DOI QR코드

DOI QR Code

Effect of fractional order on energy ratios at the boundary surface of elastic-piezothermoelastic media

  • 투고 : 2015.06.28
  • 심사 : 2016.11.30
  • 발행 : 2017.06.25

초록

In the present investigation reflection and transmission of plane waves at an elastic half space and piezothermoelastic solid half space with fractional order derivative is discussed. The piezothermoelastic solid half space is assumed to have 6 mm type symmetry and assumed to be loaded with an elastic half space. It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence, frequency of incident wave and are influenced by the piezothermoelastic properties of media. The expressions of amplitude ratios and energy ratios are obtained in closed form. The energy ratios are computed numerically using amplitude ratios for a particular model of graphite and Cadmium Selenide (CdSe). The variations of energy ratios with angle of incidence are shown graphically. The conservation of energy across the interface is verified. Some cases of interest are also deduced from the present investigation.

키워드

참고문헌

  1. Abo-el-nour, N. and Alsheikh, F.A. (2009), "Reflection and refraction of plane quasi-longitudinal waves at an interface of two piezoelectric media under initial stresses", Arch. Appl. Mech., 79(9), 843-857. https://doi.org/10.1007/s00419-008-0257-y
  2. Abo-el-nour, N., Al-sheikh, F.A. and Al-Hossain, A.Y. (2012), "The reflection phenomena of quasi-vertical transverse waves in piezoelectric medium under initial stresses", Meccan., 47(3), 731-744. https://doi.org/10.1007/s11012-011-9485-2
  3. Achenbach, J.D. (1973), Wave Propagation in Elastic Solids, North Holland Pub., Amsterdam, The Netherlands.
  4. Bassiouny, E. and Sabry, R. (2013), "Fractional order two temperature thermo-elastic behavior of piezoelectric materials", J. Appl. Math. Phys., 1(5), 110. https://doi.org/10.4236/jamp.2013.15017
  5. Bullen, K.E. (1963), An Introduction to the Theory of Seismology, Cambridge University Press, U.K.
  6. Chandrasekharaiah, D.S. (1988), "A generalized linear thermoelasticity theory for piezoelectric media", Acta Mech., 71(1-4), 39-49. https://doi.org/10.1007/BF01173936
  7. Chandrasekharaiah, D.S. (1986), "Thermoelasticity with second sound: A review", Appl. Mech. Rev., 39(3), 355-376. https://doi.org/10.1115/1.3143705
  8. Chen, W.Q. (2000), "Three dimensional green's function for two-phase transversely isotropic piezothermoelastic media", ASME J. Appl. Mech., 67, 705. https://doi.org/10.1115/1.1328349
  9. Dhaliwal, R.S. and Sheroef, H.H. (1980), "Generalized thermoelasticity for anisotropic media", Q. Appl. Math., 1-8.
  10. Hetnarski, R.B. and Ignaczak, J. (1999), "Generalized thermoelasticity", J. Therm. Str., 22(4-5), 451-476. https://doi.org/10.1080/014957399280832
  11. Ikeda, T. (1996), Fundamentals of Piezoelectricity, Oxford University Press, New York, U.S.A.
  12. Kuang, Z.B. (2010), "Variational principles for generalized thermodiffusion theory in pyroelectricity", Acta Mech., 214(3-4), 275-289. https://doi.org/10.1007/s00707-010-0285-x
  13. Kuang, Z.B. and Yuan, X.G. (2011), "Reflection and transmission of waves in pyroelectric and piezoelectric materials", J. Sound Vibr., 330(6), 1111-1120. https://doi.org/10.1016/j.jsv.2010.09.026
  14. Kumar, R. and Gupta, V. (2013), "Plane wave propagation in an anisotropic thermoelastic medium with fractional order derivative and void", J. Thermoelast., 1(1), 21-34.
  15. Lord, H.W. and Shulman, Y. (1967), "The generalised dynamic theory of thermoelasticity", J. Mech. Phys. Sol., 15, 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  16. Majhi, M.C. (1995), "Discontinuities in generalized thermoelastic wave propagation in a semi-infinite piezoelectric rod", J. Technol. Phys., 36(3), 269-278.
  17. Mindlin, R.D. (1974), "Equations of high frequency vibrations of thermopiezoelectric crystal plates", J. Sol. Struct., 10(6), 625-637. https://doi.org/10.1016/0020-7683(74)90047-X
  18. Meral, F.C. and Royston, T.J. (2009), "Surface response of a fractional order viscoelastic halfspace to surface and subsurface sources", J. Acoust. Soc. Am., 126(6), 3278-3285. https://doi.org/10.1121/1.3242351
  19. Meral, F.C., Royston, T.J. and Magin, R.L. (2011), "Rayleigh-lamb wave propagation on a fractional order viscoelastic plate", J. Acoust. Soc. Am., 129(2), 1036-1045. https://doi.org/10.1121/1.3531936
  20. Meerschaert, M.M. and McGough, R.J. (2014), "Attenuated fractional wave equations with anisotropy", J. Vibr. Acoust., 136(5), 050902.
  21. Nowacki, W. (1978), "Some general theorems of thermopiezoelectricity", J. Therm. Str., 1(2), 171-182. https://doi.org/10.1080/01495737808926940
  22. Nowacki, W. (1979), Foundation of Linear Piezoelectricity, Interactions in Elastic Solids, Springer, Wein.
  23. Othman, M.I.A., Atwa, S.Y., Hasona, W.M. and Ahmed, E.A.A. (2015), "Propagation of plane waves in generalised piezo-thermoelastic medium: Comparison of different theories", J. Inn. Res. Sci. Eng. Technol., 4(7).
  24. Rao, S.S. and Sunar, M. (1993), "Analysis of thermopiezoelectric sensors and acutators in advanced intelligent structures", AIAA J., 31(7), 1280-1286. https://doi.org/10.2514/3.11764
  25. Scott, N.H. (1996), "Energy and dissipation of inhomogeneous plane waves in thermoelasticity", Wave Mot., 23(4), 393-406. https://doi.org/10.1016/0165-2125(96)00003-0
  26. Sherief, H.H., El-Sayed, A.M.A. and El-Latief, A.A. (2010), "Fractional order theory of thermoelasticity", J. Sol. Struct., 47(2), 269-275. https://doi.org/10.1016/j.ijsolstr.2009.09.034
  27. Sur, A. and Kanoria, M. (2014), "Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell", Lat. Am. J. Sol. Struct., 11(7), 1132-1162. https://doi.org/10.1590/S1679-78252014000700005
  28. Vashishth, A.K. and Sukhija, H. (2014), "Inhomogeneous waves at the boundary of an anisotropic piezothermoelastic medium", Acta Mech., 225(12), 3325-3338. https://doi.org/10.1007/s00707-014-1139-8
  29. Vashishth, A.K. and Sukhija, H. (2015), "Reflection and transmission of plane waves from fluidpiezothermoelastic solid interface", Appl. Math. Mech., 36(1), 11-36. https://doi.org/10.1007/s10483-015-1892-9