A mathematical model is presented to describe the propagation of torsional surface waves in a corrugated loosely bonded orthotropic layer sandwiched between two initially stressed viscoelastic half-spaces. The dispersion relation in a closed form is obtained for the analytical model. It is found that the initial stress, hydrostatic stress, viscoelasticity, and the bonding and flatness parameters have a great effect on the phase velocity of torsional surface waves. The method of separation of variables is employed to obtain an analytical solution in the present study. Some particular cases are discussed, and it is found that the results obtained well agree with the classical Love wave equation. Numerical simulations have also been performed to show results of the present analytical study graphically.
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I. Vardoulakis, “Torsional surface waves in inhomogeneous elastic media.” Int. J. Numer. Anal. Methods Geomech., 8, No. 3, 287-296 (1984).
H. G., Georgiadis, I. Vardoulakis, and G. Lykotrafitis, “Torsional surface waves in a gradient-elastic half-space.” Wave Motion, 31, No. 4, 333-348 (2000).
L. Bao, H. Yuan, M. Sakurai, M. Nakazawa, and K. Kemmochi, “A study on the torsional wave of fiber reinforced composite materials.” J. Compos. Mater, 40, No. 4, 338-391 (2006)
S. K. Vishwakarma, and S. Gupta, “Torsional surface wave in a homogeneous crustal layer over a viscoelastic mantle.” Int. J. Appl. Math. Mech., 8 (16), 38-50 (2012).
M.M. Selim, “Static deformation of an irregular initially stressed medium.” Appl Math Comput, 188, 1274-1284, (2007).
R. Zhang, M. Shinozuka, “Effects of irregular boundaries in a layered half-space on seismic waves.” J. Sound Vib. 1951–16(1996)
X. F. Chen, “Generation and propagation of seismic SH waves in multi-layered media with irregular interfaces,” Adv. Geophys., 48, 191-264 (2007).
S.S. Singh, SK. Tomar, “qP-wave at a corrugated interface between two dissimilar pre-stressed elastic half-spaces.” J Sound Vibr 317 (3), 687-708 (2008)
S. S. Singh, “Love Wave at a Layer Medium Bounded by Irregular Boundary Surfaces,” J. Vibr. Control, 17, 789-795 (2011).
S, Kundu S., Manna and S. Gupta, “Love wave dispersion in pre-stressed homogeneous medium over a porous halfspace with irregular boundary surfaces.” Int J Solids Struct, 51 No. 21-22, 3689-3697 (2014)
A. Chattopadhyay, S.Gupta, V. K., and P.Kumari, “Propagation of shear waves in viscoelastic medium at irregular boundaries.” Acta Geoph. 58 (2) 195-214 (2010)
J. Du, X. Jin, and J. Wang, “Love wave propagation in layered magneto-electro-elastic structures with initial stress,” Acta Mech., 192 No. 1-4, 169-189. (2007)
M. A. Biot, “The influence of initial stress on elastic waves,” J. Appl. Phys., 11, 522-530 (1940).
A. N. Guz, “Elastic waves in bodies with initial (residual) stresses,” Int. Appl. Mech., 38, No. 1, 23-59 (2002).
S. Akbarov and N. Ilhan, “Dynamics of a system comprising a pre-stressed orthotropic layer and pre-stressed orthotropic half-plane under the action of a moving load,” Int. J. Solids. Struct. 45, 4222-4235 (2008)
A. K. Singh, Z. Parveen, and A. Das, “Influence of loosely bonded sandwiched initially stressed visco-elastic layer on torsional wave Propagation,” J. of Mechanics, Doi. https://doi.org/10.1017/jmech.2016.107
Z. J. Dai, Z. B. Kuang, and S. X. Zhao, “Rayleigh waves in a double porosity half-space,” J. Sound Vibr. , 298, 319-332 (2006)
Z. J. Dai and Z. B. Kuang, “Love waves in double porosity media,” J. Sound Vib. , 296, 1000-1012 (2006)
L. L. Ke, Y. S. Wang and Z. M. Zhang, “Love waves in an inhomogeneous fluid saturated porous layered half-space with linearly varying properties,” Soil Dyn. Earthq. Eng. 26, 574-581 (2006)
M. S. Son and Y. J. Kang, “Propagation of shear waves in a poroelastic layer constrained between two elastic layers,” Appl. Math. Model, 36, 3685-3695 (2012)
A. K. Singh and A. Lakshman, “Effect of loosely bonded undulated boundary surfaces of doubly layered half-space on the propagation of torsional wave,” Mech. Res. Commun. 73, 91-206 (2016)
G. S. Murty, “A theoretical model for the attenuation and dispersion of Stoneley waves at the loosely-bonded interface of elastic half-spaces,” Phys. Earth planet. Inter. 11, 65-79 (1975).
G. S. Murty, “Reflection, transmission and attenuation of elastic waves at a loosely bonded interface of two half-spaces,” Geophys. J. R. Astronom. Soc. 44, 389-404 (1976)
S. Asano, “Reflection and refraction of elastic waves at a corrugated interface,” Bull Seismol. Soc. Am., 56, No. 1, 201-221 (1966)
M. A. Biot, Mechanics of Incremental Deformations, John Wiley and Sons Inc., New York, 1965.
D. Gubbins, Seismology and Plate Tectonics, Cambridge University Press, Cambridge, 1990.
W. H. Prosser and R. E. Green “Characterization of the nonlinear elastic properties of graphite/epoxy composites using ultrasound,” J. Reinf. Plast. Compos., 9, No. 2, 162-173 (1990).
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Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 54, No. 3, pp. 473-488, May-June, 2018.
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Sahu, S.A., Singh, M.K. & Pankaj, K.K. Analysis of Torsional Waves in a Prestressed Composite Structure with Loosely Bonded and Corrugated Boundaries. Mech Compos Mater 54, 321–332 (2018). https://doi.org/10.1007/s11029-018-9742-8
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DOI: https://doi.org/10.1007/s11029-018-9742-8