 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 41, Issue 2 / 2006 | Next article >> |
| Edoardo Scarpetta and Vincenzo Tibullo, "In-plane problem for P-wave propagation through elastic solids with a periodic array of cracks: oblique incidence," Mech. Solids. 41 (2), 10-18 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
2 |
Pages |
10-18 |
| Title |
In-plane problem for P-wave propagation through elastic solids with a periodic array of cracks: oblique incidence |
| Author(s) |
Edoardo Scarpetta (Italy)
Vincenzo Tibullo (Italy) |
| Abstract |
In the context of wave propagation in damaged (elastic) solids, an analytical
method previously introduced for scalar problems, is now applied to study the
(vector) problem for oblique penetration of a longitudinal plane wave into a
periodic array of collinear cracks. The problem is reduced to integral equations
holding over the openings, an approximation of one-mode type leads to
analytical solutions and then to explicit representations for the scattering
parameters. Some graphs will finally compare our results with the numerical
ones obtained by other authors. |
| References |
| 1. | E. Scarpetta and M. A. Sumbtyan, "Explicit analytic results for one-mode
normal reflection and transmission by a periodic array of screens," J. Math.
Anal. Appl., Vol. 195, pp. 736-749, 1995. |
| 2. | E. Scarpetta and M. A. Sumbtyan, "Explicit analytic results for one-mode
oblique penetration into a periodic array of screens," IMA J. Appl. Math.,
Vol. 56, pp. 109-120, 1996. |
| 3. | E. Scarpetta and M. A. Sumbtyan, "On wave propagation in elastic solids
with a doubly periodic array of cracks," Wave Motion, Vol. 25, pp. 61-72,
1997. |
| 4. | E. Scarpetta and M. A. Sumbtyan, "On the oblique wave penetration in
elastic solids with a doubly periodic array of cracks," Quart. Appl. Math.,
Vol. 58, pp. 239-250, 2000. |
| 5. | V. V. Malin, "Theory of strip grating of finite period," Radio Eng.
Electron. Phys., Vol. 8, pp. 185-193, 1963. |
| 6. | P. M. Van den Berg and O.J. Voorman, "Diffraction by a grating of
cylinders with an arbitrary cross-section," Appl. Sci. Res., Vol. 26,
pp. 175-182, 1972. |
| 7. | J. W. Miles, "On Rayleigh scattering by a grating," Wave Motion,
Vol. 4, pp. 285-292, 1982. |
| 8. | D. S. Jones, Acoustic and Electromagnetic Waves, Clarendon
Press, Oxford, 1986. |
| 9. | J. D. Achenbach and Z. L. Li, "Reflection and transmission of scalar
waves by a periodic array of screens," Wave Motion, Vol. 8, pp. 225-234, 1986. |
| 10. | Y. C. Angel and J. D. Achenbach, "Reflection and transmission of elastic
waves by a periodic array of cracks," J. Appl. Mech., Vol. 52, pp. 33-41,
1985. |
| 11. | E. Scarpetta, "In-plane problem for wave propagation through elastic
solids with a periodic array of cracks," Acta Mechanica, Vol. 154,
pp. 179-187, 2002. |
| 12. | Y. C. Angel and J. D. Achenbach, "Reflection and transmission of elastic
waves by a periodic array of cracks: oblique incidence," Wave Motion, Vol. 7,
pp. 375-397, 1985. |
| 13. | J. D. Achenbach, Wave Propagation in Elastic Solids,
North-Holland, Oxford, 1973. |
|
| Received |
18 August 2003 |
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