Magnetoelastic shear wave propagation in pre-stressed anisotropic media under gravity

• Autorzy: Kumari N. , Chattopadhyay A. , Singh A. K. , Sahu S. A.

Identyfikatory

DOI

10.1007/s11600-017-0016-y

• Języki publikacji: EN

Abstrakty

EN

The present study investigates the propagation of shear wave (horizontally polarized) in two initially stressed heterogeneous anisotropic (magnetoelastic transversely isotropic) layers in the crust overlying a transversely isotropic gravitating semi-infinite medium. Heterogeneities in both the anisotropic layers are caused due to exponential variation (case-I) and linear variation (case-II) in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relations have been established in closed form using Whittaker’s asymptotic expansion and were found to be in the well-agreement to the classical Love wave equations. The substantial effects of magnetoelastic coupling parameters, heterogeneity parameters, horizontal compressive initial stresses, Biot’s gravity parameter, and wave number on the phase velocity of shear waves have been computed and depicted by means of a graph. As a special case, dispersion equations have been deduced when the two layers and half-space are isotropic and homogeneous. The comparative study for both cases of heterogeneity of the layers has been performed and also depicted by means of graphical illustrations.

Słowa kluczowe

EN

heterogeneity; magnetoelasticity; transversely isotropic; shear wave; initial stress

PL

niejednorodność; zjawisko magnetosprężyste; transwersalna izotropia; fala poprzeczna; naprężenia pierwotne

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2017
• Tom: Vol. 65, no. 1
• Strony: 189--205
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Kumari N.

• Department of Applied Mathematics, Indian School of Mines, Dhanbad, India

autor

Chattopadhyay A.

• Department of Applied Mathematics, Indian School of Mines, Dhanbad, India

autor

Singh A. K.

• Department of Applied Mathematics, Indian School of Mines, Dhanbad, India

autor

Sahu S. A.

• Department of Applied Mathematics, Indian School of Mines, Dhanbad, India

Bibliografia

• 1. Abd-Alla AM, Ahmad SM (1999) Propagation of Love waves in a non-homogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium. Appl Math Comput 106(2–3):265–275. doi:10.1016/S0096-3003(98)10128-5Google Scholar
• 2. Acharya DP, Roy I, Sengupta S (2009) Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media. Acta Mech 202(1–4):35–45. doi:10.1007/s00707-008-0027-5CrossRefGoogle Scholar
• 3. Anderson DL (1989) Theory of the Earth. Blackwell Scientific Publ, BostonGoogle Scholar
• 4. Backus GE (1962) Long-wave elastic anisotropy produced by horizontal layering. J Geophys Res 67(11):4427–4440. doi:10.1029/JZ067i011p04427CrossRefGoogle Scholar
• 5. Bhattacharya J (1962) On the dispersion curve for Love wave due to irregularity in the thickness of the transversely isotropic crustal layer. Gerl Beitr Geophys 6:324–334Google Scholar
• 6. Bieńkowski A, Szewczyk R, Salach J (2010) Industrial application of magnetoelastic force and torque sensors. Acta Phys Pol A 118(5):1008–1009CrossRefGoogle Scholar
• 7. Biot MA (1965) Mechanics of incremental deformations. Wiley, New YorkGoogle Scholar
• 8. Chattopadhyay A (1975) On the propagation of Love type waves in an intermediate non- homogeneous layers lying between two semi-infinite homogeneous elastic media. Gerl Beitr Geophys 84(3/4):327–334Google Scholar
• 9. Chattopadhyay A, Choudhury S (1990) Propagation, reflection and transmission of magnetoelastic shear waves in a self-reinforced medium. Int J Eng Sci 28(6):485–495. doi:10.1016/0020-7225(90)90051-JCrossRefGoogle Scholar
• 10. Chattopadhyay A, Kar BK (1977a) On the propagation of Love-type waves in a non-homogeneous internal stratum of finite thickness lying between two semi-infinite isotropic media. Gerl Beitr Geophys 86(5):407–412Google Scholar
• 11. Chattopadhyay A, Kar BK (1977b) On the dispersion curves of Love type waves in an internal stratum of finite thickness under initial stress lying between two semi-infinite isotropic elastic media. Gerl Beitr Geophys 86:493–497Google Scholar
• 12. Chattopadhyay A, Singh AK (2014) Propagation of a crack due to magneto-elastic shear waves in a self-reinforced medium. J Vib Cont 20(3):406–420. doi:10.1177/1077546312458134CrossRefGoogle Scholar
• 13. Chattopadhyay A, Gupta S, Sharma VK, Kumari P (2009) Propagation of shear waves in viscoelastic medium at irregular boundaries. Acta Geophys 58(2):195–214. doi:10.2478/s11600-009-0060-3Google Scholar
• 14. Chattopadhyay A, Gupta S, Sharma VK, Kumari P (2010) Effect of point source and heterogeneity on the propagation of SH waves. Int J Appl Math Mech 6(9):76–89Google Scholar
• 15. Dey S, Addy SK (1978) Love waves under initial stresses. Acta Geophys Pol 26(1):47–54Google Scholar
• 16. Ding G, Dravinski M (1996) Scattering of in multi-layered media with irregular interfaces. Earthq Eng Struct Dyn 25(12):1391–1404. doi:10.1002/(SICI)1096-9845(199612)25:12<1391:AID-EQE617>3.0.CO;2-WCrossRefGoogle Scholar
• 17. Dutta S (1963) Love wave in a non-homogeneous internal stratum lying between two semi-infinite isotropic media. Geophysics 28(2):156–160. doi:10.1190/1.1439162CrossRefGoogle Scholar
• 18. Gogna ML (1976) On Love waves in heterogeneous layered media. Geophys J Roy Astr Soc 45(2):357–370. doi:10.1111/j.1365-246X.1976.tb00331.xCrossRefGoogle Scholar
• 19. Guz AN (2002) Elastic waves in bodies with initial (residual) stresses. Int Appl Mech 38(1):23–59. doi:10.1023/A:1015379824503CrossRefGoogle Scholar
• 20. Kumari N, Sahu SA, Chattopadhyay A, Singh AK (2015) Influence of heterogeneity on the propagation behavior of Love-type waves in a layered isotropic structure. Int J Geomech 16(2):04015062. doi:10.1061/(ASCE)GM.1943-5622.0000541CrossRefGoogle Scholar
• 21. Sahu SA, Saroj PK, Paswan B (2014) Shear waves in a heterogeneous fiber-reinforced layer over a half-space under gravity. Int J Geomech 15(2):04014048. doi:10.1061/(ASCE)GM.1943-5622.0000404CrossRefGoogle Scholar
• 22. Sur SP (1963) Note on stresses produced by a shearing force moving over the boundary of a semi-infinite transversely isotropic solid. Pure Appl Geophys 55(1):72–76. doi:10.1007/BF02011217CrossRefGoogle Scholar
• 23. Whittaker ET, Watson GN (1991) A Course of Modern Analysis. Universal Book Stall, New Delhi