DOI QR코드

DOI QR Code

Shear waves propagation in an initially stressed piezoelectric layer imperfectly bonded over a micropolar elastic half space

  • Kumar, Rajneesh (Department of Mathematics, Kurukshetra University) ;
  • Singh, Kulwinder (Department of Mathematics, Lovely Professional University) ;
  • Pathania, D.S. (Department of Mathematics, GNDEC)
  • 투고 : 2017.10.11
  • 심사 : 2018.08.08
  • 발행 : 2019.01.25

초록

The present study investigates the propagation of shear waves in a composite structure comprised of imperfectly bonded piezoelectric layer with a micropolar half space. Piezoelectric layer is considered to be initially stressed. Micropolar theory of elasticity has been employed which is most suitable to explain the size effects on small length scale. The general dispersion equations for the existence of waves in the coupled structure are obtained analytically in the closed form. Some particular cases have been discussed and in one particular case the dispersion relation is in well agreement to the classical-Love wave equation. The effects of various parameters viz. initial stress, interfacial imperfection and micropolarity on the phase velocity are obtained for electrically open and mechanically free system. Numerical computations are carried out and results are depicted graphically to illustrate the utility of the problem. The phase velocity of the shear waves is found to be influenced by initial stress, interface imperfection and the presence of micropolarity in the elastic half space. The theoretical results obtained are useful for the design of high performance surface acoustic devices.

키워드

참고문헌

  1. Baltazar, A., Wang, L., Xie, B. and Rokhlin, S.I. (2003), "Inverse ultrasonic determination of imperfect interfaces and bulk properties of a layer between two solids", J. Acoust. Soc. Am., 114(3), 1424-1434. https://doi.org/10.1121/1.1600723
  2. Bleustein, J.L. (1968). "A new surface wave in piezoelectric materials", Appl. Phys. Lett., 13(12), 412-413. https://doi.org/10.1063/1.1652495
  3. Chaudhary, S., Sahu, S.A. and Singhal, A. (2018), "On secular equation of SH waves propagating in pre-stressed and rotating piezo-composite structure with imperfect interface", J. Intell. Mater. Syst. Struct., 29(10), 2223-2235. https://doi.org/10.1177/1045389X18758192
  4. Chen, W.Q., Cai, J.B., Ye, G.R. and Wang, Y.F. (2004), "Exact three-dimensional solutions of laminated orthotropic piezoelectric rectangular plates featuring interlaminar bonding imperfections modeled by a general spring layer", Int. J. Sol. Struct., 41(18-19), 5247-5263. https://doi.org/10.1016/j.ijsolstr.2004.03.010
  5. Chen, Z.G., Hu, Y.T. and Yang, J.S. (2008), "Shear horizontal piezoelectric waves in a piezoceramic plate imperfectly bonded to two piezoceramic half-spaces", J. Mech., 24(3), 229-239. https://doi.org/10.1017/S172771910000229X
  6. Curtis, R.G. and Redwood, M. (1973), "Transverse surface waves on a piezoelectric material carrying a metal layer of finite thickness", J. Appl. Phys., 44(5), 2002-2007. https://doi.org/10.1063/1.1662506
  7. El-Karamany, A.S. and Ezzat, M.A. (2005), "Propagation of discontinuities in thermopiezoelectric rod", J. Therm. Stress., 28(10), 997-1030. https://doi.org/10.1080/01495730590964954
  8. El-Karamany, A.S. and Ezzat, M.A. (2009), "Uniqueness and reciprocal theorems in linear micropolar electro-magnetic thermoelasticity with two relaxation times", Mech. Time-Depend. Mater., 13(1), 93-115. https://doi.org/10.1007/s11043-008-9068-3
  9. El-Karamany, A.S. and Ezzat, M.A. (2013), "On the three-phase-lag linear micropolar thermoelasticity theory", Eur. J. Mech. A/Sol., 40, 198-208. https://doi.org/10.1016/j.euromechsol.2013.01.011
  10. Eringen, A.C. (1966), "Linear theory of micropolar elasticity", J. Math. Mech., 15, 909-923.
  11. Eringen, A.C. (1999), Microcontinuum Field Theories-I, Springer- Verlag, New York, U.S.A.
  12. Eringen, A.C. and Suhubi, E.S. (1964), "Nonlinear theory of simple micro-elastic solid-I", Int. J. Eng. Sci., 2(2), 189-203. https://doi.org/10.1016/0020-7225(64)90004-7
  13. Ezzat, M.A., El-Karamany, A.S. and Awad, E.S. (2010), "On the coupled theory of thermo-piezoelectric/piezomagnetic materials with two temperatures", Can. J. Phys., 88(5), 307-315. https://doi.org/10.1139/P10-015
  14. Ezzat, M.A., Hamza, F. and Awad, E.S. (2010), "Electro-magneto-thermoelastic plane waves in micropolar solid involving two temperatures", Acta. Mech. Sol. Sin., 23(3), 200-212. https://doi.org/10.1016/S0894-9166(10)60022-5
  15. Ezzat, M.A. and Awad, E.S. (2010), "Constitutive relations, uniqueness of solution, and thermal shock application in the linear theory of micropolar generalized thermoelasticity involving two temperatures", J. Therm. Stress., 33(3), 226-250. https://doi.org/10.1080/01495730903542829
  16. Gauthier, R.D. (1982), Experimental Investigation on Micropolar Media, Mechanics of Micropolar Media, World Scientific, Singapore.
  17. Jin, F., Wang, Z. and Kishimoto, K. (2011), "The propagation behavior of Bleustein-Gulyaev waves in a pre-stressed piezoelectric layered structure", Int. J. Nonlin. Sci. Num. Sim. 4(2), 125-138. https://doi.org/10.1515/IJNSNS.2003.4.2.125
  18. Kaur, T., Sharma, S.K. and Singh, A.K. (2017), "Shear wave propagation in vertically heterogeneous viscoelastic layer over a micropolar elastic half-space", Mech. Adv. Mater. Struct., 24(2), 149-156. https://doi.org/10.1080/15376494.2015.1124948
  19. Kumar, R. and Partap, G. (2006), "Rayleigh lamb waves in micropolar isotropic elastic plate", Appl. Math. Mech., 27(8), 1049-1059. https://doi.org/10.1007/s10483-006-0805-z
  20. Kumar, R. and Deswal, S. (2006), "Some problems of wave propagation in a micropolar elastic medium with voids", J. Vibr. Contr., 12(8), 849-879. https://doi.org/10.1177/1077546306065856
  21. Kumar, R., Kaur, M. and Rajvanshi, S.C. (2014), "Propagation of waves in micropolar generalized thermoelastic materials with two temperatures bordered with layers or half-spaces of inviscid liquid", Lat. Am. J. Sol. Struct., 2(7), 1091-113.
  22. Kundu, S., Kumari, A., Pandit, D.K. and Gupta, S. (2017), "Love wave propagation in heterogeneous micropolar media", Mech. Res. Commun., 83, 6-11. https://doi.org/10.1016/j.mechrescom.2017.02.003
  23. Kurt, I., Akbarov, S.D. and Sezer, S. (2016), "The influence of the initial stresses on lamb wave dispersion in pre-stressed PZT/metal/PZT sandwich plates", Struct. Eng. Mech., 58(2), 347-378. https://doi.org/10.12989/sem.2016.58.2.347
  24. Liu, J. and Wang, Z.K. (2005), "The propagation behavior of Love waves in a functionally graded layered piezoelectric structure", Smart Mater. Struct., 14(1), 137-146. https://doi.org/10.1088/0964-1726/14/1/013
  25. Liu, J., Cao, X.S. and Wang, Z.K. (2008), "Love waves in a smart functionally graded piezoelectric composite structure", Acta Mech., 208(1-2), 63-80. https://doi.org/10.1007/s00707-008-0124-5
  26. Liu, J., Wang, Y. and Wang, B. (2010), "Propagation of shear horizontal surface waves in a layered piezoelectric half-space with an imperfect interface", IEEE Trans. Ultrason. Ferroelectr. Freq. Contr., 57(8), 1875-1879. https://doi.org/10.1109/TUFFC.2010.1627
  27. Love, A.E.H. (1920), Mathematical Theory of Elasticity, Cambridge University Press, Cambridge, U.K.
  28. Marin, M. (2008), "Weak solutions in elasticity of dipolar porous materials", Math. Probl. Eng.
  29. Marin, M. (2016), "An approach of a heat-flux dependent theory for micropolar porous media", Meccan., 51(5), 1127-1133. https://doi.org/10.1007/s11012-015-0265-2
  30. Marin, M. and Baleanu, D. (2016), "On vibrations in thermoelasticity without energy dissipation for micropolar bodies", Bound. Value Probl., 2016(1), 111. https://doi.org/10.1186/s13661-016-0620-9
  31. Marin, M. and Ochsner F. (2018), "An initial boundary value problem for modeling a piezoelectric dipolar body", Contin. Mech. Thermodyn., 30(2), 267-278. https://doi.org/10.1007/s00161-017-0599-1
  32. Midya, G.K. (2004), "On love-type surface waves in homogeneous micropolar elastic media", Int. J. Eng. Sci., 42(11-12), 1275-1288. https://doi.org/10.1016/j.ijengsci.2004.03.002
  33. Mindlin, R.D. (1952), "Forced thickness-shear and flexural vibrations of piezoelectric", J. Appl. Phys., 23(1), 83-88. https://doi.org/10.1063/1.1701983
  34. Qian, Z.H., Jin, F. and Hirose, S. (2011), "Dispersion characteristics of transverse surface waves in piezoelectric coupled solid media with hard metal interlayer", Ultrason., 51(8), 853-856. https://doi.org/10.1016/j.ultras.2011.06.005
  35. Qian, Z.H., Jin, F., Lu, T.J. and Kishimoto, K. (2009). "Transverse surface waves in a 6 mm piezoelectric material carrying a prestressed metal layer of finite thickness", Appl. Phys. Lett., 94(9), 093513. https://doi.org/10.1063/1.3095922
  36. Qian, Z.H., Jin, F., Wang, Z and Kishimoto, K. (2004), "Dispersion relations for SH-wave propagation in periodic piezoelectric composite", Int. J. Eng. Sci., 2(7), 673-689.
  37. Qian, Z.H., Jin, F., Wang, Z. and Kishimoto, K. (2004), "Love waves propagation in a piezoelectric layered structure with initial stresses", Acta Mech., 171(1-2), 41-57. https://doi.org/10.1007/s00707-004-0128-8
  38. Singh, A.K., Chaki, M.S., Hazra, B. and Mahto S. (2017), "Influence of imperfectly bonded piezoelectric layer with irregularity on propagation of Love-type wave in a reinforced composite structure", Struct. Eng. Mech., 62(3), 325-344. https://doi.org/10.12989/sem.2017.62.3.325
  39. Singh, B. and Kumar, R. (1998), "Reflection and refraction of plane waves at an interface between micropolar elastic solid and viscoelastic solid", Int. J. Eng. Sci., 36(2), 119-135. https://doi.org/10.1016/S0020-7225(97)00041-4
  40. Son, M.S. and Kang, J. (2011), "The effect of initial stress on the propagation behavior of SH waves in piezoelectric coupled plates", Ultrason., 51(4), 489-495. https://doi.org/10.1016/j.ultras.2010.11.016
  41. Tiersten, H.F. (1963), "Thickness vibrations of piezoelectric plates", J. Acoust. Soc. Am., 35(1), 53-58. https://doi.org/10.1121/1.1918413
  42. Voigt, W. (1887), "Theoretischestudienuber die elastizitatsverhaltnisse der krystalleabhandl", d. Ges. d. Wiss. zuGottingen, 34, 3-51.
  43. Wang, Q., Quek, S.T. and Varadan, V.K. (2001), "Love waves in piezoelectric coupled solid media", Smart Mater. Struct., 10(2), 380-388. https://doi.org/10.1088/0964-1726/10/2/325
  44. Wang, H.M. and Zhao, Z.C. (2013), "Love waves in a two-layered piezoelectric/elastic composite plate with an imperfect interface", Arch. Appl. Mech., 83(1), 43-51. https://doi.org/10.1007/s00419-012-0631-7