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TECHNICAL PAPERS

In-Plane Wave Propagation Through Elastic Solids With a Periodic Array of Rectangular Defects

[+] Author and Article Information
E. Scarpetta

D.I.I.M.A., University of Salerno, 84084 Fisciano (SA), Italy

M. A. Sumbatyan

Research Institute of Mechanics and Applied Mathematics, Stachki Prospect 200/1, Rostov-on-Don 344090, Russia

J. Appl. Mech 69(2), 179-188 (Aug 06, 2001) (10 pages) doi:10.1115/1.1430235 History: Received April 02, 2001; Revised August 06, 2001
Copyright © 2002 by ASME
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References

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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.
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.
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.
Malin,  V. V., 1963, “Theory of Strip Grating of Finite Period,” Radio Eng. Electron. Phys., 8, pp. 185–193.
Jones, D. S., 1986, Acoustic and Electromagnetic Waves, Clarendon Press, Oxford.
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Lewin, L., 1975, Theory of Waveguides, Butterworth, London.
Twersky,  V., 1986, “On the Scattering of Waves by an Infinite Grating,” IEEE Trans. Antennas Propag., 4, pp. 330–345.
Miles,  J. W., 1982, “On Rayleigh Scattering by a Grating,” Wave Motion, 4, pp. 285–292.
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.
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.
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.
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.
Scarpetta, E., and Sumbatyan, M. A., “Wave Penetration Through Elastic Solids With a Periodic Array of Rectangular Flaws,” MECCANICA, in press.
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Figures

Grahic Jump Location
Normal penetration of a longitudinal plane wave into a periodic array of rectangular defects 2l×2(a−b)
Grahic Jump Location
Reflection coefficient |R| versus frequency parameter ak1(c2/c1=0.497,b/a=l/a=0.5). Line 1: exact solution (from 3×3 sytems (4.9), (4.10), (4.11), (4.17), (4.18), (4.19)); line 2: approximated solution gu≈0 (from 2×2 systems (4.9), (4.10), (4.17), (4.18)); line 3: approximated solution gu±,g1,2τ≈0(from Eqs. (4.9), (4.17)); line 4; low-frequency approximation (from formula (4.21)).
Grahic Jump Location
Reflection coefficient |R| versus frequency parameter ak1(c2/c1=0.497,l/a=0.5). Line 1: b/a=0.1; line 2: b/a=0.25; line 3: b/a=0.5; line 4: b/a=0.75; line 5: b/a=0.9.
Grahic Jump Location
Transmission coefficient |T| versus frequency parameter ak1(c2/c1=0.497,l/a=0.5). Line 1: b/a=0.1; line 2: b/a=0.25; line 3: b/a=0.5; line 4: b/a=0.75; line 5: b/a=0.9.
Grahic Jump Location
Transmission coefficient |T| versus relative opening b/a(c2/c1=0.497,l/a=0.5). Line 1: ak1=0.25; line 2: ak1=0.5; line 3: ak1=0.75; line 4: ak1=1.0; line 5: ak1=1.25.
Grahic Jump Location
Reflection coefficient |R| versus relative length of rectangles l/a(c2/c1=0.497,ak1=0.75). Line 1: b/a=0.25; line 2: b/a=0.5; line 3: b/a=0.75; line 4: b/a=0.9.
Grahic Jump Location
Reflection coefficient |R| versus relative length of rectangles l/a(c2/c1=0.497,b/a=0.5). Line 1: ak1=0.25; line 2: ak1=0.5; line 3: ak1=0.75; line 4: ak1=1.0; line 5: ak1=1.25.

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