SH-Waves in a Medium Containing a Disordered Periodic Array of Cracks

[+] Author and Article Information
Y. Mikata

Department of Mechanical Engineering, Old Dominion University, 238 Kaufman / Duckworth Hall, Norfolk, VA 23529

J. Appl. Mech 62(2), 312-319 (Jun 01, 1995) (8 pages) doi:10.1115/1.2895933 History: Received March 21, 1994; Revised October 04, 1994; Online October 30, 2007


Reflection and transmission of an SH-wave by a disordered periodic array of coplanar cracks is investigated, and subsequently its application to the dispersion and attenuation of an SH-wave in a disorderedly cracked medium is also treated. This is a stochastic boundary value problem. The formulation largely follows Mikata and Achenbach (1988b). The problem is formulated for an averaged scattered field, and the governing singular integral equation is derived for a conditionally averaged crack-opening displacement using a quasi-crystalline-like approximation. Unlike our previous study (Mikata and Achenbach, 1988b) where a point scatterer approximation was used for the regular part of the integral kernel, however, no further approximation is introduced. The singular integral equation is solved by an eigenfunction expansion involving Chebyschev polynomials. Numerical results are presented for the averaged reflection and transmission coefficients of zeroth order as a function of the wave number for normal incidence, a completely disordered crack spacing, and various values of the ratio of crack length and average crack spacing. Numerical results are also presented for the dispersion and attenuation of an SH-wave in a disorderedly cracked medium.

Copyright © 1995 by The American Society of Mechanical Engineers
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