Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Transient motion of a line load on the surface of an elastic half-space


Author: Dang Dinh Ang
Journal: Quart. Appl. Math. 18 (1960), 251-256
MSC: Primary 73.00
DOI: https://doi.org/10.1090/qam/114399
MathSciNet review: 114399
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Abstract: The present paper studies the wave patterns generated in an elastic half-space by a line load moving on its surface with a velocity varying as a step function of time. The solution given in closed form is obtained by means of Fourier integral equations techniques following a Laplace transformation with respect to the time variable. The inversion of the Laplace transforms is based on a trick due to Cagniard and De Hoop.


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  • [1] Ian N. Sneddon, The stress produced by a pulse of pressure moving along the surface of a semi-infinite solid, Rend. Circ. Mat. Palermo (2) 1 (1952), 57–62. MR 0075767, https://doi.org/10.1007/BF02843720
  • [2] J. Cole and J. Huth, Stresses produced in a half plane by moving loads, J. Appl. Mech. 25 (1958), 433–436. MR 0099772
  • [3] Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774
  • [4] L. Cagniard, Réflexion et réfraction des ondes séismiques progressives, Gauthier-Villars, Paris, 1939, p. 55
  • [5] A. T. De Hopp, Representation theorems for the displacement in an elastic solid and their application to elastodynamic diffraction, Thesis, Technische Hogeschool Te Delft, pp. 35-55, 1958
  • [6] Dang Dinh Ang, Elastic waves generated by a force moving along a crack, J. Math. and Phys. 38 (1959/1960), 246–256. MR 0112396

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DOI: https://doi.org/10.1090/qam/114399
Article copyright: © Copyright 1960 American Mathematical Society


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