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The far-field spectrum of the displacement generated by a sudden SH crack

CIRES UNIVERSITY OF COLORADO/NOAA, BOULDER, COLORADO 80302

Abstract

The far-field spectrum of the displacement caused by a two-dimensional SH crack (antiplane shear crack) that appears suddenly over a strip of width 2R is obtained in terms of the elliptic cylinder Mathieu functions. The amplitude spectrum of the displacement exhibits the following four features in terms of the normalized frequency h (h = R/ß where R is the half-width of the crack, is the circular frequency and ß is the shear-wave velocity): (1) for h < 1 the amplitude spectrum behaves as h^–1,2; (2) at h = 1 the amplitude spectrum has a corner frequency; (3) for h > 1 the amplitude spectrum behaves as h^–2; (4) the azimuthal dependence of the amplitude is like sin .

The first result is a consequence of the infinite area occupied by the crack. The corner frequency at h = 1 is smaller than the value proposed in other studies (e.g., Brune, 1970; Randall, 1973), and this is attributed to the two-dimensional nature of the problem. The high-frequency falloff of h^–2 is in agreement with the model of Brune (1970). The radiation pattern of sin is identical to that obtained by Burridge and Halliday (1971) for the same problem.

Footnotes

^* Present address: ARAMCO Overseas Co., Canterbury House, Sydenham Road, Croydon, Surrey, England.