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Disturbance produced in an elastic half-space by impulsive normal pressure

Published online by Cambridge University Press:  24 October 2008

M. Mitra
M. Mitra
Affiliation:
Jadavpur University, Calcutta
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Extract

1. Introduction. The disturbance produced in an elastic half-space by different types of buried sources have been studied by various authors. However, the only exact solutions of problems for the half-space in which the disturbance is produced by impulsive surface tractions are due to Pekeris (9) and Chao (4), though for the half-plane such problems have been studied by de Hoop (5), Ang (1) and Mitra (8). Pekeris (9) evaluated the surface displacement produced by a normal point load on the surface using a method of inversion of the operational solution developed earlier (Bateman & Pekeris (2)). A finite pressure-area, however, represents physical situations better than a point load. In this paper, the displacement produced in the half-space by uniform impulsive pressure acting over a circular portion of the surface has been obtained in terms of definite integrals. On the surface, the displacement has been split up into a number of terms some of which represent the P-wave contribution, while others give the Rayleigh-wave contribution to the displacement. The method of solution involves the use of integral transforms and Cagniard's (3) method; Pekeris's method is not applicable in this case since the appropriate transformation of an integral along the real axis to one along the imaginary axis cannot be carried out.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 3 , July 1964 , pp. 683 - 696
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

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