Dispersion of Stoneley waves through the irregular common interface of two hydrostatic stressed MTI media

Document Type : Research Note

Authors

1 Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, India

2 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, Tamil Nadu, India

Abstract

The present work deals with the mathematical inspection of Stoneley wave propagation through the corrugated irregular common interface of two dissimilar magneto-elastic transversely isotropic (MTI) half-space media under the impression of hydrostatic stresses. For the enumeration of the Lorentz’s force besmeared in the structure, generalized Ohm’s law and Maxwell’s equation have been considered. The interior deformations are calculated analytically to obtain the wave frequency equation using prescribed boundary conditions. To investigate the impacts of irregularity and various affecting parameters such as magnetic couplings and hydrostatic stresses on the wave propagation, frequency curves are framed-up for the phase velocity of the wave.

Keywords

References

References:
[1].             Stoneley, R. “Elastic waves at the surface of separation of two solids”, Proc. of Royal Soc. Lond., 106, pp. 416-428 (1924).
[2].             Ashour, A.S. “Theoretical investigation of Stoneley wave attenuation and dispersion in a fluid filled fracture in transversely isotropic formation”, ARI- An Int. J. for Physics and Eng. Sci., 51, pp. 254-257 (1999).
[3].             Abo-Dahab, S.M. “Propagation of Stoneley waves in magneto-thermoelastic materials with voids and two relaxation times”, J. of Vib. and Cont., 21, pp. 1144-1153 (2015).
[4].             Tiwana, M.H., Ahmed, S., Mann, A.B. and Naqvi, Q.A. “Point source diffraction from a semi-infinite perfect electromagnetic conductor half plane”, Optik, 135, pp. 1–7 (2017).
[5].             Sanjeev, S.A., Saroj, P.K. and Paswan, B. “Shear waves in a heterogeneous fiber-reinforced layer over a half-space under gravity”, Int. J. of Geomech., 15(4), pp. 014-048 (2014).
[6].             Alam, P., Kundu, S. and Gupta, S. “Love-type wave propagation in a hydrostatic stressed magneto-elastic transversely isotropic strip over an inhomogeneous substrate caused by a disturbance point source”, J. of Intl. Material Sys. and Struc., 29, pp. 2508-2521 (2018).
[7].             Kundu, S., Alam, P. and Gupta, S. “Shear waves in magneto-elastic transversely isotropic (MTI) layer bonded between two heterogeneous elastic media”, Mech. of Adv. Materials and Struc., 26, pp. 407-415  (2019).
[8].             Singh, B. “Wave propagation in a rotating transversely isotropic two-temperature generalized thermoelastic medium without dissipation”, Int. J. of Therm., 2016. In Press, DOI: 10.1007/s10765-015-2015-z.
[9].             Vishwakarma, S.K. and Xu, R. “Rayleigh wave dispersion in an irregular sandy Earth’s crust over orthotropic mantle”, Appl. Math. Modelling, 40, pp. 8647-8659 (2016).
[10].         Singh, S.S. “Love wave at a layer medium bounded by irregular boundary surfaces”, J. of Vib. and Cont., 17, pp. 789-795 (2011).
[11].         Alam, P., Kundu, S., Gupta, S. “Dispersion study of SH-wave propagation in an irregular magneto-elastic anisotropic crustal layer over an irregular heterogeneous half-space”, J. of King Saud University –Sci., 30(3), pp. 301-310 (2016).
[12].         Saroj, P.K., Sanjeev, S.A. and Chattopadhyay, A. “Dynamic response of corrugation and rigid boundary surface on Love-type wave propagation in orthotropic layered medium”, J. of Porous Media, 21, pp. 1163-1176 (2018).
[13].         Addy, S.K. and Chakraborty, N.R. “Rayleigh waves in a viscoelastic half-space under initial hydrostatic stress in presence of the temperature field”, Int. J. of Math. and Math. Sci., 24, pp. 3883–3894 (2005).
[14].         Alam, P.,  Kundu, S.,  Gupta, S. “Effect of magneto-elasticity, hydrostatic stress and gravity on Rayleigh waves in a hydrostatic stressed magneto-elastic crystalline medium over a gravitating half-space with sliding contact”, Mech. Research  Comm., 89, pp. 11-17 (2018).
[15].         Alam, P., Kundu, S. and Gupta, S. “Dispersion and attenuation of Love-type waves due to a point source in magneto-viscoelastic layer”, J. of Mech., 34, pp. 801-816 (2018).
[16].         Said, S.M. “Influence of gravity on generalized magnetothermoelastic medium for three-phase-lag model”, J. of Comput. Appl. Math., 291, pp. 142–157 (2016).
[17].         Majhi, S., Pal, P.C. and Kumar, S. “Reflection and transmission of plane SH-waves in an initially stressed inhomogeneous anisotropic dispersion study of SH-wave propagation magnetoelastic medium”, J. of Seism., 21, pp. 155-163 (2016).
[18].         Shaw, S., Biswas, S. and Mukhopadhyay, B. "Rayleigh waves in a thermoorthotropic medium: A dynamic analysis”, Comput. Therm. Sci.: An Int. J., 10, pp. 557-574 (2018).
[19].         Sahu, S.A., Chaudhary, S., Saroj, P.K. and Chattopadhyay, A. “Rayleigh waves in liquid layer resting over an initially stressed orthotropic half-space under self-weight”, Arab. J. of Geosci., 2017. In Press, DOI: 10.1007/s12517-017-2924-1.
[20].         Biot, M.A. “Mechanics of Incremental Deformations”, John Wiley & Sons, Inc., New York (1965).
[21].         Mukhopadhyay, S. “Effects of thermal relaxations on thermoviscoelastic inter- actions in an unbounded body with a spherical cavity subjected to a periodic loading on the boundary”, J. of Therm. Stresses, 23, pp. 675–684 (2000).
[22].         Anderson, D.L. “Elastic wave propagation in layered anisotropic Media”, J. of Geophy. Research, 66, pp. 2953–2963 (1961).
[23].         Rehman, A., Khan, A. and Ali, A. “Rayleigh waves in a rotating transversely isotropic materials”, Elect. J. Tech. Acoustics, pp. 5 (2007).
[24].         Ding, H., Chien, W. and Zhang, I. “Elasticity of Transversely Isotropic Materials”, Springer Sci. and Business Media, 126, pp. 22-23 (2006).
Scientia Iranica
Volume 28, Issue 2
Transactions on Mechanical Engineering (B)
March and April 2021
Pages 837-846

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History

  • Receive Date: 09 January 2019
  • Revise Date: 04 January 2020
  • Accept Date: 01 February 2020

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