Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2017-6pp.700-707

Archive of Issues

Total articles in the database: 10864
In Russian (. . ): 8009
In English (Mech. Solids): 2855

<< 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 >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100