Skip to main content
Log in

Propagation of unsteady waves in an elastic layer

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

We consider a plane problem of propagation of unsteady waves in a plane layer of constant thickness filled with a homogeneous linearly elastic isotropic medium in the absence of mass forces and with zero initial conditions. We assume that, on one of the layer boundaries, the normal stresses are given in the form of the Dirac delta function, the tangential stresses are zero, and the second boundary is rigidly fixed. The problem is solved by using the Laplace transform with respect to time and the Fourier transform with respect to the longitudinal coordinate. The normal displacements at an arbitrary point are obtained in the form of finite sums.

This is a preview of subscription content, log in via an institution to check access.

Access this article

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. A. G. Gorshkov, A. L. Medvedskii, L. N. Rabinskii, and D. V. Tarlakovskii, Waves in Continuous Media (Fizmatlit, Moscow, 2004) [in Russian].

    Google Scholar 

  2. A. G. Gorshkov and D. V. Tarlakovskii, Dynamic Contact Problems with Moving Boundaries (Nauka, Fizmatlit, Moscow, 1995) [in Russian].

    MATH  Google Scholar 

  3. L. I. Slepyan and Yu. S. Yakovlev, Integral Transforms in Unsteady Problems in Mechanics (Sudostroenie, Leningrad, 1980) [in Russian].

    Google Scholar 

  4. V. A. Vestyak and D. V. Tarlakovskii, “Nonstationary Surface Influence Functions for Electromagnetoelastic Half-Plane,” in Proc. 15th Intern. Symp. “Dynamical and Technological Problems of Structural and Continuum Mechanics” dedicated to A. G. Gorshkov, Vol. 1 (“PARADIZ” Press, Moscow, 2009), pp. 43–44.

    Google Scholar 

  5. E. L. Kuznetsova and D. V. Tarlakovskii, “Explicit Form of the Lamb Problem Solution at an Arbitrary Point of the Half-Space,” in Proc. 12th Intern. Symp. “Dynamical and Technological Problems of Structural and Continuum Mechanics,” Selected papers (Izd-vo MAI, Moscow, 2006), pp. 104–120.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. L. Kuznetsova.

Additional information

Original Russian Text © E.L. Kuznetsova, D.V. Tarlakovskii, G.V. Fedotenkov, 2011, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2011, No. 5, pp. 144–152.

About this article

Cite this article

Kuznetsova, E.L., Tarlakovskii, D.V. & Fedotenkov, G.V. Propagation of unsteady waves in an elastic layer. Mech. Solids 46, 779–787 (2011). https://doi.org/10.3103/S0025654411050128

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654411050128

Keywords

Navigation