 1999, 225(1): 3–28.

    Article  Google Scholar 

  4. Madshus C, Kaynia A M. High-speed railway lines on soft ground: Dynamic behavior at critical train speed [J]. Journal of Sound and Vibration, 2000, 231(3): 689–701.

    Article  Google Scholar 

  5. Takemiya H. Simulation of track-ground vibrations due to a high-speed train: The case of X-2000 at Ledsgard [J]. Journal of Sound and Vibration, 2003, 261(3): 503–526.

    Article  Google Scholar 

  6. Kargarnovin M H, Younesian D. Dynamics of Timoshenko beams on Pasternak foundation under moving load [J]. Mechanics Research Communications, 2004, 31(6): 713–723.

    Article  MATH  Google Scholar 

  7. Metrikine A V, Popp K. Steady-state response of an elastic beam on a visco-elastic layer under moving load [J]. Archive of Applied Mechanics, 2000, 70(6): 399–408.

    Article  MATH  Google Scholar 

  8. 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 [J]. International Journal of Solids and Structures, 2003, 40(21): 5723–5752.

    Article  MATH  Google Scholar 

  9. Auersch L. The excitation of ground vibration by rail traffic: Theory of vehicle-track-soil interaction and measurements on high-speed lines [J]. Journal of Sound and Vibration, 2005, 284(1): 103–132.

    Article  Google Scholar 

  10. Auersch L. Dynamics of the railway track and the underlying soil: The boundary-element solution, theoretical results and their experimental verification [J]. Vehicle System Dynamics, 2005, 43(9): 671–695.

    Article  Google Scholar 

  11. Jin B. Dynamic displacement of an infinite beam on a poroelastic half space due to a moving oscillating load [J]. Archive of Applied Mechanics, 2004, 74(3–4): 277–287.

    MATH  Google Scholar 

  12. Biot M A. Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range [J]. Journal of the Acoustical Society of America, 1956, 28(2): 168–178.

    Article  MathSciNet  Google Scholar 

  13. Biot M A. Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range [J]. Journal of the Acoustical Society of America, 1956, 28(2): 179–191.

    Article  MathSciNet  Google Scholar 

  14. Biot M A. Mechanics of deformation and acoustic propagation in porous media [J]. Journal of Applied Psychology, 1962, 33(4): 1482–1498.

    MATH  MathSciNet  Google Scholar 

  15. Johnson D L, Koplik J, Dashen R. Theory of dynamic permeability and tortuosity in fluid-saturated porous-media [J]. Journal of Fluid Mechanics, 1987, 176: 379–402.

    Article  MATH  Google Scholar 

  16. Xu B, Lu J F, Wang J H. Dynamic response of a layered and water-saturated poro-elastic half-space subjected to a moving load [J]. Computer and Geotechnics, 2008, 35(1): 1–10.

    Article  Google Scholar 

  17. Deresiewicz H, Skalak R. On uniqueness in dynamic poroelasticity [J]. Bulletin of the Seismological Society of America, 1963, 53(4): 783–788.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Shanghai Jiaotong University, Shanghai, 200240, China

    Zhi-fan Xia  (夏志凡), Jian-hua Wang  (王建华) & Bin Xu  (徐 斌)

  2. Department of Civil Engineering, Nanchang Institute of Technology, Nanchang, 330099, China

    Zhi-fan Xia  (夏志凡) & Bin Xu  (徐 斌)

  3. Department of Civil Engineering, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

    Jian-fei Lu  (陆建飞)

Authors
  1. Zhi-fan Xia  (夏志凡)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian-hua Wang  (王建华)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bin Xu  (徐 斌)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jian-fei Lu  (陆建飞)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian-hua Wang  (王建华).

Additional information

Foundation item: the National Natural Science Foundation of China (No. 50679041) and the Foundation of Jiangxi Educational Committee (No. GJJ09367)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xia, Zf., Wang, Jh., Xu, B. et al. Equivalent stiffness of the saturated poro-elastic half space interacting with an infinite beam to harmonic moving loads. J. Shanghai Jiaotong Univ. (Sci.) 14, 385–392 (2009). https://doi.org/10.1007/s12204-009-0385-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12204-009-0385-8

Key words

CLC number

Search

Navigation