Summary
In this paper the problem of disturbance in an elastic semi-infinite medium due to the torsional motion of a circular ring source on the free surface of a medium are studied. Two cases, when the medium is either homogeneous or inhomogeneous, are treated. In order to solve the problem, the Laplace transform and the Hankel transform and the Laplace inversion by Cagniard's method as modified byDe Hoop (1959) are applied. Finally, the integrals for displacement are evaluated numerically. The displacement on the free surface as a function of time is shown by means of graphs, in the case of both a homogeneous and an inhomogeneous medium, indicating clearly the variation in displacement due to the presence of an inhomogeneity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cagniard, L., Flinn, E. A. andDix, C. H. (1962),Reflection and refraction of progressive seismic waves, McGraw-Hill.
Chakraborty, S. K. andDe, T. K. (1971), Pure Appl. Geophys.85, 214–218.
De Hoop, A. T. (1959), Applied Scientific Research B8, 349–356.
Eason, G. (1964), Qtly. J. Mech. Appl. Math.17 Part 3, 279–292.
Erdelyi, A. et al. (1966),Higher transcendental functions, vol. 2, McGraw-Hill.
Gakenheimer, D. C. (1971), J. Appl. Mech. Trans. ASME38, 99–110.
Ghosh, M. L. (1971), Applied Scientific Research24, 149–167.
Jones, D. S. (1966),Generalized functions, McGraw-Hill.
Lamb, H. (1904), Phil. Trans. R. Soc. London A203, 1–42.
Mitra, M. (1964), Proc. Camb. Phil. Soc.60, 683–696.
Watson, G. N. (1966),A treatise on the theory of Bessel functions, 2nd ed., Chap. XI, University Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ghosh, M. Displacement produced in an elastic half-space by the impulsive torsional motion of a circular ring source. PAGEOPH 119, 102–117 (1980). https://doi.org/10.1007/BF00878725
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00878725