High-Frequency Spectra of SH GuidedWaves in Continuously Layered Plates

  • Vladimir I. Alshits
  • Jerzy P. Nowacki
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)


The spectra of SH guided waves in an isotropic continuously layered plate with arbitrary profile of the limiting slowness ŝ(y) across the plate are explicitly analyzed for high frequencies ω in the framework of “adiabatic” approximation. Dispersion equations and their solutions are analytically found for free, clamped or free-clamped faces of the plate. The positions of horizontal asymptotes for dispersion branches are determined by extreme points y i of the dependence ŝ(y) including also inflection points and “linear” (non-extreme) min/max points. In the vicinity of all asymptotic levels, apart from the upper one, spectra form specific ladder-like patterns. Explicit asymptotics of dispersion curves are derived for a series of particular local dependencies ŝ(y) in the vicinity of points y i .


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors are grateful to D.A. Bessonov for the help in computing.


  1. Alshits VI, Kirchner HOK (1995) Elasticity of multilayers I. Basic equations and solutions. Philosophical Magazine A 72(6):1431–1444Google Scholar
  2. Alshits VI, Maugin GA (2005) Dynamics of multilayers: elastic waves in an anisotropic graded or stratified plate. Wave Motion 41(4):357–394Google Scholar
  3. Alshits VI, Maugin GA (2008) Dynamics of anisotropic multilayers. Wave Motion 45(5):629–640Google Scholar
  4. Alshits VI, Deschamps M, Maugin GA (2003) Elastic waves in anisotropic plates: short-wavelength asymptotics of the dispersion branches vn(k). Wave Motion 37(3):273–292Google Scholar
  5. Alshits VI, Deschamps M, Lyubimov VN (2005) Dispersion anomalies of shear horizontal guided waves in two- and three-layered plates. The J Acoust Soc America 118(5):2850–2859Google Scholar
  6. Bakirtas AI, Maugin GA (1982) Ondes de surface SH pures en élasticité inhomogène. J Mècan Theor Appl 1:995–1013Google Scholar
  7. Baron C, Poncelet O, Shuvalov A (2003) Calculation of the velocity spectrum of the vertically inhomogeneous plates. In: Proceedings of 5thWorld Congress on Ultrasonics, Paris, pp 605–608Google Scholar
  8. Gantmacher FR (1989) The Theory of Matrices. Chelsea, New YorkGoogle Scholar
  9. Landau LD, Lifshitz EM (1991) Quantum Mechanics. Pergamon Press, New YorkGoogle Scholar
  10. Maugin GA (1983) Elastic surface waves with transverse horizontal polarization. In: Hutchinson JW (ed) Advances in Applied Mechanics, Academic Press, New York, vol 23, pp 373–434Google Scholar
  11. Nayfeh AH (1995) Wave Propagation in Layered Anisotropic Media. North-Holland, AmsterdamGoogle Scholar
  12. Shilov GE (1996) Elementary Functional Analysis. Dover, New YorkGoogle Scholar
  13. Shuvalov AL, Poncelet O, Deschamps M (2004) General formalism for plane guided waves in transversely inhomogeneous anisotropic plates. Wave Motion 40(4):413–426Google Scholar
  14. Shuvalov AL, Poncelet O, Deschamps M, Baron C (2005) Long-wavelength dispersion of acoustic waves in transversely inhomogeneous anisotropic plates. Wave Motion 42(4):367–382Google Scholar
  15. Shuvalov AL, Poncelet O, Kiselev AP (2008) Shear horizontal waves in transversely inhomogeneous plates. Wave Motion 45(5):605–615Google Scholar
  16. Stroh AN (1962) Steady state problems in anisotropic elasticity. J Math Phys 41(1-4):77–103Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Shubnikov Institute of CrystallographyRussian Academy of SciencesMoscowRussia
  2. 2.Polish-Japanese Academy of Information TechnologyWarsawPoland

Personalised recommendations