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.

**[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