 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
|
| << Previous article | Volume 52, Issue 6 / 2017 | Next article >> |
| R.V. Goldstein and S.V. Kuznetsov, "Long-Wave Asymptotics of Lamb Waves," Mech. Solids. 52 (6), 700-707 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
6 |
Pages |
700-707 |
| DOI |
10.3103/S0025654417060097 |
| Title |
Long-Wave Asymptotics of Lamb Waves |
| Author(s) |
R.V. Goldstein (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5 str. 1, Moscow, 105005 Russia, goldst@ipmnet.ru)
S.V. Kuznetsov (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5 str. 1, Moscow, 105005 Russia, kuzn-sergey@yandex.ru) |
| Abstract |
The six-dimensional complex formalism is used to obtain equations for determining long-wave asymptotics of symmetric fundamental modes of Lamb waves in an anisotropic layer. Analytic expressions are obtained for long-wave asymptotics of phase velocities of Lamb waves propagating in an isotropic layer. |
| Keywords |
long-wave asymptotics, Lamb wave, anisotropy, polarization |
| References |
| 1. | M. Planat and M. Hoummady,
"Observation of Soliton-Like Envelope Modulations Generated
in an Anisotropic Quartz Plate by Metallic Interdigital Transducers,"
Appl. Phys. Lett.
55, 103-105 (1989). |
| 2. | R. M. Davies,
"A Critical Study of the Hopkinson Pressure Bar,"
Phil. Trans. Roy. Soc. Lond.
240 (821), 375-457 (1948). |
| 3. | R. D. Mindlin and H. D. McNiven,
"Axially Symmetric Waves in Elastic Rods,"
J. Appl. Mech.
27 (1), 145-151 (1960). |
| 4. | M. Onoe, H. D. McNiven, and R. D. Mindlin,
"Dispersion of Axially Symmetric Waves in Elastic Rods,"
J. Appl. Mech.
29 (4), 729-734 (1962). |
| 5. | K. F. Graff,
Wave Motion in Elastic Solids
(Clarendon Press, Oxford, 1975). |
| 6. | D. G. Harkrider,
"Surface Waves in Multilayered Elastic Media. I.
Rayleigh and Love Waves from Buried Sources in a Multilayered Elastic Half-Space,"
Bull. Seism. Soc. Amer.
54 (2), 627-629 (1964). |
| 7. | N. A. Haskell,
"Dispersion of Surface Waves on Multilayered Media,"
Bull. Seism. Soc. Amer.
43, 17-34 (1953). |
| 8. | D. G. Harkrider and D. L. Anderson,
"Computation of Surface-Wave Dispersion for Multilayered Anisotropic Media,"
Bull. Seism. Soc. Amer.
52, 321-332 (1962). |
| 9. | T. Kawahara,
"Oscillatory Solitary Waves in Dispersive Media,"
J. Phys. Soc. Japan
33, 260-264 (1972). |
| 10. | M. P. Soersen, P. L. Christiansen, and P. S. Lomdahl,
"Solitary Waves on Nonlinear Elastic Rods. I,"
J. Acoust. Soc. Amer.
76 (3), 871-879 (1984). |
| 11. | I. V. Porubov, A. M. Samsonov, M. G. Velarde, and A. V. Bukhanovsky,
"Strain Solitary Waves in an Elastic Rod Embedded in Another External Medium with Sliding,"
Phys. Rev. Ser. E
58 (3), 3854-3864 (1998). |
| 12. | H. Lamb,
"On Waves in an Elastic Plate,"
Proc. Roy. Soc. A
93 (648), 114-128 (1917). |
| 13. | S. V. Kuznetsov,
"Subsonic Lamb Waves in Anisotropic Plates,"
Quart. Appl. Math.
60 (3), 577-587 (2002). |
| 14. | W. T. Thomson,
"Transmission of Elastic Waves through a Stratified Solid Medium,"
J. Appl. Phys.
21, 89-93 (1950). |
| 15. | N. A. Haskell,
"The Dispersion of Surface Waves on Multilayered Media,"
Bull. Seism. Soc. Amer.
43 (1), 17-34 (1953). |
| 16. | L. A. Knopoff,
"A Matrix Method for Elastic Wave Problems,"
Bull. Seism. Soc. Amer.
54 (1), 431-438 (1964). |
| 17. | A. K. Mal and L. Knopoff,
"A Differential Equation for Surface Waves in Layers with Varying Thickness,"
J. Math. Anal. Appl.
21, 431-441 (1968). |
| 18. | S. V. Kuznetsov,
"Surface Waves of Non-Rayleigh Type,"
Quart. Appl. Math.
61, 575-582 (2003). |
| 19. | S. V. Kuznetsov,
"Love Waves in Nondestructive Diagnostics of Layered Composites. Survey,"
Acoust. Phys.
56 (6), 877-892 (2010). |
| 20. | S. V. Kuznetsov,
"Lamb Waves in Anisotropic Plates,"
Akust. Zh.
60 (1), 90-100 (2014). |
| 21. | S. A. Markus,
"Low-Frequency Approximations for Zero Modes of Normal Modes in Anisotropic Plates,"
Akust. Zh.
33 (6), 1091-1095 (1987). |
| 22. | I. P. Getman and Yu. A. Ustinov,
Mathematical Theory of Irregular Solid Waveguides
(Izdat. RGU, Postov-on-Don, 1993)
[in Russian]. |
| 23. | I. A. Viktorov,
Physical Foundations of Application of Ultrasonic Rayleigh and Lamb Waves in Technology
(Nauka, Moscow, 1966)
[in Russian]. |
| 24. | P. Chadwick and G. D. Smith,
"Foundation of the Theory of Surface Waves in Anisotropic Elastic Materials,"
Adv. Appl. Mech.,
303-376 (1977). |
| 25. | C. D. Meier,
Matrix Analysis and Applied Linear Algebra
(SIAM, New York, 2002). |
| 26. | R. V. Goldstein,
"Rayleigh Waves and Resonance Phenomena in Elastic Bodies,"
Prikl. Mat. Mekh.
29 (3), 516-525 (1965)
[J. Appl. Math. Mech. (Engl. Transl.)
29 (3), 608-619 (1965)]. |
| 27. | R. V. Goldstein,
"Surface Waves and Resonance Phenomena in Elastic Bodies,"
Soros. Obrazovat. Zh.,
No. 11, 123-127 (1996). |
| 28. | R. V. Goldstein,
"On Surface Waves in Joined Elastic Materials and Their Relation to Crack Propagation along the Junction,"
Prikl. Math. Mekh.
31 (3), 468-475 (1967)
[J. Appl. Math. Mech. (Engl. Transl.)
31 (3), 497-502 (1967)]. |
| 29. | L. I. Slepyan,
Unsteady Elastic Waves
(Sudostroenie, Leningrad, 1972)
[in Russian]. |
| 30. | K. B. Broberg,
"On the Behavior of the Process Region at a Fast Running Crack Tip,"
in High Velocity Deformation of Solids,
Ed. by K. Kawada and J. Shiori
(Springer, Berlin, 1979). |
| 31. | K. B. Broberg,
"Dynamic Crack Propagation in a Layer,"
Int. J. Solids Struct.
32, 883-896 (1995). |
| 32. | A. J. Rosakis, O. Samudrala, and D. Coker,
"Crack Faster then Shear Wave Speed,"
Science
284, 1337-1340 (1999). |
| 33. | D. Coker and A. J. Rosakis,
"Experimental Observations of Intersonic Crack Growth
in Asymmetrically Loaded Unidirectional Composites Plates,"
Phil. Mag. A
81, 571-595 (2001). |
| 34. | A. V. Zvyagin and G. A. Romashev,
"Surface waves under constrained deformation,"
Vestnik Moskov. Univ. Ser. I Mat. Mekh.,
No. 2, 59-62 (2012)
[Moscow Univ. Mech. Bull. (Engl. Transl.)
67 (2), 43-45 (2012)]. |
| 35. | A. V. Avershieva, R. V. Goldstein, and S. V. Kuznetsov,
"Limit Velocities of Lamb Waves: Analytic and Numerical Studies,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 79-84 (2016)
[Mech. Solids (Engl. Transl.)
51 (5), 571-575 (2016)]. |
|
| Received |
08 August 2017 |
| Link to Fulltext |
|
| << Previous article | Volume 52, Issue 6 / 2017 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English