Lamb waves in cubic crystals: crossing fundamental branches

References

• I. Tolstoy, Resonant frequencies and high modes in layered wave guides, J. Acoust. Soc. Am., vol. 28, no. 6, pp. 1182–1192, 1956. DOI: 10.1121/1.1908587.
   Web of Science ®Google Scholar
• I. Tolstoy and E. Usdin, Wave propagation in elastic plates: low and high mode dispersion, J. Acoust. Soc. Am., vol. 29, no. 1, pp. 37–42, 1957. DOI: 10.1121/1.1908675.
   Web of Science ®Google Scholar
• R. D. Mindlin. Mathematical theory of vibrations of elastic plates, In: Proc. 11th Annual Symp. Freq. Control, U.S. Army Signal Eng. Labs., Fort Monmouth, New Jersey, 1957, pp. 1–40.
   Google Scholar
• A. G. Every, Intersections of the Lamb mode dispersion curves of free isotropic plates, J. Acoust. Soc. Am., vol. 139, no. 4, pp. 1793–1798, 2016. DOI: 10.1121/1.4946771.
   PubMed Web of Science ®Google Scholar
• A. Freedman, The variation, with the Poisson ratio, of Lamb modes in a free plate, I: General spectra, J. Sound Vib., vol. 137, pp. 209–230, 1990a.
   Web of Science ®Google Scholar
• A. Freedman, The variation, with the Poisson ratio, of Lamb modes in a free plate, II: At transitions and coincidence values, J. Sound Vib., vol. 137, no. 2, pp. 231–247, 1990b. 1990). DOI: 10.1016/0022-460X(90)90790-7.
   Web of Science ®Google Scholar
• A. Freedman, The variation, with the Poisson ratio, of Lamb modes in a free plate, III: Behavior of individual modes, J. Sound Vib., vol. 137, no. 2, pp. 249–266, 1990c. DOI: 10.1016/0022-460X(90)90791-W.
   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. Royer, D. Clorennec, and C. Prada, Lamb mode spectra versus the Poisson ratio in a free isotropic elastic plate, J. Acoust. Soc. Am., vol. 125, no. 6, pp. 3683–3687, 2009. DOI: 10.1121/1.3117685.
   PubMed Web of Science ®Google Scholar
• A. Freedman, Comment on ‘On the crossing points of Lamb wave velocity dispersion curves, J. Acoust. Soc. Am., vol. 98, no. 4, pp. 2363–2364, 1995. DOI: 10.1121/1.413282.
   Web of Science ®Google Scholar
• I. A. Veres, et al., On the crossing points of the Lamb modes and the maxima and minima of displacements observed at the surface, Ultrasonics., vol. 54, no. 3, pp. 759–762, 2014. DOI: 10.1016/j.ultras.2013.10.018.
   PubMed Web of Science ®Google Scholar
• Q. Zhu and W. G. Mayer, On the crossing points of Lamb wave velocity dispersion curves, J. Acoust. Soc. Am., vol. 93, no. 4, pp. 1893–1895, 1993. DOI: 10.1121/1.406704.
   Web of Science ®Google Scholar
• B. R. Mace and E. Manconi, Wave motion and dispersion phenomena: veering, locking and strong coupling effects, J. Acoust. Soc. Am., vol. 131, no. 2, pp. 1015–1028, 2012. DOI: 10.1121/1.3672647.
   PubMed Web of Science ®Google Scholar
• E. Manconi and S. Sorokin, On the effect of damping on dispersion curves in plates, Int. J. Solids Struct., vol. 50, no. 11/12, pp. 1966–1973, 2013. DOI: 10.1016/j.ijsolstr.2013.02.016.
   Web of Science ®Google Scholar
• N. C. Perkins and C. D. Mote, Jr., Comments on curve veering in eigenvalue problems, J. Sound Vibr., vol. 106, no. 3, pp. 451–463, 1986. DOI: 10.1016/0022-460X(86)90191-4.
   Web of Science ®Google Scholar
• B. Wu, et al., On guided circumferential waves in soft electroactive tubes under radially inhomogeneous biasing fields, J. Mech. Phys. Solids., vol. 99, pp. 116–145, 2017. DOI: 10.1016/j.jmps.2016.11.004.
   Web of Science ®Google Scholar
• F. Zhu, et al., Waves in a generally anisotropic viscoelastic composite laminated bilayer: Impact of the imperfect interface from perfect to complete delamination, Int. J. Solids Struct., vol. 202, pp. 262–277, 2020. DOI: 10.1016/j.ijsolstr.2020.05.031.
   Web of Science ®Google Scholar
• F. Zhu, et al., Accurate characterization of 3D dispersion curves and mode shapes of waves propagating in generally anisotropic viscoelastic/elastic plates, Int. J. Solids Struct., vol. 150, pp. 52–65, 2018. DOI: 10.1016/j.ijsolstr.2018.06.001.
   Web of Science ®Google Scholar
• V. I. Arnold, Mathematical Method of Classical Mechanics, 2nd ed., Springer-Verlag, New York, Berlin, Heidelberg, 1989.
   Google Scholar
• J. L. Du Bois, S. Adhikari, and N. A. J. Lieven, On the quantification of eigenvalue curve veering: A veering index, ASME J. Appl. Mech., vol. 78, no. 4, pp. 041007, 2011. Page
   Web of Science ®Google Scholar
• A. G. Every, A. A. Maznev, W. Grill, M. Pluta, J. D. Comins, O. B. Wright, O. Matsuda, W. Sachse, and J. P. Wolfe, Bulk and surface acoustic wave phenomena in crystals: Observation and interpretation, Wave Motion, vol. 50, no. 8, pp. 1197–1217, 2013. DOI: 10.1016/j.wavemoti.2013.02.007.
   Web of Science ®Google Scholar
• O. Giannini and A. Sestieri, Experimental characterization of veering crossing and lock-in in simple mechanical systems, Mech. Syst. Signal Proc., vol. 72–73, pp. 846–864, 2016.
   Web of Science ®Google Scholar
• J. Kaplunov and A. Nobili, Multi-parametric analysis of strongly inhomogeneous periodic waveguideswith internal cutoff frequencies, Math. Methods Appl. Sci., pp. 1–12, 2016. DOI: 10.1002/mma.3900.
   Web of Science ®Google Scholar
• R. S. MacKay. Stability of equilibria of Hamiltonian systems. In: Sarben Sarkar (ed.), Nonlinear Phenomena and Chaos, Adam Hilger, Bristol, UK, 1986, pp. 54–70.
   Google Scholar
• A. Nobili and D. Prikazchikov, Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane, Eur. J. Mech. A: Solids., vol. 70, pp. 86–94, 2018. DOI: 10.1016/j.euromechsol.2018.01.012.
   Web of Science ®Google Scholar
• A. P. Seyranian, O. N. Kirillov, and A. A. Mailybaev, Coupling of eigenvalues of complex matrices at diabolic and exceptional points, J. Phys. A: Math. Gen., vol. 38, no. 8, pp. 1723–1740, 2005. DOI: 10.1088/0305-4470/38/8/009.
   Google Scholar
• M. S. Triantafyllou and G. S. Triantafyllou, Frequeney coalescence and mode localisation phenomena: A geometric theory, J. Sound Vib., vol. 150, no. 3, pp. 485–500, 1991. DOI: 10.1016/0022-460X(91)90899-U.
   Google Scholar
• S. V. Kuznetsov, Anomalous dispersion of Lamb waves in Ge cubic crystal, Waves Random Complex Media, pp. 17, 2022. DOI: 10.1080/17455030.2022.2026523.
   Web of Science ®Google Scholar
• H. Ledbetter and A. Migliori, A general elastic-anisotropy measure, J. Appl. Phys., vol. 100, no. 6, pp. 063516, 2006. Paper 063516. DOI: 10.1063/1.2338835.
   Web of Science ®Google Scholar
• C. Zener. Elasticity and Anelasticity of Metals, University of Chicago Press, Chicago, IL, 1948.
   Google Scholar
• A. G. Every, Ballistic phonons and the shape of the ray surface in cubic crystals, Phys. Rev. B, vol. 24, no. 6, pp. 3456–3467, 1981. DOI: 10.1103/physrevb.24.3456.
   Web of Science ®Google Scholar
• A. G. Every and A. Stoddart, Phonon focusing in cubic crystals in which transverse phase velocities exceed the longitudinal phase velocity in some direction, Phys. Rev. B: Condens. Matter., vol. 32, no. 2, pp. 1319–1322, 1985.
   PubMed Web of Science ®Google Scholar
• T. S. Duffy, Single-crystal elastic properties of minerals and related materials with cubic symmetry, Am. Mineralogist., vol. 103, no. 6, pp. 977–988, 2018. DOI: 10.2138/am-2018-6285.
   Web of Science ®Google Scholar
• G. Teschl, 2012. Ordinary Differential Equations and Dynamical Systems, American Mathematical Society, Providence, RI.
   Google Scholar
• T. Paszkiewicz and S. Wolski, Elastic properties of cubic crystals: Every’s versus Blackman’s diagram, J. Phys.: Conf. Ser., vol. 104, pp. 1–8, 2008. Paper 012038. DOI: 10.1088/1742-6596/104/1/012038.
   Google Scholar
• X. Luan, et al., The mechanical properties and elastic anisotropies of cubic Ni3Al from first principles calculations, Crystals, vol. 8, no. 8, pp. 307, 2018. Paper 307. DOI: 10.3390/cryst808030.
   Web of Science ®Google Scholar
• T. Kato, 1995. Perturbation Theory for Linear Operators, Classics in Mathematics, Berlin: Springer-Verlag.
   Google Scholar
• E. Manconi and B. Mace, Veering and strong coupling effects in structural dynamics, J. Vibr. Acoust., vol. 139, no. 2, pp. 1–12, 2017. Paper 021009.
   Web of Science ®Google Scholar
• A. Nobili, B. Erbaş, and C. Signorini, Veering of Rayleigh–Lamb waves in orthorhombic materials, Math. Mech. Solids., pp. 108128652110734, 2022. DOI: 10.1177/10812865211073467.
   Web of Science ®Google Scholar