Advertisement

Journal of Mathematical Sciences

, Volume 203, Issue 2, pp 193–201 | Cite as

Plane Nonstationary Problem of Motion of the Surface Load Over an Elastic Half Space

  • L. A. Igumnov
  • A. S. Okonechnikov
  • D. V. Tarlakovskii
  • G. V. Fedotenkov
Article

We study the response of an elastic half space to the action of a normal concentrated load moving along its boundary. In the general case, the law of motion of the load is arbitrary. The solution of the problem is based on the principle of superposition. We construct a one-dimensional integral representation of the solution. The results are obtained for the case of uniform motion of the load. We show the dependence of the solution on the velocity of motion of the load, reveal singularities of the solution, and present graphic results.

Keywords

Rayleigh Wave Half Plane Normal Displacement Elastic Half Space Influence Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. G. Gorshkov, A. L. Medvedskii, L. N. Rabinskii, and D. V. Tarlakovskii, Waves in Continua [in Russian], FIZMATLIT, Moscow (2004).Google Scholar
  2. 2.
    A. G. Gorshkov and D. V. Tarlakovskii, Dynamic Contact Problems with Moving Boundaries [in Russian], FIZMATLIT, Moscow (1995).Google Scholar
  3. 3.
    Yu. D. Kaplunov, Nonstationary Dynamics of an Elastic Half Plane under the Action of a Moving Load [in Russian], Preprint No. 277, Institute for Problems in Mechanics, Academy of Sciences of the USSR (1986).Google Scholar
  4. 4.
    Yu. V, Mastinovskii and A. V. Zasovanko, “Nonstationary deformation of a single-span beam under the action of a moving load,” Novi Mater. Tekhnol. Metallurh. Mashynobud., No. 2, 40–43 (2008).Google Scholar
  5. 5.
    D. D. Ang, “Transient motion of a line load on the surface of an elastic half space,” Quart. Appl. Math., 18, No. 3, 251–256 (1960).MathSciNetGoogle Scholar
  6. 6.
    N. Higuchi and K.-I. Hirashima, “Unsteady stresses produced in an elastic half plane by moving loads,” Theor. Appl. Mech. (Proc. of the 27th Jap. Nat. Congr. Appl. Mech., Tokyo, 1977), 27, 359–370 (1979).Google Scholar
  7. 7.
    M. Mitra, “Note on the disturbance produced in an elastic half space by transient pressure applied over a portion of the boundary,” Proc. Natl. Acad. Sci. India. A, A28, No. 1, 199–205 (1962).Google Scholar
  8. 8.
    S. Nath and P. R. Sengupta, “Steady-state response to moving loads in an elastic solid media,” Indian J. Pure Appl. Math., 30, No. 3, 317–327 (1999).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • L. A. Igumnov
    • 1
  • A. S. Okonechnikov
    • 1
  • D. V. Tarlakovskii
    • 1
  • G. V. Fedotenkov
    • 1
  1. 1.Moscow Aviation Institute (National Research University)MoscowRussia

Personalised recommendations