Love Wave Propagation in a Fiber-reinforced Layer with Corrugated Boundaries Overlying Heterogeneous Half-space

Document Type: Research Paper


Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), India


Love-type wave generation in a fiber-reinforced medium placed over an inhomogeneous orthotropic half-space is analysed. The upper and lower boundary surfaces of the fiber reinforced medium are periodically corrugated. Inhomogeneity of half-space is caused by variable density and variable shear modules. Displacement components for layer and half-space are derived by applying separable variable technique. Dispersion relation for Love wave is obtained in closed form. Numerical calculations for the achieved dispersion equation are performed. In the numerical examples, the main attention is focused on the effect of corrugation investigation, reinforced parameters and inhomogeneity on the relations between wave number and phase velocity.


Main Subjects

[1] Ewing, W.M., Jardetzky, W.S., Press, F., Beiser, A., Elastic waves in layered media, Physics Today, 10(12), 1957, 27p.

[2] Gubbins, D., Seismology and plate tectonics, Cambridge University Press, 1990.

[3] Biot, M.A., Mechanics of incremental deformations, Wiley, 1964.

[4] Park, S.J., Seo, M.K., Interface science and composites, Academic Press, 2011.

[5] Pipkin, A.C., Rogers, T.G., Plane deformations of incompressible fiber-reinforced materials, Journal of Applied Mechanics, 38(3), 1971, 634-640.

[6] Belfield, A.J., Rogers, T.G., Spencer, A.J., Stress in elastic plates reinforced by fibres lying in concentric circles, Journal of the Mechanics and Physics of Solids, 31(1), 1983, 25-54.

[7] Upadhyay, S.K., Love wave propagation in anisotropic inhomogeneous medium: Elastic parameters for equivalent isotropic case, Pure and Applied Geophysics, 81(1), 1970, 45-50.

[8] Nayfeh, A.H., Chimenti, D.E., Propagation of guided waves in fluid‐coupled plates of fiber‐reinforced composite, The Journal of the Acoustical Society of America, 83(5), 1988, 1736-43.

[9] Pradhan, A., Samal, S.K., Mahanti, N.C., Influence of anisotropy on the love waves in a self-reinforced medium, Tamkang Journal of Science and Engineering, 6(3), 2003, 173-178.

[10] Ranjan, C., Samal, S.K., Love waves in the fiber-reinforced layer over a gravitating porous half space, Acta Geophysica, 61(5), 2013, 1170-1183.

[11] Khan, A., Abo-Dahab, S.M., Abd-Alla, A.M., Gravitational effect on surface waves in a homogeneous fibre-reinforced anisotropic general viscoelastic media of higher and fractional order with voids, International Journal of Physical Sciences, 10(24), 2015, 604-13.

[12] Abd-Alla, A.M., Abo-Dahab, S.M., Khan, A., Rotational effect on Thermoelastic Stoneley, Love and Rayleigh waves in fibre-reinforced anisotropic general viscoelastic media of higher order, Structural Engineering and Mechanics, 61(2), 2017, 221-230.

[13] Vishwakarma, S.K., Torsional wave propagation in a self-reinforced medium sandwiched between a rigid layer and a viscoelastic half space under gravity, Applied Mathematics and Computation, 242, 2014, 1-9.

[14] Samal, S.K., Chattaraj, R., Surface wave propagation in fiber-reinforced anisotropic elastic layer between liquid saturated porous half space and uniform liquid layer, Acta Geophysica, 59(3), 2011, 470-82.

[15] Manna, S., Kundu, S., Gupta, S., Love wave propagation in a piezoelectric layer overlying in an inhomogeneous elastic half-space, Journal of Vibration and Control, 21(13), 2015, 2553-68.

[16] Sahu, S.A., Saroj, P.K., Paswan, B., Shear waves in a heterogeneous fiber-reinforced layer over a half-space under gravity, International Journal of Geomechanics, 15(2), 2014, 04014048.

[17] Deresiewicz, H., A note on Love waves in a homogeneous crust overlying an inhomogeneous substratum, Bulletin of the Seismological Society of America, 52(3), 1962, 639-45.

[18] Ke, L.L., Wang, Y.S., Zhang, Z.M., Love waves in an inhomogeneous fluid saturated porous layered half-space with linearly varying properties, Soil Dynamics and Earthquake Engineering, 26(6-7), 2006, 574-81.

[19] Asano, S., Reflection and refraction of elastic waves at a corrugated interface, Bulletin of the Seismological Society of America, 56(1), 1966, 201-21.

[20] Singh, S.S., Tomar, S.K., qP-wave at a corrugated interface between two dissimilar pre-stressed elastic half-spaces, Journal of Sound and Vibration, 317(3-5), 2008, 687-708.

[21] Chow, T.S., On the propagation of flexural waves in an orthotropic laminated plate and its response to an impulsive load, Journal of Composite Materials, 5(3), 1971, 306-19.

[22] Destrade, M., Surface waves in orthotropic incompressible materials, The Journal of the Acoustical Society of America, 110(2), 2001, 837-40.

[23] Ahmed, S.M., Abo-Dahab, S.M., Propagation of Love waves in an orthotropic granular layer under initial stress overlying a semi-infinite granular medium, Journal of Vibration and Control, 16(12), 2010, 1845-58.

[24] Abd-Alla, A.M., Ahmed, S.M., Propagation of Love waves in a non-homogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium, Applied Mathematics and Computation, 106(2-30), 1999, 265-75.

[25] Lotfy, K., Abo-Dahab, S.M., Hobiny, A.D., Plane waves on a gravitational rotating fibre-reinforced thermoelastic medium with thermal shock problem, Journal of Advanced Physics, 7(1), 2018, 58-69.

[26] Abo-Dahab, S.M., Surface waves in fiber-reinforced anisotropic general viscoelastic media of higher orders with voids, rotation, and electromagnetic field, Mechanics of Advanced Materials and Structures, 25(4), 2018, 319-34.

[27] Singh, A.K., Das, A., Kumar, S., Chattopadhyay, A., Influence of corrugated boundary surfaces, reinforcement, hydrostatic stress, heterogeneity and anisotropy on Love-type wave propagation, Meccanica, 50(12), 2015, 2977-94.

[28] Vinh, P.C., Anh, V.T., Linh, N.T., On a technique for deriving the explicit secular equation of Rayleigh waves in an orthotropic half-space coated by an orthotropic layer, Waves in Random and Complex Media, 26(2), 2016, 176-88.

[29] Vishwakarma, S.K., Kaur, R., Panigrahi, T.R., Love wave frequency in an orthotropic crust over a double-layered anisotropic mantle, Soil Dynamics and Earthquake Engineering, 110, 2018, 86-92.

[30] Kakar, R., Kakar, S., Dispersion of torsional surface wave in an intermediate vertical prestressed inhomogeneous layer lying between heterogeneous half spaces, Journal of Vibration and Control, 23(19), 2017, 3292-305.

[31] Sahu, S. A., Nirwal, S., An asymptotic approximation of Love wave frequency in a piezo-composite structure, WKB approach, Waves in Random and Complex Media, 2019, doi: 10.1080/17455030.2019.1567955.

[32] Spencer, A.J., Deformations of fibre-reinforced materials, Clarendon Press, 1972.

[33] Biot, M.A., Mechanics of incremental deformations, Wiley, 1965.

[34] Prosser, W.H., Green, Jr. R.E., Characterization of the nonlinear elastic properties of graphite/epoxy composites using ultrasound, Journal of Reinforced Plastics and Composites, 9, 1990, 162-73.

[35] Markham, M.F., Measurement of the elastic constants of fibre composites by ultrasonics, Composites, 1(2), 1969, 145-149.