Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T22:45:24.185Z Has data issue: false hasContentIssue false
  • English
  • Français

Lamb Waves in Anisotropic Functionally Graded Plates: A Closed Form Dispersion Solution

Published online by Cambridge University Press:  08 August 2019

S. V. Kuznetsov Open the ORCID record for S. V. Kuznetsov [Opens in a new window]
S. V. Kuznetsov*
Affiliation:
Institute for Problems in Mechanics Bauman Moscow State Technical University Moscow State University of Civil Engineering Moscow, Russia
*
*Corresponding author ([email protected])
Get access

Abstract

Propagation of harmonic Lamb waves in plates made of functionally graded materials (FGM) with transverse inhomogeneity is studied by combination of the Cauchy six-dimensional formalism and matrix exponential mapping. For arbitrary transverse inhomogeneity a closed form implicit solution for dispersion equation is derived and analyzed. Both the dispersion equation and the corresponding solution resemble ones obtained for stratified media. The dispersion equation and the corresponding solution are applicable to media with arbitrary elastic (monoclinic) anisotropy.

Keywords

Functionally graded materialLamb waveCauchy formalismanisotropy
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 1 , February 2020 , pp. 1 - 6
Copyright
Copyright © 2019 The Society of Theoretical and Applied Mechanics 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Liu, G.R., Tani, J., Ohyoshi, T., “Lamb waves in a functionally gradient material plates and its transient response. Part 1: Theory; Part 2: Calculation result”, Transactions of the Japan Society of Mechanical Engineers, 57A, 131–42 (1991)Google Scholar
Koizumi, M., “The concept of FGM” Ceramic Transactions: Functionally Gradient Materials. 34, 3–10 (1993)Google Scholar
Liu, G.R., Tani, J., “Surface waves in functionally gradient piezoelectric plates”, Transactions of the American Society of Mechanical Engineers, 116, 440–448 (1994)Google Scholar
Miyamoto, Y., Kaysser, W.A., Brain, B.H., Kawasaki, A., Ford, R.G., “Functionally graded materials” Kluwer, Academic Publishers (1999)CrossRefGoogle Scholar
Han, X., Liu, G.R., Lam, K.Y., Ohyoshi, T., “A quadratic layer element for analyzing stress waves in FGMs and its application in material characterization”, Journal of Sound and Vibration, 236, 307–321 (2000)CrossRefGoogle Scholar
Vlasie, V., Rousseau, M., “Guide modes in a plane elastic layer with gradually continuous acoustic properties”, NDT&E International, 37, 633–644 (2004)CrossRefGoogle Scholar
Baron, C., Naili, S., “Propagation of elastic waves in a fluid-loaded anisotropic functionally graded waveguide: application to ultrasound characterization”, Journal of the Acoustical Society of America, 127(3), 1307–1317 (2010)CrossRefGoogle Scholar
Amor, M.B., Ghozlen, M.H.B., “Lamb waves propagation in functionally graded piezoelectric materials by Peano-series method”, Ultrasonics, 4905, 1–5 (2014)Google Scholar
Nanda, N., Kapuria, S., “Spectral finite element for wave propagation analysis of laminated composite curved beams using classical and first order shear deformation theories”, Composite Structures, 132, 310–320 (2015)CrossRefGoogle Scholar
Xu, Chao, Yu, Zexing, “Numerical simulation of elastic wave propagation in functionally graded cylinders using time-domain spectral finite element method”, Advances in Mechanical Engineering, 9(11), 1–17 (2017)CrossRefGoogle Scholar
Lefebvre, J.E., et al., “Acoustic wave propagation in continuous functionally graded plates: an extension of the Legendre polynomial approach”, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 48, 1332–1340 (2001)CrossRefGoogle ScholarPubMed
Qian, Z.H., Jin, F., Wang, Z.K., Kishimoto, K., “Transverse surface waves on a piezoelectric material carrying a functionally graded layer of finite thickness”, International Journal of EngineeringScience, 45, 455–466 (2007)Google Scholar
Kielczynski, P., Szalewski, M., Balcerzak, A., Wieja, K., “Propagation of ultrasonic Love waves in nonhomogeneous elastic functionally graded materials”, Ultrasonics, 65, 220–227 (2016)CrossRefGoogle ScholarPubMed
Kielczynski, P. M., Szalewski, M., “An inverse method for determining the elastic properties of thin layers using Love surface waves”, Inverse Problems in Science and Engineering, 19, 31–43 (2011).CrossRefGoogle Scholar
Kuznetsov, S.V., “Lamb waves in anisotropic plates (Review)”, Acoustical Physics, 60(1), 95–103 (2014)CrossRefGoogle Scholar
Kuznetsov, S.V., “Love waves in stratified monoclinic media”, Quarterly of Applied Mathematics, 62, 749–766 (2004)CrossRefGoogle Scholar
Djeran-Maigre, I., Kuznetsov, S.V., “Solitary SH waves in two-layered traction-free plates”, Comptes Rendus, Mécanique, 336, 102–107 (2008)CrossRefGoogle Scholar
Chadwick, P., Smith, G.D., “Foundations of the theory of surface waves in anisotropic elastic materials”, Advances in Applied Mechanics, 17, 303–376 (1977)CrossRefGoogle Scholar
Ting, T.C.T., Barnett, D.M., “Classifications of surface waves in anisotropic elastic materials” Wave Motion, 26, 207–218 (1997)CrossRefGoogle Scholar
Tanuma, K., “Stroh formalism and Rayleigh waves”, Journal of Elasticity, 89, 5–154 (2007)CrossRefGoogle Scholar
Wang, L. & Rokhlin, S.I., “Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media”, Ultrasonics, 39, 413–424 (2001)CrossRefGoogle ScholarPubMed
Ilyashenko, A., Kuznetsov, S., “SH waves in anisotropic (monoclinic) media”, Zeitschrift für angewandte Mathematik und Physik, 69, 1–7 (2018)CrossRefGoogle Scholar