Abstract
Propagation of the torsional surface waves in a medium consisting of a functionally graded (FG) substrate bonded to a thin piezoelectric over-layer has been analytically formulated in the mathematical framework of surface/interface elasticity theory. In the cases where the wavelength and/or the thickness of the over-layer are comparable to the surface/interface characteristic length, then the surface/interface effects are not negligible. It is assumed that the over-layer is made of hexagonal 622 crystals with a single axis of rotational symmetry coinciding with the axis of polarization. The half-space is made of an FG transversely isotropic material in which the elasticity tensor and the mass density vary linearly with depth. Accounting for the surface/interface effects, the pertinent dispersion relation is derived analytically and verified for five different limiting cases of the proposed problem. The effect of the inhomogeneity parameters of the FG half-space and the surface/interface parameters on the dispersion relation is studied numerically, and the results are compared with those obtained from the classical theory.
Similar content being viewed by others
References
Ezzin, H., Amor, M.B., Ghozlen, M.H.B.: Love waves propagation in a transversely isotropic piezoelectric layer on a piezomagnetic half-space. Ultrasonics 69, 83–89 (2016)
Jin, F., Qian, Z., Wang, Z., Kishimoto, K.: Propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress. Smart Mater. Struct. 14(4), 515 (2005)
Liu, H., Wang, Z.K., Wang, T.J.: Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure. Int. J. Solids Struct. 38(1), 37–51 (2001)
Salah, I.B., Njeh, A., Ghozlen, M.H.B.: A theoretical study of the propagation of Rayleigh waves in a functionally graded piezoelectric material (FGPM). Ultrasonics 52(2), 306–314 (2012)
Achenbach, J.: Wave Propagation in Elastic Solids, vol. 16. Elsevier, Amsterdam (2012)
Eringen, A.C., Suhubi, E.S.: Elastodynamics, vol. II. Academic, New York (1975)
Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57(4), 291–323 (1975)
Gurtin, M.E., Murdoch, A.I.: Surface stress in solids. Int. J. Solids Struct. 14(6), 431–440 (1978)
Enzevaee, C., Shodja, H.M.: Crystallography and surface effects on the propagation of Love and Rayleigh surface waves in fcc semi-infinite solids. Int. J. Solids Struct. 138, 109–117 (2018)
Mi, C., Jun, S., Kouris, D.A., Kim, S.Y.: Atomistic calculations of interface elastic properties in noncoherent metallic bilayers. Phys. Rev. B 77(7), 075425 (2008)
Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(3), 139 (2000)
Pahlevani, L., Shodja, H.M.: Surface and interface effects on torsion of eccentrically two-phase fcc circular nanorods: determination of the surface/interface elastic properties via an atomistic approach. J. Appl. Mech. 78(1), 011011 (2011)
Shodja, H.M., Enzevaee, C.: Surface characterization of face-centered cubic crystals. Mech. Mater. 129, 15–22 (2019)
Chen, Q., Wang, G., Pindera, M.J.: Homogenization and localization of nanoporous composites—a critical review and new developments. Compos. Part B Eng. 155, 329–368 (2018)
Enzevaee, C., Gutkin, M.Y., Shodja, H.M.: Surface/interface effects on the formation of misfit dislocation in a core-shell nanowire. Philos. Mag. 94(5), 492–519 (2014)
Fang, Q.H., Liu, Y.W.: Size-dependent interaction between an edge dislocation and a nanoscale inhomogeneity with interface effects. Acta Mater. 54(16), 4213–4220 (2006)
Gutkin, M.Y., Enzevaee, C., Shodja, H.M.: Interface effects on elastic behavior of an edge dislocation in a core–shell nanowire embedded to an infinite matrix. Int. J. Solids Struct. 50(7–8), 1177–1186 (2013)
Shodja, H.M., Enzevaee, C., Gutkin, M.Y.: Interface effect on the formation of a dipole of screw misfit dislocations in an embedded nanowire with uniform shear eigenstrain field. Eur. J. Mech. A/Solids 51, 154–159 (2015)
Wang, G., Chen, Q., He, Z., Pindera, M.J.: Homogenized moduli and local stress fields of unidirectional nano-composites. Compos. Part B Eng. 138, 265–277 (2018)
Wolfer, W.G.: Elastic properties of surfaces on nanoparticles. Acta Mater. 59(20), 7736–7743 (2011)
Ru, Y., Wang, G.F., Wang, T.J.: Diffractions of elastic waves and stress concentration near a cylindrical nano-inclusion incorporating surface effect. J. Vib. Acoust. 131(6), 061011 (2009)
Shodja, H.M., Ghafarollahi, A., Enzevaee, C.: Surface/interface effect on the scattering of love waves by a nano-size surface-breaking crack within an ultra-thin layer bonded to an elastic half-space. Int. J. Solids Struct. 108, 63–73 (2017)
Dey, S., Gupta, A.K., Gupta, S.: Propagation of torsional surface waves in a homogeneous substratum over a heterogeneous half-space. Int. J. Numer. Anal. Methods Geomech. 20(4), 287–294 (1996)
Heywang, W., Lubitz, K., Wersing, W. (eds.): Piezoelectricity: Evolution and Future of a Technology, vol. 114. Springer, Berlin (2008)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Enzevaee, C., Shodja, H.M. Torsional surface wave propagation in a transversely isotropic FG substrate with piezoelectric over-layer within surface/interface theory. Acta Mech 231, 2203–2216 (2020). https://doi.org/10.1007/s00707-020-02638-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-020-02638-2