 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| M.Yu. Remizov and M.A. Sumbatyan, "One-Mode Propagation of Elastic Waves through a Doubly Periodic Array of Cracks," Mech. Solids. 53 (3), 295-306 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
3 |
Pages |
295-306 |
| DOI |
10.3103/S0025654418070099 |
| Title |
One-Mode Propagation of Elastic Waves through a Doubly Periodic Array of Cracks |
| Author(s) |
M.Yu. Remizov (South Federal University, ul. Mil'chakova 8a, Rostov-on-Don, 344090 Russia)
M.A. Sumbatyan (South Federal University, ul. Mil'chakova 8a, Rostov-on-Don, 344090 Russia, sumbatma@mail.ru) |
| Abstract |
The article is devoted to the derivation of analytical expressions for the reflection and propagation coefficients, when a plane longitudinal wave falls on a system of a finite number of consecutively located identical flat gratings, each of which consists of a periodic array of rectilinear cracks in an elastic isotropic medium. The problem is solved in a flat statement. In the mode of single-mode frequency range, the problem is reduced to a system of hypersingular integral equations, the solution of which gives the reflection and propagation coefficients, as well as the representation of the wave field inside the medium. |
| Keywords |
reflection and propagation coefficients, doubly periodic lattice, hypersingular integral equation, crack system, acoustic filter |
| References |
| 1. | J. D. Achenbach and Z. L. Li,
"Reflection and Propagation of Scalar Waves by a Periodic Array
of Screens,"
Wave Motion
8, 225-234 (1986). |
| 2. | J. W. Miles,
"On Rayleigh Scattering by a Grating,"
Wave Motion
4, 285-292 (1982). |
| 3. | E. L. Shenderov,
"Sound Propagation through a Hard Screen of Finite Thickness with Holes,"
Akust Zh.
16 (2), 295-304 (1970). |
| 4. | Z. Liu, X. Zhang, Y. Mao, et al.
"Locally Resonant Sonic Materials,"
Science
289 (5485), 1734-1736 (2000). |
| 5. | M. A. Sumbatyan,
"Low-Frequency Propagation of Acoustic Waves through a Periodic
Arbitrary-Shaped Grating: the Three-Dimensional Problem,"
Wave Motion
22, 133-144 (1995). |
| 6. | E. Scarpetta and M. A. Sumbatyan,
"On Wave Propagation in Elastic Solids with a Doubly
Periodic Array of Cracks,"
Wave Motion
25, 61-72 (1997). |
| 7. | E. Scarpetta and M. A. Sumbatyan,
"On the Oblique Wave Propagation in Elastic Solids with a
Doubly Periodic Array of Cracks,"
Quart. Appl. Math.
58, 239-250 (2000). |
| 8. | E. Scarpetta,
"In-Plane Problem for Wave Propagation through Elastic Solids with a
Periodic Array of Cracks,"
Acta Mech.
154, 179-187 (2002). |
| 9. | E. Scarpetta and V. Tibullo,
"On the Three-Dimensional Wave Propagation through Cascading
Screens Having a Periodic System of Arbitrary Openings,"
Int. J. Engng Sci.
46, 105-118 (2008). |
| 10. | M. A. Sumbatyan and M. Yu. Remizov,
"On the Theory of Acoustic Metamaterials with a Triple-Periodic System of Interior Obstacles,"
in M. Sumbatyan (Editor), Wave Dynamics and Composite Mechanics for Microstructured Materials
and Metamaterials. Advanced Structured Materials, Vol 59 (Springer, Singapore, 2017),
pp. 19-33. |
| 11. | M. A. Sumbatyan and M. Yu. Remizov,
"Asymptotic Analysis in the Anti-Plane High-Frequency
Diffraction by Interface Cracks,"
Appl. Math. Lett.
34, 72-75 (2014). |
| 12. | M. Yu. Remizov and M. A. Sumbatyan,
"Semi-Analytical Method for Solving Problems of
High-Frequency Diffraction of Elastic Waves on Cracks,"
Appl. Math. Mech.
77 (4), 629-635 (2013). |
| 13. | M. A. Sumbatyan, M. Yu. Remizov, and V. Zampoli,
"A Semi-Analytical Approach in the High-Frequency Diffraction by Cracks,"
Mech. Res. Comm.
38, 607-609 (2011). |
| 14. | R. V. Craster and S. Guenneau,
Acoustic Metamaterials
(Springer, Dordrecht, 2013). |
| 15. | R. C. McPhedran, A. B. Movchan, and N. V. Movchan,
"Platonic Crystals: Bloch Bands, Neutrality
and Defects,"
Mech. Mater.
41, 356-363 (2009). |
| 16. | N. V. Movchan, R. C. McPhedran, A. B. Movchan, and C. G. Poulton,
"Wave Scattering by Platonic
Grating Stacks,"
Proc. Royal Soc. A
465, 3383-3400 (2009). |
| 17. | V. V. Mykhaskiv, I. Ya. Zhbadynskyi, and Ch. Zhang,
"Dynamic Stresses Due to Time-Harmonic
Elastic Wave Incidence on Doubly Periodic Array of Penny-Shaped Cracks,"
J. Math. Sci.
203, 114-122 (2014). |
| 18. | H. H. Huang, C. T. Sun, and G. L. Huang,
"On the Negative Effective Mass Density in Acoustic
Metamaterials,"
Int. J. Engng Sci.
47, 610-617 (2009). |
| 19. | Ch. Yang and J. D. Achenbach,
"Time Domain Scattering of Elastic Waves
by a Cavity, Represented by Radiation from Equivalent Body Forces,"
Int. J. Engng Sci.
115, 43-50 (2017). |
| 20. | W. Nowacki,
Theory of Elasticity
(PWN, Warsaw, 1970; Mir, Moscow, 1975). |
| 21. | I. N. Sneddon and M. Lowengrub,
Crack Problems in the Classical Theory of Elasticity
(Wiley, London, 1969). |
| 22. | S. M. Belotserkovsky and I. K. Lifanov,
Numerical Methods in Singular Integral Equations and
Their Application in Aerodynamics, Elasticity Theory, Electrodynamics
(Nauka, Moscow, 1985)
[in Russian]. |
| 23. | E. Scarpetta and V. Tibullo,
"P-Wave Propagation through Elastic Solids with a Doubly
Periodic Array of Cracks,"
Quart. J. Mech. Appl. Math.
58, 535-550 (2005). |
| 24. | G. A. Kriegsmann,
"Scattering Matrix Analysis of a Photonic Fabry-Perot Resonator,"
Wave Motion
37, 43-61 (2003). |
| 25. | S. K. Datta,
"Diffraction of Plane Elastic Waves by Ellipsoidal Inclusions,"
J. Acoust. Soc. Am.
61, 1432-1437 (1977). |
| 26. | J. R. Willis,
"A Polarization Approach to the Scattering of Elastic Waves - II. Multiple
Scattering from Inclusions,"
J. Mech. Phys. Solids
28, 307-327 (1980). |
| 27. | S. V. Kuznetsov,
"Elastic Wave Scattering in Porous Media,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 81-86 (1995)
[Mech. Solids (Engl. Transl.)
30 (3), 71-76 (1995)]. |
|
| Received |
22 January 2017 |
| Link to Fulltext |
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