The reflection and transmission of ultrasonic waves by an array of planar defects are investigated using the cavity-opening tensor (COT) method, whereby each defect or flaw can be simulated as a three-dimensional tensor in terms of the displacement distribution over the surface of the defect. The closed-form expressions of reflection and transmission coefficients represented by one set of COTs are derived, and the interaction factors of COTs are computed using the boundary integral equation with the approximate integral only on the single defect surface. Moreover, the analytical expressions of scattered fields at a distance from the defects are given by the representation of COT. As compared with the conventional numerical method, the COT method greatly simplifies the calculations, and also makes it possible to more efficiently characterize defects with more complicated distributions.

Issue Section:
Research Papers
Topics:
Cavities, Reflection, Tensors, Ultrasonic waves, Displacement, Integral equations, Numerical analysis
1.
Achenbach
J. D.
, and
Kitahara
M.
,
1986
, “
Reflection and transmission of an obliquely incident wave by an array of a spherical cavities
,”
J. Acoust. Soc. Am.
, Vol.
80
, pp.
1209
–
1214
.
2.
Achenbach
J. D.
, and
Kitahara
M.
,
1987
, “
Hormonic waves in a solid with a periodic distribution of spherical cavities
,”
J. Acoust. Soc. Am.
, Vol.
81
, pp.
595
–
598
.
3.
Achenbach
J. D.
, and
Li
Z.
,
1986
, “
Propagation of horizontally polarized transverse waves in a solid with a periodic distribution of cracks
,”
Wave Motion
, Vol.
8
, pp.
371
–
379
.
4.
Angel
Y. C.
, and
Achenbach
J. D.
,
1985
, “
Reflection and transmission of elastic wave by a periodic array of cracks: oblique incidence
,”
Wave Motion
, Vol.
7
, pp.
375
–
397
.
5.
Angel
Y. C.
, and
Achenbach
J. D.
,
1987
, “
Hormonic waves in an elastic solid containing a doubly periodic array of cracks
,”
Wave Motion
, Vol.
9
, pp.
377
–
385
.
6.
Baik
J.-M.
, and
Thompson
R. B.
,
1984
, “
Ultrasonic scattering from imperfect interface: A quasi-static model
,”
J. Nondestr. Eval.
, Vol.
4
, pp.
177
–
196
.
7.
Delph
T. J.
,
Hermann
G.
, and
Kaul
R. K.
,
1978
, “
Harmonic Wave Propagation in Aperiodically Layered, Infinite Elastic Body: Antiplane Strain
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
45
, pp.
343
–
349
.
8.
Delph
T. J.
,
Hermann
G.
, and
Kaul
R. K.
,
1979
, “
Harmonic Wave Propagation in a Periodically Layered, Infinite Elastic Body: Plane Strain, Analytical Results
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
46
, pp.
343
–
349
.
9.
Sotiropoulos
D. A.
, and
Achenbach
J. D.
,
1988
, “
Reflection of elastic wave by a distribution of coplanar cracks
,”
J. Acoust, Soc. Am.
, Vol.
84
, pp.
752
–
759
.
10.
Margetan
F. J.
,
Thompson
R. B.
,
Rose
J. H.
, and
Gray
T. A.
,
1992
, “
The interaction of ultrasound with imperfect interface: Experimental studies of model structures
,”
J. Nondestr. Eval.
, Vol.
11
, pp.
109
–
126
.
11.
Mikata
Y.
,
1995
, “
SH-Waves in a Medium Containing a Disordered Periodic Array of Cracks
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
62
, pp.
312
–
319
.
12.
Mikata
Y.
, and
Achenbach
J. D.
,
1988
a, “
Interaction of harmonic wave with a periodic array of inclined cracks
,”
Wave Motion
, Vol.
10
, pp.
59
–
72
.
13.
Mikata
Y.
, and
Achenbach
J. D.
,
1988
b, “
Reflection and transmission of an infinite array of randomly oriented crack
,”
J. Acoust. Soc. Am.
, Vol.
83
, pp.
38
–
45
.
14.
Mikata
Y.
,
1993
, “
Reflection and Transmission by a Periodic Array of Coplanar Crack: Normal and Oblique Incidence
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
60
, pp.
911
–
919
.
15.
Xu
Y.
,
1992
, “
Reflection and Transmission of Plane Wave by an Array of Cavities in the Interface of Two Solids
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
59
, pp.
102
–
108
.
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