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IssuesArchive of Issues2016-5pp.571-575

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A.V. Avershieva, R.V. Goldstein, and S.V. Kuznetsov, "Limit Velocities of Lamb Waves: Analytic and Numerical Studies," Mech. Solids. 51 (5), 571-575 (2016)
Year 2016 Volume 51 Number 5 Pages 571-575
DOI 10.3103/S0025654416050095
Title Limit Velocities of Lamb Waves: Analytic and Numerical Studies
Author(s) A.V. Avershieva (Moscow State University of Civil Engineering, Yaroslavskoe sh. 26, Moscow, 129337 Russia)
R.V. Goldstein (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, goldst@ipmnet.ru)
S.V. Kuznetsov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia)
Abstract The Lamb wave propagation in elastic isotropic and orthotropic layers is studied by numerical and analytic methods. An analytic solution is obtained by using the Cauchy formalism for the entire frequency range. Numerical solutions are obtained in a neighborhood of the second limit velocity corresponding to very small frequencies. The influence of variations in the layer geometry on the dispersion curves is studied.
Keywords isotropic layer, Cauchy formalism, Lamb wave, second limit velocity
References
1.  R. V. Goldstein and S. V. Kuznetsov, "Surface Acoustic Waves in the Testing of Layered Media. The Waves' Sensitivity to Variations in the Properties of the Individual Layers," Prikl. Mat. Mekh. 77 (1), 74-82 (2013) [J. Appl. Math. Mech. (Engl. Transl.) 77 (1), 51-56 (2013)].
2.  W. Yang and T. Kundu, "Guidedd Waves in Multilayered Plates for Internal Defect Detection," J. Engng Mech. ASCE 124, 311-318 (1998).
3.  J. W. Rayleigh, "On the Free Vibrations of an Infinite Plate of Homogeneous Isotropic Elastic Matter," Proc. Math. Soc. London 20, 225-234 (1889).
4.  H. Lamb, "On Waves in an Elastic Plate," Proc. Roy. Soc. A A93, 114-128 (1917).
5.  S. V. Kuznetsov, "Subsonic Lamb Waves in Anisotropic Plates," Quart. Appl. Math. 60, 577-587 (2002).
6.  J. L. Rose, Ultrasonic Guided Waves in Solid Media (Cambridge Univ. Press, Cambridge, 2014).
7.  Y. M. Wang and T. C. T. Ting, "The Stroh Formalism for Anisotropic Materials that Possess an Almost Extraordinary Degenerate Matrix N," Int. J. Solids Struct. 34, 401-413 (1997).
8.  P. Chadwick and G. D. Smith, "Foundation of the Theory of Surface Waves in Anisotropic Elastic Materials," Adv. Appl. Mech., 303-376 (1977).
9.  V. N. Kukudzhanov, "Numerical Solution of Non-One-Dimensional Problems of Stress Wave Propagation in Solids," in Reports on Applied Mathematics, No. 6 (Computer Center, AN SSSR, Moscow, 1976) [in Russian].
Received 15 April 2016
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