DIRAC CONES DURING LAMB WAVE PROPAGATION IN A FUNCTIONALLY GRADIENTED LAYER

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

This paper analyzes the appearance of proper and degenerate Dirac cones arising during Lamb wave propagation in an isotropic functionally graded layer satisfying the Wiechert condition. It is found that Dirac cones appear in a layer with a distribution of physical properties asymmetric with respect to the midsurface and for any Poisson’s ratio. The study is based on the Cauchy formalism and the exponential fundamental matrix method.

About the authors

S. G Saiyan

National Research Moscow State University of Civil Engineering (NRU MGSU)

Email: Berformert@gmail.com
Moscow, Russia

S. V Kuznetsov

Ishlinsky Institute for Problems in Mechanics, RAS

Email: kuzn-sergey@yandex.ru

References

  1. Mindlin R.D. An Introduction to the Mathematical Theory of Vibrations of Elastic Plates. Singapore: World Scientific, 2006. 212 p.
  2. Maznev A.A. Dirac cone dispersion of acoustic waves in plates without phononic crystals (L) // J. Acoust. Soc. Am. 2014. V. 135. № 2. P. 577–580.
  3. Dieulesaint E., Royer D. Elastic Waves in Solids. New York: Wiley, 1980. 511 p.
  4. Hayes M. A note on group velocity // Proc. Roy. Soc. A. 1977. V. 354. № 1679. P. 533–535.
  5. Maznev A.A., Every A.G. Existence of backward propagating acoustic waves in supported layers // Wave Motion. 2011. V. 48. P. 401–407.
  6. Stobbe D.M., Grünsteidl C.M., Murray T.W. Propagation and scattering of Lamb waves at conical points in plates // Sci. Rep. 2019. V. 9. P. 15216.
  7. Stobbe D.M., Murray T.W. Conical dispersion of Lamb waves in elastic plates // Phys. Rev. B. 2017. V. 96. P. 144101.
  8. Chantelot P., Domino L., Eddi A. How capillarity affects the propagation of elastic waves in soft gels // Phys. Rev. E. 2020. V. 101. P. 032609.
  9. Lanoy M., Lemoult F., Eddi A., Prada C. Dirac cones and chiral selection of elastic waves in a soft strip // Proc. Natl. Acad. Sci. USA. 2020. V. 117. № 48. P. 30186–30190.
  10. Laurent J., Royer D., Prada C. In-plane backward and zero-group-velocity guided modes in rigid and soft strips // J. Acoust. Soc. Am. 2020. V. 147. P. 1302–1310.
  11. Gurtin M.E. The Linear Theory of Elasticity // Handbuch der Physik. V. VIa/2 / Ed. Truesdell C. Berlin: Springer-Verlag, 1972. P. 1–296.
  12. Cherednichenko K.D., Cooper S. On the existence of high-frequency boundary resonances in layered elastic media // Proc. Roy. Soc. A. 2015. V. 471. № 2178. P. 20140878.
  13. Kaplunov J., Prikazchikov D., Sultanova L. Rayleigh-type waves on a coated elastic half-space with a clamped surface // Phil. Trans. Roy. Soc. A. 2019. V. 377. 20190111.
  14. Wiechert E., Geiger L. Bestimmung des Weges der Erdbebenwellen im Erdinnern // Phys. Z. 1910. V. 11. P. 294–311.
  15. Stoneley R. Elastic waves at the surface of separation of two solids // Proc. Roy. Soc. London. Ser. A. 1924. V. 106. P. 416–428.
  16. Ma G. and Sheng P. Acoustic metamaterials: From local resonances to broad horizons // Sci. Adv. V. 2(2). e1501595.
  17. Bilal O.R., Foehr A., Daraio C. Bistable metamaterial for switching and cascading elastic vibrations // Proc. Nat. Acad. Sci. 2017. V. 114(18). P. 4603–4606.
  18. Kuznetsov S.V. Stoneley waves at the Wiechert condition // Z. Angew. Math. Phys. 2020. V. 71. P. 180.
  19. Ilyashenko A.V. Stoneley waves in a vicinity of the Wiechert condition // Int. J. Dynam. Control. 2021. V. 9. P. 30–32.
  20. Kuznetsov S.V. Closed form analytical solution for dispersion of Lamb waves in FG plates // Wave Motion. 2019. V. 84. P. 1–7.
  21. Murty G.S. Wave propagation at an unbounded interface between two elastic half-spaces // J. Acoust. Soc. Am. 1975. V. 58. P. 1094–1095.
  22. Meleshko V.V. Energy analysis of Stoneley surface waves // Soviet Appl. Mech. 1980. V. 16. P. 382–385.
  23. Vinh P.C., Malischewsky P.G., Giang P.T.H. Formulas for the speed and slowness of Stoneley waves in bonded isotropic elastic half-spaces with the same bulk wave velocities // Int. J. Eng. Sci. 2012. V. 60. P. 53–58.
  24. Torrent D., Sа́nchez-Dehesa J. Acoustic analogue of graphene: Observation of Dirac cones in acoustic surface waves // Phys. Rev. Lett. 2012. V. 108(17). P.174301.
  25. Wang D., Dong J., Liu Y., Lai Y. Topology-optimized square-lattice sonic crystals with multi-fold degenerate Dirac cones // J. Sound Vibr. 2021. V. 504. 116121.
  26. Li S., Brun M., Djeran-Maigre I., Kuznetsov S.V. Explicit/implicit multi-time step co-simulation in unbounded medium with Rayleigh damping and application for wave barrier // Europ. J. Environ. Civil Eng. 2020. V. 24. № 14. P. 2400–2421.
  27. Li S., Brun M., Djeran-Maigre I., Kuznetsov S.V. Benchmark for three-dimensional explicit asynchronous absorbing layers for ground wave propagation and wave barriers // Comp. Geotech. 2021. V. 131. 103808.
  28. Dudchenko A.V., Dias D., Kuznetsov S.V. Vertical wave barriers for vibration reduction // Arch. Appl. Mech. 2021. V. 91. P. 257–276.
  29. Brock L.M. Stoneley wave generation in joined materials with and without thermal relaxation due to thermal mismatch // ASME J. Appl. Mech. 2007. V. 74. № 5. P. 1019–1025.
  30. Morocha A.K., Rozhkov A.S. On new types of Stoneley waves and the possibility of using them in integrated acoustoelectronics // Russ. Microelectron. 2017. V. 46. P. 443–448.
  31. Kuznetsov S.V. Abnormal dispersion of flexural Lamb waves in functionally graded plates // Z. Angew. Math. Phys. 2019. V. 70. P. 89.
  32. Hartman Ph. Ordinary Differential Equations (Classics in Applied Mathematics). 2-nd ed. Ed. N.Y.: SIAM, 1987. 632 p.
  33. Marcus M., Minc H. A Survey of Matrix Theory and Matrix Inequalities. Revised ed. Dover Publication: New York, 2010. 208 p.
  34. Barnett D.M., Lothe J. Consideration of the existence of surface wave (Rayleigh wave) solutions in anisotropic elastic crystals // J. Phys. F: Metal Phys. 1974. V. 4. P. 671–686.
  35. Chadwick P., Smith G.D. Foundations of the theory of surface waves in anisotropic elastic materials // Adv. Appl. Mech. 1977. V. 17. P. 303–376.
  36. textit. Kuznetsov S.V. Subsonic Lamb waves in anisotropic plates // Quart. Appl. Math. 2002. V. 60. № 3. P. 577–587.
  37. Fu Y.B. Hamiltonian interpretation of the Stroh formalism in anisotropic elasticity // Proc. Roy. Soc. A. 2007. V. 463. № 2088. P. 3073–3087.
  38. Fu Y., Kaplunov J., Prikazchikov D. Reduced model for the surface dynamics of a generally anisotropic elastic half-space // Proc. Roy. Soc. A. 2020. V. 476. P. 20190590.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2025 Russian Academy of Sciences

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).