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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. G. Gorshkov, A. L. Medvedskii, L. N. Rabinskii, and D. V. Tarlakovskii, Waves in Continua [in Russian], FIZMATLIT, Moscow (2004).
A. G. Gorshkov and D. V. Tarlakovskii, Dynamic Contact Problems with Moving Boundaries [in Russian], FIZMATLIT, Moscow (1995).
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).
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).
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).
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).
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).
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).
Author information
Authors and Affiliations
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 2, pp. 157–163, April–June, 2013.
Rights and permissions
About this article
Cite this article
Igumnov, L.A., Okonechnikov, A.S., Tarlakovskii, D.V. et al. Plane Nonstationary Problem of Motion of the Surface Load Over an Elastic Half Space. J Math Sci 203, 193–201 (2014). https://doi.org/10.1007/s10958-014-2100-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-014-2100-z