zbMATH — the first resource for mathematics

Rayleigh wave on the half-space with a gradient piezoelectric layer and imperfect interface. (English) Zbl 07163017
Summary: In this study, we consider the propagation of a Rayleigh wave on an anisotropic half-space with a piezoelectric gradient covering layer and imperfect interface. First, the state transfer equation is derived from the governing equations and constitutive relations. The transfer matrix of the state vector is then obtained by solving the state transfer equation and the stiffness matrix is obtained. The total surface stiffness matrix is obtained by combining the transfer matrices and the stiffness matrices of the piezoelectric half-space, the gradient covering layer, and the imperfect interface. Finally, the application of the electrically open circuit, short circuit conditions, and mechanically traction-free conditions gives the frequency dispersive relation. We investigate five types of gradient profiles for the covering layer where the material parameters vary gradually from the top to the bottom, and two types of imperfect interfaces, i.e., dielectrically weakly and highly conducting but mechanically compliant interfaces. The numerical results show that the surface wave speed is sensitive to the gradient profile of the covering layer with the mechanically and dielectrically imperfect interfaces between the covering layer and the substrate.

78 Optics, electromagnetic theory
74 Mechanics of deformable solids
Full Text: DOI
[1] Lothe, J.; Barnett, D. M., On the existence of surface-wave solutions for anisotropic elastic half-spaces with free surface, J. Appl. Phys., 47, 2, 428-433 (1976)
[2] Currie, P. K., The secular equation for Rayleigh waves on elastic crystals, Quart. J. Mech. Appl. Math., 32, 2, 163-173 (1979) · Zbl 0417.73036
[3] Crampin, S.; Taylor, D. B., The propagation of surface waves in anisotropic media, Geophys. J. Int., 25, 1-3, 71-87 (1997)
[4] Barnett, D. M., Bulk, surface, and interfacial waves in anisotropic linear elastic solids, Int. J. Solids Struct., 37, 1-2, 45-54 (2000) · Zbl 1073.74553
[5] Mielke, A.; Fu, Y. B., Uniqueness of the surface-wave speed: a proof that is independent of the Stroh formalism, Math. Mech. Solids, 9, 5-15 (2004) · Zbl 1043.74025
[6] Nathalie, F. C.; Dimitri, K.; Carcione, J. M.; Cavallini, F., Elastic surface waves in crystals. Part 1: review of the physics, Ultrasonics, 51, 6, 653-660 (2011)
[7] Ting, T. C.T., Existence of anti-plane shear surface waves in anisotropic elastic half-space with depth-dependent material properties, Wave Motion, 47, 6, 350-357 (2010) · Zbl 1231.74215
[8] Achenbach, J. D.; Balogun, O., Anti-plane surface waves on a half-space with depth-dependent properties, Wave Motion, 47, 1, 59-65 (2010) · Zbl 1231.74203
[9] Norris, A. N.; Shuvalov, A. L.; Kutsenko, A. A., The matrix sign function for solving surface wave problems in homogeneous and laterally periodic elastic half-spaces, Wave Motion, 50, 8, 1239-1250 (2013) · Zbl 1454.74078
[10] Godoy, E.; Durán, M.; Nédélec, J. C., On the existence of surface waves in an elastic half-space with impedance boundary conditions, Wave Motion, 49, 6, 585-594 (2012) · Zbl 1360.74075
[11] Chiriţă, S., Thermoelastic surface waves on an exponentially graded half-space, Mech. Res. Commun., 49, 27-35 (2013)
[12] Li, L.; Wei, P. J., The piezoelectric and piezomagnetic effect on the surface wave velocity of magneto-electro-elastic solids, J. Sound Vib., 333, 8, 2312-2326 (2014) · Zbl 1308.93073
[13] Li, L.; Wei, P. J., Direction dependence of surface wave speed at the surface of magneto-electro-elastic half-space, Acta Mech. Solida Sin., 28, 1, 102-110 (2015)
[14] Adler, E. L., SAW and Pseudo-SAW properties using matrix methods, IEEE Trans. Ultrason. Ferroelectr. Freq. Control., 41, 6, 876-882 (1994)
[15] Wang, L.; Rokhlin, S. I., Recursive geometric integrators for wave propagation in a functionally graded multilayered elastic medium, J. Mech. Phys. Solids, 52, 2473-2506 (2004) · Zbl 1134.74375
[16] Smith, P. M., Dyadic Green’s functions for multilayer SAW substrates, IEEE Trans. Ultrason. Ferroelectr. Freq. Control., 48, 1, 171-179 (2001)
[17] Li, X. Y.; Wang, Z. K.; Huang, S. H., Love waves in functionally graded piezoelectric materials, Int. J. Solids Struct., 26, 7309-7328 (2004) · Zbl 1124.74311
[18] Qian, Z. H.; Jin, F.; Wang, Z. K., Transverse surface waves on a piezoelectric material carrying a functionally graded layer of finite thickness, Int. J. Eng. Sci., 45, 2-8, 455-466 (2007)
[19] Collet, B.; Destrade, M.; Maugin, G. A., Bleustein-Gulyaev waves in some functionally graded materials, Eur. J. Mech. A Solids, 25, 5, 695-706 (2006) · Zbl 1101.74037
[20] Ben Salah, I.; Wali, Y.; Ben Ghozlen, M. H., Love waves in functionally graded piezoelectric materials by stiffness matrix method, Ultrasonics, 51, 3, 310-316 (2011)
[21] Ben Salah, I.; Njeh, A.; Ben Ghozlen, M. H., A theoretical study of the propagation of Rayleigh waves in a functionally graded piezoelectric material, Ultrasonics, 52, 2, 306-314 (2012)
[22] Li, P.; Jin, F., Bleustein-Gulyaev waves in a transversely isotropic piezoelectric layered structure with an imperfectly bonded interface, Smart Mater Struct, 21, Article 045009 pp. (2012)
[23] Cao, X. S.; Jin, F.; Jeon, I., Rayleigh surface wave in a piezoelectric wafer with subsurface damage, Appl. Phys. Lett., 95, Article 261906 pp. (2009)
[24] Blanes, S.; Casas, F.; Ros, J., Improved high order integrators based on Magnus expansion, Bit Numer. Math., 40, 3, 434-450 (2000) · Zbl 0962.65102
[25] Blanes, S.; Casas, F.; Ros, J., High order optimized geometric integrators for linear differential equations, Bit Numer. Math., 42, 2, 262-284 (2002) · Zbl 1008.65045
[26] Moler, C.; Loan, C. V., Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev., 45, 1, 3-49 (2003) · Zbl 1030.65029
[27] Wang, X.; Sudak, L. J., A piezoelectric screw dislocation interacting with an imperfect piezoelectric bimaterial interface, Int. J. Solids Struct., 44, 10, 3344-3358 (2007) · Zbl 1121.74366
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.