Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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] I. N. Sneddon, The stress produced by a pulse of pressure moving along the surface of a semi-infinite solid, R. C. Circ. Mat. Palermo, 2, 57-62 (1952) MR 0075767
  • [2] J. D. Cole and J. Huth, Stresses produced in a half-plane by moving loads, J. Appl. Mech. 25, 433-36 (Dec. 1958) MR 0099772
  • [3] P. M. Morse and H. Feshbach, Methods of theoretical physics, vol. 1, McGraw-Hill, 1953, pp. 142-148 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] D. D. Ang, Elastic waves generated by a force moving along a crack, J. Math. Phys. 38, 246-256 (1960) 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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