On long-wave limiting velocities of guided waves in anisotropic plates

References

• I. Argatov and A. Iantchenko, Rayleigh surface waves in functionally graded materials – long-wave limit, Quart. J. Mech. Appl. Math., vol. 72, no. 2, pp. 197–211, 2019. DOI: 10.1093/qjmam/hbz002.
   Web of Science ®Google Scholar
• R. V. Craster, L. M. Joseph, and J. Kaplunov, Long-wave asymptotic theories: The connection between functionally graded waveguides and periodic media, Wave Motion., no. 4, vol. 51, pp. 581–588, 2014. DOI: 10.1016/j.wavemoti.2013.09.007.
   Web of Science ®Google Scholar
• R. V. Goldstein, et al., Long-wave asymptotics of Lamb waves, Mech. Solids., vol. 52, no. 6, pp. 700–707, 2017. DOI: 10.3103/S0025654417060097.
   Web of Science ®Google Scholar
• A. N. Holden, Longitudinal modes of elastic waves in isotropic cylinders and slabs, Bell Sys. Tech. J., vol. 30, no. 4, pp. 956–969, 1951. DOI: 10.1002/j.1538-7305.1951.tb03691.x.
   Google Scholar
• J. Kaplunov, D. Prikazchikov, and L. Sultanova, Rayleigh-type waves on a coated elastic half-space with a clamped surface, Philos Trans A Math Phys Eng Sci., vol. 377, no. 2156, pp. 20190111, 2019a. DOI: 10.1098/rsta.2019.0111.
   PubMed Web of Science ®Google Scholar
• J. Kaplunov D. Prikazchikov, and L. Sultanova, Elastic contact of a stiff thin layer and a half-space, Zeit. Angew. Math. Phys., vol. 70, no. 1, ARTN 22, 2019b.
   Web of Science ®Google Scholar
• J. Kaplunov and D. Prikazchikov, Asymptotic theory for Rayleigh and Rayleigh-type waves, Adv. App. Mech., vol. 50, pp. 1–106, 2017.
   Web of Science ®Google Scholar
• M. Onoe, A study of the branches of the velocity-dispersion equations of elastic plates and rods, In: Joint commitee on ultrasonics of the Institute of Electrical Communication Engineers and the Acoustical Society of Japan., ASJ, Tokyo, pp. 1–21, 1955.
   Google Scholar
• T. R. Meeker, and A. H. Meitzler, Guided wave propagation in elongated cylinders and plates. In: W.P. Mason (ed.), Physical Acoustics, Vol. 1, Part A, Chap. 2. Academic Press, New York, 1964.
   Google Scholar
• A. L. Shuvalov, and A. G. Every, Some properties of surface acoustic waves in anisotropic coated solids, studied by the impedance method, Wave Motion., vol. 36, no. 3, pp. 257–273, 2002. DOI: 10.1016/S0165-2125(02)00013-6.
   Web of Science ®Google Scholar
• A. L. Shuvalov, and A. G. Every, On the long-wave onset of dispersion of the surface-wave velocity in coated solids, Wave Motion., vol. 45, no. 6, pp. 857–863, 2008. DOI: 10.1016/j.wavemoti.2007.12.002.
   Web of Science ®Google Scholar
• I. Djeran-Maigre, et al., Solitary SH waves in two-layered traction-free plates, Comptes Rendus. Mécanique., vol. 336, no. 1–2, pp. 102–107, 2008. DOI: 10.1016/j.crme.2007.11.001.
   Web of Science ®Google Scholar
• S. V. Kuznetsov, Love waves in stratified monoclinic media, Quart. Appl. Math., vol. 62, no. 4, pp. 749–766, 2004. DOI: 10.1090/qam/2104272.
   Web of Science ®Google Scholar
• H.-H. Dai, J. Kaplunov, and D. A. Prikazchikov, A long-wave model for the surface elastic wave in a coated half-space, Proc. R Soc. A., vol. 466, no. 2122, pp. 3097–3116, 2010. DOI: 10.1098/rspa.2010.0125.
   Google Scholar
• S. V. Kuznetsov, Low frequency limits for Lamb waves in homogeneous, stratified and functionally graded anisotropic plates, Mech. Adv. Mater. Struct., vol. 28. pp. 1–7, 2021.
   Web of Science ®Google Scholar
• D. D. Zakharov, Low-frequency asymptotics of complex dispersion curves for Lamb waves in layered elastic plate, Acoust. Phys., vol. 63, no. 5, pp. 497–507, 2017. DOI: 10.1134/S1063771017050141.
   Web of Science ®Google Scholar
• N. Bochud, J. Laurent, F. Bruno, D. Royer, and C. Prada, Towards real-time assessment of anisotropic plate properties using elastic guided waves, J. Acoust. Soc. Am., vol. 143, no. 2, pp. 1138–1147, 2018.
   PubMed Web of Science ®Google Scholar
• N. Bochud, Q. Vallet, Y. Bala, H. Follet, J.-G. Minonzio, and P. Laugier, Genetic algorithms-based inversion of multimode guided waves for cortical bone characterization, Phys. Med. Biol., vol. 61, no. 19, pp. 6953–6974, 2016.
   PubMed Web of Science ®Google Scholar
• V. Dayal and V. K. Kinra, Leaky Lamb waves in an anisotropic plate. I: An exact solution and experiments, J. Acoust. Soc. Am., vol. 85, no. 6, pp. 2268–2276, 1989. DOI: 10.1121/1.397772.
   Web of Science ®Google Scholar
• F. Honarvar, E. Enjilela, and A. N. Sinclair, An alternative method for plotting dispersion curves, Ultrasonics., vol. 49, no. 1, pp. 15–18, 2009.
   PubMed Web of Science ®Google Scholar
• S.-H. Rhee, J.-K. Lee, and J.-J. Lee, The group velocity variation of Lamb wave in fiber reinforced composite plate, Ultrasonics., vol. 47, no. 1–4, pp. 55–63, 2007. DOI: 10.1016/j.ultras.2007.07.005.
   PubMed Web of Science ®Google Scholar
• L. Taupin, A. Lhémery, and G. Inquiété, A detailed study of guided wave propagation in a viscoelastic multilayered anisotropic plate, J. Phys: Conf. Ser., vol. 269, pp. 012002, 2011. DOI: 10.1088/1742-6596/269/1/012002.
   Google Scholar
• M.E. Gurtin, The linear theory of elasticity. In: C. Truesdell (ed.), Linear Theories of Elasticity and Thermoelasticity. Springer, Berlin, Heidelberg, 1973.
   Google Scholar
• D. Royer, and E. Dieulesaint, Elastic waves in solids I: Free and guided propagation. In: Advanced Texts in Physics, Springer, Berlin, 1999.
   Google Scholar
• G. Treschl, Ordinary Differential Equations and Dynamical Systems, AMS, New York, 2012.
   Google Scholar
• M. C. Pease, III, Methods of Matrix Algebra, Academic Press, New York, 1965.
   Google Scholar
• T. C. T. Ting, and D. M. Barnett, Classification of surface waves in anisotropic elastic materials, Wave Motion., vol. 26, no. 3, pp. 207–218, 1997. DOI: 10.1016/S0165-2125(97)00027-9.
   Web of Science ®Google Scholar
• S. V. Kuznetsov, Cauchy formalism for Lamb waves in functionally graded plates, J. Vibr. Control., vol. 25, no. 6, pp. 1227–1232, 2019. DOI: 10.1177/1077546318815376.
   Web of Science ®Google Scholar
• D. H. Chung and W. R. Buessem, The elastic anisotropy of crystals, J. Appl. Phys., vol. 38, no. 5, pp. 2010–2012, 1967. DOI: 10.1063/1.1709819.
   Web of Science ®Google Scholar
• A. G. Every and A. J. Stoddart, Phonon focusing in cubic crystals in which transverse phase velocities exceed the longitudinal phase velocity in some direction, Phys. Rev. B., vol. 32, no. 2, pp. 1319–1322, 1985. DOI: 10.1103/PhysRevB.32.1319.
   PubMed Web of Science ®Google Scholar
• R. Camattari, L. Lanzoni, V. Bellucci, and V. Guidi, AniCryDe: Calculation of elastic properties in silicon and germanium crystals, J. Appl. Crystallogr., vol. 48, no. 3, pp. 943–949, 2015. DOI: 10.1107/S1600576715005087.
   Google Scholar
• S. Dey, A. K. Gupta, and S. Gupta, Propagation of torsional surface waves in dry sandy medium under gravity, Math. Mech. Solids., vol. 3, no. 2, pp. 229–235, 1998. DOI: 10.1177/108128659800300207.
   Web of Science ®Google Scholar
• W. H. Weiskopf, Stresses in soils under a foundation, J. Franklin Inst., vol. 239, no. 6, pp. 445–465, 1945. DOI: 10.1016/0016-0032(45)90189-X.
   Google Scholar
• M. Abdel-Jawad, M. Kennett, L. Balicas, et al., Anisotropic scattering and anomalous normal-state transport in a high-temperature superconductor, Nature Phys., vol. 2, no. 12, pp. 821–825, 2006. DOI: 10.1038/nphys449.
   Web of Science ®Google Scholar