In the context of wave propagation in damaged (elastic) solids, an analytical approach is developed to study normal penetration of a longitudinal plane wave into a periodic array of rectangular defects. Reducing the problem to some integral equations holding over the base and height of the openings, a direct numerical method is applied to give a complete solution for various exact or approximated forms. Several figures show the peculiarities of the structure and lead to physical conclusions.
Issue Section:
Technical Papers
1.
Achenbach
, J. D.
, and Kitahara
, M.
, 1987
, “Harmonic Waves in a Solid With a Periodic Distribution of Spherical Cavities
,” J. Acoust. Soc. Am.
, 81
, pp. 595
–599
.2.
Angel
, Y. C.
, and Achenbach
, J. D.
, 1987
, “Harmonic Waves in an Elastic Solid Containing a Doubly Periodic Array of Cracks
,” Wave Motion
, 9
, pp. 377
–385
.3.
Achenbach
, J. D.
, and Li
, Z. L.
, 1986
, “Reflection and Transmission of Scalar Waves by a Periodic Array of Screens
,” Wave Motion
, 8
, pp. 225
–234
.4.
Angel
, Y. C.
, and Achenbach
, J. D.
, 1985
, “Reflection and Transmission of Elastic Waves by a Periodic Array of Cracks
,” ASME J. Appl. Mech.
, 52
, pp. 33
–41
.5.
Achenbach
, J. D.
, and Li
, Z. L.
, 1986
, “Propagation of Horizontally Polarized Transverse Waves in a Solid With a Periodic Distribution of Cracks
,” Wave Motion
, 8
, pp. 371
–379
.6.
Malin
, V. V.
, 1963
, “Theory of Strip Grating of Finite Period
,” Radio Eng. Electron. Phys.
, 8
, pp. 185
–193
.7.
Jones, D. S., 1986, Acoustic and Electromagnetic Waves, Clarendon Press, Oxford.
8.
Collin, R. E., 1991, Field Theory of Guided Waves, 2nd Ed., IEEE Press, New York.
9.
Lewin, L., 1975, Theory of Waveguides, Butterworth, London.
10.
Twersky
, V.
, 1986
, “On the Scattering of Waves by an Infinite Grating
,” IEEE Trans. Antennas Propag.
, 4
, pp. 330
–345
.11.
Miles
, J. W.
, 1982
, “On Rayleigh Scattering by a Grating
,” Wave Motion
, 4
, pp. 285
–292
.12.
Scarpetta
, E.
, and Sumbatyan
, M. A.
, 1995
, “Explicit Analytical Results for One-Mode Normal Reflection and Transmission by a Periodic Array of Screens
,” J. Math. Anal. Appl.
, 195
, pp. 736
–749
.13.
Scarpetta
, E.
, and Sumbatyan
, M. A.
, 1996
, “Explicit Analytical Results for One-Mode Oblique Penetration Into a Periodic Array of Screens
,” IMA J. Appl. Math.
, 56
, pp. 109
–120
.14.
Scarpetta
, E.
, and Sumbatyan
, M. A.
, 1997
, “On Wave Propagation in Elastic Solids With a Doubly Periodic Array of Cracks
,” Wave Motion
, 25
, pp. 61
–72
.15.
Scarpetta
, E.
, and Sumbatyan
, M. A.
, 2000
, “On the Oblique Wave Penetration in Elastic Solids With a Doubly Periodic Array of Cracks
,” Q. Appl. Math.
, 58
, pp. 239
–250
.16.
Scarpetta, E., and Sumbatyan, M. A., “Wave Penetration Through Elastic Solids With a Periodic Array of Rectangular Flaws,” MECCANICA, in press.
17.
Shenderov
, Ye. L.
, 1970
, “Propagation of Sound Through a Screen of Arbitrary Wave Thickness With Gaps
,” Sov. Phys. Acoust.
, 16
, No. 1
No. 1
.18.
Solokin
, N. V.
, and Sumbatyan
, M. A.
, 1994
, “Artificial Layer
,” Res. Nondestruct. Eval.
, 6
, pp. 19
–34
.19.
Achenbach, J. D., 1973, Wave Propagation in Elastic Solids, North-Holland, Amsterdam.
20.
Gel’fand, L. M., and Shilov, G. E., 1964, Generalized Functions, Vol. 1, Academic Press, San Diego.
21.
Banerjee, P. K., and Butterfield, R., 1981, Boundary Element Methods in Engineering Sciences, McGraw-Hill, New York.
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