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.
- 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 75767, DOI https://doi.org/10.1007/BF02843720
- J. Cole and J. Huth, Stresses produced in a half plane by moving loads, J. Appl. Mech. 25 (1958), 433–436. MR 0099772
- Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774
L. Cagniard, Réflexion et réfraction des ondes séismiques progressives, Gauthier-Villars, Paris, 1939, p. 55
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
- Dang Dinh Ang, Elastic waves generated by a force moving along a crack, J. Math. and Phys. 38 (1959/60), 246–256. MR 112396
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)
J. D. Cole and J. Huth, Stresses produced in a half-plane by moving loads, J. Appl. Mech. 25, 433–36 (Dec. 1958)
P. M. Morse and H. Feshbach, Methods of theoretical physics, vol. 1, McGraw-Hill, 1953, pp. 142–148
L. Cagniard, Réflexion et réfraction des ondes séismiques progressives, Gauthier-Villars, Paris, 1939, p. 55
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
D. D. Ang, Elastic waves generated by a force moving along a crack, J. Math. Phys. 38, 246–256 (1960)
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Article copyright:
© Copyright 1960
American Mathematical Society
