Abstract
The problems concerned with the dispersion and attenuation of surface wave propagations due to imperfect elasticity are of great interest to seismologists. The present work reports the dispersion and attenuation characteristics of Love-type wave propagation in a fiber-reinforced layer laid on an inhomogeneous viscoelastic half-space. The inhomogeneity in the viscoelastic medium arises due to the hyperbolic trigonometric variation in depth. A complex frequency equation for the Love-type wave has been procured using the suitable boundary conditions. Thus, the dispersion and damping equations have been calculated to analyze the dispersion and attenuation peculiarities of the wave. Results for the uniform homogeneous isotropic media have been compared with existing solutions. Numerical computation and graphical sketches have been set forth for the relevant parametric variations.
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References
A.J. Belfield, T.G. Rogers and A.J.M. Spencer, “Stresses in Elastic Plates Reinforced by Fibres Lying in Concentric Circles,” J. Mech. Phys. Solids, 31(1), 25 (1983).
M.I.A. Othman and I.A. Abbas, “Effect of Rotation on Plane Waves at the Free Surface of a Fibre-Reinforced Thermoelastic Half-Space Using the Finite Element Method,” Meccanica. 46, 413 (2011).
S. Kundu, S. Gupta, and S. Manna, “Propagation of Love Wave in Fiber-Reinforced Medium Lying over an Initially Stressed Orthotropic Half-Space,” Int. J. Num. Anal. Meth. Geomech. 38(11), 1172 (2014).
S.M. Abo-Dahab and E. Edfawy, “Secular Equation of Magnetic Field and Gravity Variation on Propagation of Surface Waves in Fiber-Reinforced Anisotropic Thermoelastic Solid with Two Relaxation Times,” J. Comp. Theor. Nanosci. 11(11), 2339 (2014).
P. Alam, S. Kundu, and S. Gupta, “Dispersion Study of SH-Wave Propagation in an Irregular Magneto-Elastic Anisotropic Crustal Layer over an Irregular Heterogeneous Half-Space,” J.K.S. Uni.-Sci. 30(3), 301 (2018).
M. Romeo, “Interfacial Viscoelastic SH-Wave,” Int. J. Sol. Struct. 40(9), 2057 (2003).
P. Kumari, V. K. Sharma, and C. Modi, “Torsional Wave in a Viscoelastic Layer over a Viscoelastic Substratum of Voigt Types,” J. Earthq. Eng. 20(8), 1278 (2016) [DOI: https://doi.org/10.1080/13632469.2016.1138163].
S. Kumar, P.C. Pal, and S. Bose, “Propagation of SH-Type Waves in Inhomogeneous Anisotropic Layer Overlying an Anisotropic Viscoelastic Half-Space,” Int. J. Eng. Sci. Tech. 6(4), 24 (2014).
G.D. Manolis and R.P. Shaw, “Harmonic Wave Propagation through Viscoelastic Heterogeneous Media Exhibiting Mild Stochasticity-I. Fundamental Solutions,” Soil Dynam. Earthq. Eng. 15(2), 119 (1996).
S. Kundu, P. Alam, S. Gupta, and D.K. Pandit, “Impacts on the Propagation of SH-Waves in a Heterogeneous Viscoelastic Layer Sandwiched Between an Anisotropic Porous Layer and an Initially Stressed Isotropic Half Space,” J. Mech. 33(1), 13 (2016).
N. Kumari, S.A. Sahu, A. Chattopadhyay, and A.K. Singh, “Influence of Heterogeneity on the Propagation Behavior of Love-Type Waves in a Layered Isotropic Structure,” Int. J. Geom. 16(2), 04015062 (2015).
N. Kumari, A. Chattopadhyay, A.K. Singh, and S.A. Sahu, “Magnetoelastic Shear Wave Propagation in Pre-Stressed Anisotropic Media under Gravity,” Acta Geophys. 65(1), 189 (2017).
P. Alam, S. Kundu, and S. Gupta, “Dispersion and Attenuation of Torsional Wave in a Viscoelastic Layer Bonded Between a Layer and a Half-Space of Dry Sandy Media,” Appl. Math. Mech. 38(9), 1313 (2017).
P. Alam, S. Kundu, and S. Gupta, “Dispersion and Attenuation of Love-Type Waves Due to a Point Source in Magneto-Viscoelastic Layer,” J. Mech. 34(6), 801 (2018) [DOI: https://doi.org/10.1017/jmech.2017.110].
S.A. Sahu, P.K. Saroj, and N. Dewangan, “SH-Waves in Viscoelastic Heterogeneous Layer over Half-Space with Self-Weight,” Arch. Appl. Mech. 84(2), 235 (2014).
A.M. Abd-Alla, S.M. Abo-Dahab, and T.A. Al-Thamali, “Love Waves in a Non-Homogeneous Orthotropic Magneto-Elastic Layer under Initial Stress Overlying a Semi-Infinite Medium,” J. Comp. Theor. Nanosci. 10, 10 (2013).
R. Kakar and S. Kakar, “Modelling of SH-Waves in a Fiber-Reinforced Anisotropic Layer over a Pre-Stressed Heterogeneous Half-Space,” J. Theor. Appl. Mech. 54(2), 463 (2016).
S.A. Sahu, A. Singhal, and S. Chaudhary, “Influence of Heterogeneity on Rayleigh Wave Propagation in an Incompressible Medium Bonded Between Two HalfSpaces,” J. Solid Mech. 9(3), 555 (2017).
M.A. Biot, Mechanics of Incremental Deformations (Wiley, N.Y., 1965).
A.E.H. Love, Mathematical Theory of Elasticity (Cambridge University Press, Cambridge, 1920).
M. Ewing, W. Jardetzky, and F. Press, Elastic Waves in Layered Media (McGraw-Hill, N.Y., 1957).
D. Gubbins, Seismological and Plate Tectonics (Cambridge University Press, Cambridge, 1990).
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The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through a research groups program under grant number R.G.P.1/85/40.
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Alam, P., Kundu, S., Badruddin, I.A. et al. Dispersion and Attenuation Characteristics of Love-Type Waves in a Fiber-Reinforced Composite over a Viscoelastic Substrate. Phys. Wave Phen. 27, 281–289 (2019). https://doi.org/10.3103/S1541308X19040083
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DOI: https://doi.org/10.3103/S1541308X19040083