Applied Physics A

, 124:301 | Cite as

Effect of humid-thermal environment on wave dispersion characteristics of single-layered graphene sheets

Article

Abstract

In the present article, the hygro-thermal wave propagation properties of single-layered graphene sheets (SLGSs) are investigated for the first time employing a nonlocal strain gradient theory. A refined higher-order two-variable plate theory is utilized to derive the kinematic relations of graphene sheets. Here, nonlocal strain gradient theory is used to achieve a more precise analysis of small-scale plates. In the framework of the Hamilton’s principle, the final governing equations are developed. Moreover, these obtained equations are deemed to be solved analytically and the wave frequency values are achieved. Some parametric studies are organized to investigate the influence of different variants such as nonlocal parameter, length scale parameter, wave number, temperature gradient and moisture concentration on the wave frequency of graphene sheets.

References

  1. 1.
    A.C. Eringen, Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10(5), 425–435 (1972)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54(9), 4703–4710 (1983)ADSCrossRefGoogle Scholar
  3. 3.
    M. Aydogdu, A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration. Phys. E 41(9), 1651–1655 (2009)CrossRefGoogle Scholar
  4. 4.
    Y.Z. Wang, F.M. Li, K. Kishimoto, Scale effects on the longitudinal wave propagation in nanoplates. Phys. E 42(5), 1356–1360 (2010)CrossRefGoogle Scholar
  5. 5.
    P. Malekzadeh, A.R. Setoodeh, A.A. Beni, Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates. Compos. Struct. 93(7), 1631–1639 (2011)CrossRefGoogle Scholar
  6. 6.
    S. Narendar, S. Gopalakrishnan, Temperature effects on wave propagation in nanoplates. Compos. Part B: Eng. 43(3), 1275–1281 (2012)CrossRefMATHGoogle Scholar
  7. 7.
    S. Narendar, S. Gopalakrishnan, Study of terahertz wave propagation properties in nanoplates with surface and small-scale effects. Int. J. Mech. Sci. 64(1), 221–231 (2012)CrossRefGoogle Scholar
  8. 8.
    M.A. Eltaher, A.E. Alshorbagy, F.F. Mahmoud, Vibration analysis of Euler–Bernoulli nanobeams by using finite element method. Appl. Math. Model. 37(7), 4787–4797 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    M. Ghadiri, N. Shafiei, Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen’s theory using differential quadrature method. Microsyst. Technol. 22(12), 2853–2867 (2016)CrossRefGoogle Scholar
  10. 10.
    F. Ebrahimi, F. Ghasemi, E. Salari, Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica 51(1), 223–249 (2016)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    F. Ebrahimi, M.R. Barati, A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment. Appl. Phys. A 122(9), 792 (2016)ADSCrossRefGoogle Scholar
  12. 12.
    F. Ebrahimi, M.R. Barati, P. Haghi, Nonlocal thermo-elastic wave propagation in temperature-dependent embedded small-scaled nonhomogeneous beams. Eur. Phys. J. Plus 131(11), 383 (2016)CrossRefGoogle Scholar
  13. 13.
    F. Ebrahimi, M.R. Barati, A. Dabbagh, Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams. Appl. Phys. A 122(11), 949 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    F. Ebrahimi, A. Dabbagh, M.R. Barati, Wave propagation analysis of a size-dependent magneto-electro-elastic heterogeneous nanoplate. Eur. Phys. J. Plus 131(12), 433 (2016)CrossRefGoogle Scholar
  15. 15.
    F. Ebrahimi, S.H.S. Hosseini, Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates. J. Therm. Stresses 39(5), 606–625 (2016)CrossRefGoogle Scholar
  16. 16.
    F. Ebrahimi, A. Dabbagh, Wave propagation analysis of smart rotating porous heterogeneous piezo-electric nanobeams. Eur. Phys. J. Plus 132, 1–15 (2017)CrossRefGoogle Scholar
  17. 17.
    F. Ebrahimi, M.R. Barati, A. Dabbagh, Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects. Waves Random Complex Media 1–21 (2017)Google Scholar
  18. 18.
    D.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51(8), 1477–1508 (2003)ADSCrossRefMATHGoogle Scholar
  19. 19.
    C.W. Lim, G. Zhang, J.N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids 78, 298–313 (2015)ADSMathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    L. Li, Y. Hu, Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. Int. J. Eng. Sci. 97, 84–94 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    L. Li, X. Li, Y. Hu, Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. Int. J. Eng. Sci. 102, 77–92 (2016)CrossRefGoogle Scholar
  22. 22.
    A. Farajpour, M.H. Yazdi, A. Rastgoo, M. Mohammadi, A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment. Acta Mech. 227(7), 1849–1867 (2016)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    F. Ebrahimi, M.R. Barati, P. Haghi, Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams. J. Therm. Stresses 1–13 (2016)Google Scholar
  24. 24.
    F. Ebrahimi, M.R. Barati, A. Dabbagh, A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates. Int. J. Eng. Sci. 107, 169–182 (2016)CrossRefGoogle Scholar
  25. 25.
    F. Ebrahimi, A. Dabbagh, On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory. Compos. Struct. 162, 281–293 (2017)CrossRefGoogle Scholar
  26. 26.
    F. Ebrahimi, A. Dabbagh, Nonlocal strain gradient based wave dispersion behavior of smart rotating magneto-electro-elastic nanoplates. Mater. Res. Express 4(2), 025003 (2017)ADSCrossRefGoogle Scholar
  27. 27.
    F. Ebrahimi, A. Dabbagh, Wave propagation analysis of embedded nanoplates based on a nonlocal strain gradient-based surface piezoelectricity theory. Eur. Phys. J. Plus 132(11), 449 (2017)CrossRefGoogle Scholar
  28. 28.
    F. Ebrahimi, A. Dabbagh, Wave dispersion characteristics of rotating heterogeneous magneto-electro-elastic nanobeams based on nonlocal strain gradient elasticity theory. J. Electromagn. Waves Appl. 32(2), 138–169 (2018)CrossRefGoogle Scholar
  29. 29.
    F. Ebrahimi, A. Dabbagh, (2018). Wave propagation analysis of magnetostrictive sandwich composite nanoplates via nonlocal strain gradient theory. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 0954406217748687Google Scholar
  30. 30.
    F. Ebrahimi, E. Salari, Thermo-mechanical vibration analysis of a single-walled carbon nanotube embedded in an elastic medium based on higher-order shear deformation beam theory. J. Mech. Sci. Technol. 29(9), 3797–3803 (2015)CrossRefGoogle Scholar
  31. 31.
    C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321(5887), 385–388 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    J.H. Seol, I. Jo, A.L. Moore, L. Lindsay, Z.H. Aitken, M.T. Pettes, et al. Two-dimensional phonon transport in supported graphene. Science 328(5975), 213–216 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    T. Murmu, S.C. Pradhan, Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory. J. Appl. Phys. 105(6), 064319 (2009)ADSCrossRefGoogle Scholar
  34. 34.
    S.C. Pradhan, T. Murmu, Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory. Phys. E 42(5), 1293–1301 (2010)CrossRefGoogle Scholar
  35. 35.
    S.C. Pradhan, A. Kumar, Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method. Compos. Struct. 93(2), 774–779 (2011)CrossRefGoogle Scholar
  36. 36.
    S. Rouhi, R. Ansari, Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets. Phys. E 44(4), 764–772 (2012)CrossRefGoogle Scholar
  37. 37.
    B. Arash, Q. Wang, K.M. Liew, Wave propagation in graphene sheets with nonlocal elastic theory via finite element formulation. Comput. Methods Appl. Mech. Eng. 223, 1–9 (2012)ADSMathSciNetCrossRefMATHGoogle Scholar
  38. 38.
    T. Murmu, M.A. McCarthy, S. Adhikari, In-plane magnetic field affected transverse vibration of embedded single-layer graphene sheets using equivalent nonlocal elasticity approach. Compos. Struct. 96, 57–63 (2013)CrossRefGoogle Scholar
  39. 39.
    A.G. Arani, E. Haghparast, H.B. Zarei, Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field. Phys. B 495, 35–49 (2016)ADSCrossRefGoogle Scholar
  40. 40.
    A.M. Zenkour, Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium. Physica E 79, 87–97 (2016)ADSCrossRefGoogle Scholar
  41. 41.
    F. Ebrahimi, N. Shafiei, Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy’s higher-order shear deformation plate theory. Mech. Adv. Mater. Struct. 24(9), 761–772 (2017)CrossRefGoogle Scholar
  42. 42.
    W. Xiao, L. Li, M. Wang, Propagation of in-plane wave in viscoelastic monolayer graphene via nonlocal strain gradient theory. Appl. Phys. A 123(6), 388 (2017)ADSCrossRefGoogle Scholar
  43. 43.
    F. Ebrahimi, A. Dabbagh, On wave dispersion characteristics of double-layered graphene sheets in thermal environments. J. Electromagn. Waves Appl. 1–20 (2017)Google Scholar
  44. 44.
    X. Zhu, L. Li, Twisting statics of functionally graded nanotubes using Eringen’s nonlocal integral model. Compos. Struct. 178, 87–96 (2017)CrossRefGoogle Scholar
  45. 45.
    X. Zhu, L. Li, Closed form solution for a nonlocal strain gradient rod in tension. Int. J. Eng. Sci. 119, 16–28 (2017)MathSciNetCrossRefGoogle Scholar
  46. 46.
    X. Zhu, L. Li, On longitudinal dynamics of nanorods. Int. J. Eng. Sci. 120, 129–145 (2017)CrossRefGoogle Scholar
  47. 47.
    B. Karami, D. Shahsavari, M. Janghorban, L. Li, Wave dispersion of mounted graphene with initial stress. Thin-Walled Struct. 122, 102–111 (2018)CrossRefGoogle Scholar
  48. 48.
    L. Li, H. Tang, Y. Hu, The effect of thickness on the mechanics of nanobeams. Int. J. Eng. Sci. 123, 81–91 (2018)MathSciNetCrossRefGoogle Scholar
  49. 49.
    S. Natarajan, S. Chakraborty, M. Thangavel, S. Bordas, T. Rabczuk, Size-dependent free flexural vibration behavior of functionally graded nanoplates. Comput. Mater. Sci. 65, 74–80 (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of EngineeringImam Khomeini International UniversityQazvinIran
  2. 2.School of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran

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