Structural Engineering and Mechanics

  • 제77권4호
  • /
  • Pages.473-479
  • /
  • 2021
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Nonlocal effects on propagation of waves in a generalized thermoelastic solid half space

  • 투고 : 2019.04.15
  • 심사 : 2020.11.19
  • 발행 : 2021.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

The propagation of plane waves in a linear, homogeneous and isotropic nonlocal generalized thermoelastic solid medium is considered in the framework of Lord and Shulman generalization. The governing field equations are formulated and specialized in a plane. Plane wave solutions of governing equations show that there exists three plane waves, namely, P, thermal and SV waves which propagate with distinct speeds. Reflection of P and SV waves from thermally insulated or isothermal boundary of a half-space is considered. The relevant boundary conditions are applied at stress free boundary and a non-homogeneous system of three equations in reflection coefficients is obtained. For incidence of both P and SV waves, the expressions for energy ratios of reflected P, thermal and SV waves are also obtained. The speeds and energy ratios of reflected waves are computed for relevant physical constants of a thermoelastic material. The speeds of plane waves are plotted against nonlocal parameter and frequency. The energy ratios of reflected waves are also plotted against the angle of incidence of P wave at a thermally insulated stress-free surface. The effect of nonlocal parameter is shown graphically on the speeds and energy ratios of reflected waves.

키워드

참고문헌

  1. Abbas, I.A. and Mohamed, E.A.E. (2016), "Wave propagation in a generalized thermoelastic transversely isotropic plate using eigenvalue approach", J. Comput. Theor. Nanosci., 13(3), 1629-1634. https://doi.org/10.1166/jctn.2016.5090.
  2. Abd-Alla, A.M., Abo-Dahab, S.M. and Khan, A. (2017), "Rotational effect on thermoelastic Stoneley, Love and Rayleigh waves in fibre-reinforced anisotropic general viscoelastic media of higher order", Struct. Eng. Mech., 61(2), 221-230. https://doi.org/10.12989/sem.2017.61.2.221.
  3. Achenbach, J.D. (1973), Wave Propagation in Elastic Solids, North-Holland Series in Applied Mathematics and Mechanics, Amsterdam, Netherland.
  4. Altan, B.S. (1989), "Uniqueness of initial-boundary value problems in nonlocal elasticity", Int. J. Solid. Struct., 25(11), 1271-1278. https://doi.org/10.1016/0020-7683(89)90091-7.
  5. Bachher, M. and Sarkar, N. (2018), "Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer", Wave. Random Complex Media, 29(4), 1-19. https://doi.org/10.1080/17455030.2018.1457230.
  6. Balta, F. and Suhubi, E.S. (1977), "Theory of nonlocal generalized thermoelasticity", Int. J. Eng. Sci.,6 35(9-10), 579-588. https://doi.org/10.1016/0020-7225(77)90054-4.
  7. Das, N., Sarkar, N. and Lahiri, A. (2019), "Reflection of plane waves from the stress-free isothermal and insulated boundaries of a nonlocal thermoelastic solid", Appl. Math. Model., 73, 526-544. https://doi.org/10.1016/j.apm.2019.04.028.
  8. Deresiewicz, H. (1960), "Effect of boundaries on waves in a thermoelastic solid: Reflection of plane waves from plane boundary", J. Mech. Phys. Solid., 8(3), 164-172. https://doi.org/10.1016/0022-5096(60)90035-1.
  9. Dhaliwal, R.S. and Wang, J. (1994), "Some theorems in generalized nonlocal thermoelastcity", Int. J. Eng. Sci., 32(3), 473-479. https://doi.org/10.1016/0020-7225(94)90135-X.
  10. Edelen, D.G.B. and Laws, N. (1971), "On the thermodynamics of systems with nonlocality", Arch. Ration. Mech. Anal., 43, 24-35. https://doi.org/10.1007/BF00251543.
  11. Edelen, D.G.B., Green, A.E. and Laws, N. (1971), "Nonlocal continuum mechanics", Arch. Ration. Mech. Anal., 43, 36-44. https://doi.org/10.1007/BF00251544.
  12. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X.
  13. Eringen, A.C. (1974), "Theory of nonlocal thermoelastcity", Int. J. Eng. Sci., 12(12), 1063-1077. https://doi.org/10.1016/0020-7225(74)90033-0.
  14. Eringen, A.C. (2001), Nonlocal Continuum Field Theories, Springer Verlag, New York, USA.
  15. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0.
  16. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elast., 2, 1-7. https://doi.org/10.1007/BF00045689.
  17. Hetnarski, R.B. and Ignaczak, J. (1999), "Generalized thermoelasticity", J. Therm. Stress., 22(4-5), 451-476. https://doi.org/10.1080/014957399280832.
  18. Hosseini, S.M. (2020), "A GN-based modified model for size-dependent coupled thermoelasticity analysis in nano scale, considering nonlocality in heat conduction and elasticity: An analytical solution for a nano beam with energy dissipation", Struct. Eng. Mech., 73(3), 287-302. https://doi.org/10.12989/sem.2020.73.3.287.
  19. Iesan, D. (1977), "Reciprocal theorems and variational theorems in nonlocal elastodynamics", Int. J. Eng. Sci., 15(12), 693-699. https://doi.org/10.1016/0020-7225(77)90019-2.
  20. Ignaczak, J. and Ostoja-Starzewski, M. (2009), Thermoelasticity with Finite Wave Speeds, Oxford University Press, Oxford, UK. https://doi.org/10.1093/acprof:oso/9780199541645.001.0001.
  21. Inan, E. and Eringen, A.C. (1991), "Nonlocal theory of wave propagation in thermoelastic plates", Int. J. Eng. Sci., 29(7), 831-843. https://doi.org/10.1016/0020-7225(91)90005-N.
  22. Khan, A., Sohail, A., Beg, O.A. and Tariq, R. (2019), "Important paradigms of the thermoelastic waves", Arab. J. Sci. Eng., 44, 663-671. https://doi.org/10.1007/s13369-018-3649-5.
  23. Khurana, A. and Tomar, S.K. (2016), "Wave propagation in nonlocal microstretch solid", Appl. Math. Model., 40(11), 5858-5875.https://doi.org/10.1016/j.apm.2016.01.035.
  24. Lata, P. (2018), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., 66(1), 113-124. https://doi.org/10.12989/sem.2018.66.1.113.
  25. Li, Y. and We. P. (2018), "Reflection and transmission of thermo-elastic waves without energy dissipation at the interface of two dipolar gradient elastic solids", J. Acoust. Soc. Am., 143, 550-560. https://doi.org/10.1155/S0161171200004221.
  26. Lord, H. and Shulman, Y. (1967), "A generalised dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  27. Mondal, S., Sarkar, N. and Sarkar, N. (2019), "Waves in dual-phase lag thermoelastic materials with voids based on Eringena€™s nonlocal elasticity", J. Therm. Stress., 42(8), 1035-1050. https://doi.org/10.1080/01495739.2019.1591249.
  28. Narasimhan, M.N.L. and McCay, B.M. (1981), "Dispersion of surface waves in nonlocal dielectric fluids", Arch. Mech., 33(3), 385-400.
  29. Narendar, S. (2012), "Spectral finite element and nonlocal continuum mechanics based formulation for tortional wave propagation in nanorods", Finite Elem. Anal. Des., 62, 65-75. https://doi.org/10.1016/j.finel.2012.06.012.
  30. Nowinski, J.L. (1990), "On a three-dimensional Kelvin problem for an elastic nonlocal medium", Acta Mech., 84, 77-87. https://doi.org/10.1007/BF01176089.
  31. Othman, M.I.A. and Song, Y. (2007), "Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation", Int. J. Solid. Struct., 44(17), 5651-5664. https://doi.org/10.1016/j.ijsolstr.2007.01.022.
  32. Roy, I., Acharya, D.P. and Acharya, S. (2015), "Rayleigh wave in a rotating nonlocal magnetoelastic half-plane", J. Theor. Appl. Mech. Sofia, 45(4), 61-78. https://doi.org/10.1515/jtam-2015-0024.
  33. Sapora, A., Cornetti, P. and Carpinteri, A. (2013), "Wave propagation in nonlocal elastic continua modelled by a fractional calculus approach", Commun. Nonlin. Sci. Numer. Simulat., 18(1), 64-73. https://doi.org/10.1016/j.cnsns.2012.06.017.
  34. Sarkar, N. and Tomar, S.K. (2019), "Plane waves in nonlocal thermoelastic solid with voids", J. Therm. Stress., 42(5), 580-606. https://doi.org/10.1080/01495739.2018.1554395.
  35. Sarkar, N., De, S. and Sarkar, N. (2019), "Waves in nonlocal thermoelastic solids of type II", J. Therm. Stress., 42(9), 1153-1170. https://doi.org/10.1080/01495739.2019.1618760.
  36. Sharma, J.N., Kumar, V. and Chand, D. (2003), "Reflection of generalized thermoelastic waves from the boundary of a halfspace", J. Therm. Stress., 26(10), 925-942. https://doi.org/10.1080/01495730306342.
  37. Sheokand, S.K., Kumar, S., Kumar, R. and Deswal, S. (2019), "Propagation of plane waves in an orthotropic magneto-thermodiffusive rotating half-space", Struct. Eng. Mech., 72(4), 455-468. https://doi.org/10.12989/sem.2019.72.4.455.
  38. Singh, B. (2005), "Reflection of P and SV waves from the free surface of an elastic solid with generalized thermodiffusion", J. Earth Syst. Sci., 114, 159-168. https://doi.org/10.1007/BF02702017.
  39. Singh, B. (2010), "Reflection of plane waves at the free surface of a monoclinic thermoelastic solid half-space", Eur. J. Mech. A-Solid., 29(5), 911-916. https://doi.org/10.1016/j.euromechsol.2010.05.005.
  40. Sinha, A.N. and Sinha S.B. (1974), "Reflection of thermoelastic waves at a solid half space with thermal relaxation", J. Phys. Earth, 22(2), 237-244. https://doi.org/10.4294/jpe1952.22.237.
  41. Sinha, S.B. and Elsibai, K.A. (1996), "Reflection of thermoelastic waves at a solid half-space with two thermal relaxation times" J. Therm. Stress., 19(8), 763-777. https://doi.org/10.1080/01495739608946205.
  42. Sinha, S.B. and Elsibai, K.A. (1997), "Reflection and refraction of thermoelastic waves at an interface of two semi-infinite media with two thermal relaxation times", J. Therm. Stress., 20(2), 129-146. https://doi.org/10.1080/01495739708956095.
  43. Tong, L., Yu, Y., Hu, W., Shi, W. and Xu, C. (2016), "On wave propagation characteristics in fluid saturated porous materials by a non local Biot theory", J. Sound Vib., 379, 106-118. https://doi.org/10.1016/j.jsv.2016.05.042.