Advertisement

Employing an analytical approach to study the thermo-mechanical vibration of a defective size-dependent graphene nanosheet

  • Ehsan Allahyari
  • Ali Kiani
Regular Article
  • 45 Downloads

Abstract.

In this study, an analytical method is developed to study the free vibration of a defected nano graphene sheet coupled with temperature change and embedded on foundation based on Reddy’s third-order shear deformation plate theory. The graphene sheet may be opposed to the structural defect during the production process. Therefore, it is important to analyze the vibration behavior of graphene sheet. Here, some of the defects are modelled as a hole. Reddy’ third-order shear deformation plate theory is employed because it satisfies the zero shear stress condition at the free surfaces and need not use any shear correction coefficient to obtain equations of motion of the defected nanosheet. The interaction of the defected graphene sheet with a viscoelastic medium is simulated as a visco-Pasternak foundation. The influence of the surrounding viscoelastic medium on the natural frequencies is analyzed. To get the equations of dynamic equilibrium and natural boundary conditions of the nanosheet, the Hamilton’s principle is implemented. The presented method is verified by comparing the results with their counterparts reported in the open literature and good agreement is observed. Effects of different boundary conditions such as C-C, S-S, C-F, C-S, inner-radius-outer-radius ratio, Winkler foundation parameter, damping modulus, shear modulus, nonlocal parameter and temperature change on the frequency of the defected graphene sheet are examined. Various natural frequencies in nondimensional form and mode shapes are developed. The results show that, by increasing the inner-radius-outer-radius ratio, the natural frequency has an increasing behavior for all kinds of boundary condition. It is observed that increasing the size of defect has a significant effect on the natural frequency. Moreover, it can be concluded that decreasing the nonlocal parameter as the small-scale effect makes the plate stiffer. Therefore, the natural frequency of the nanoplate increases.

References

  1. 1.
    J.N. Reddy, Theory and Analysis of Elastic Plates and Shells (CRC Press, 2006)Google Scholar
  2. 2.
    R. Ansari, R. Gholami, Compos. Struct. 154, 707 (2016)CrossRefGoogle Scholar
  3. 3.
    Y. Zhou, J. Zhu, Compos. Struct. 153, 712 (2016)CrossRefGoogle Scholar
  4. 4.
    T. Van Do, D.K. Nguyen, N.D. Duc, D.H. Doan, T.Q. Bui, Thin-Walled Struct. 119, 687 (2017)CrossRefGoogle Scholar
  5. 5.
    P. Raghu, K. Preethi, A. Rajagopal, J.N. Reddy, Compos. Struct. 139, 13 (2016)CrossRefGoogle Scholar
  6. 6.
    T.Q. Bui et al., Compos. Part B Eng. 92, 218 (2016)CrossRefGoogle Scholar
  7. 7.
    S.-Y. Lee, S.-C. Wooh, S.-S. Yhim, Int. J. Solids Struct. 41, 1879 (2004)CrossRefGoogle Scholar
  8. 8.
    L.S. Ma, T.J. Wang, Int. J. Solids Struct. 41, 85 (2004)CrossRefGoogle Scholar
  9. 9.
    Y.X. Hao, W. Zhang, J. Yang, Compos. Part B Eng. 42, 402 (2011)CrossRefGoogle Scholar
  10. 10.
    A.R. Saidi, A. Rasouli, S. Sahraee, Compos. Struct. 89, 110 (2009)CrossRefGoogle Scholar
  11. 11.
    K.S. Novoselov et al., Science 306, 666 (2004)ADSCrossRefGoogle Scholar
  12. 12.
    C. Lee, X. Wei, J.W. Kysar, J. Hone, Science 321, 385 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    A. Belhadj, A. Boukhalfa, S.A. Belalia, Eur. Phys. J. Plus 132, 513 (2017)CrossRefGoogle Scholar
  14. 14.
    F. Ebrahimi, S.H.S. Hosseini, Eur. Phys. J. Plus 132, 172 (2017)CrossRefGoogle Scholar
  15. 15.
    S. Sahmani, A.M. Fattahi, Eur. Phys. J. Plus 132, 231 (2017)CrossRefGoogle Scholar
  16. 16.
    F. Ebrahimi, A. Dabbagh, Eur. Phys. J. Plus 132, 449 (2017)CrossRefGoogle Scholar
  17. 17.
    H. Wu, S. Kitipornchai, J. Yang, Mater. Des. 132, 430 (2017)CrossRefGoogle Scholar
  18. 18.
    H.-S. Shen, Y. Xiang, F. Lin, D. Hui, Compos. Part B Eng. 119, 67 (2017)CrossRefGoogle Scholar
  19. 19.
    R. Nazemnezhad, M. Zare, S. Hosseini-Hashemi, Appl. Math. Model. 47, 459 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    H.-S. Shen, Y. Xiang, F. Lin, Thin-Walled Struct. 118, 229 (2017)CrossRefGoogle Scholar
  21. 21.
    B. Yang, S. Kitipornchai, Y.-F. Yang, J. Yang, Appl. Math. Model. 49, 69 (2017)MathSciNetCrossRefGoogle Scholar
  22. 22.
    S.F.A. Namin, R. Pilafkan, Physica E 93, 257 (2017)ADSCrossRefGoogle Scholar
  23. 23.
    L.W. Zhang, Y. Zhang, K.M. Liew, Compos. Part B Eng. 118, 96 (2017)CrossRefGoogle Scholar
  24. 24.
    L.W. Zhang, Y. Zhang, K.M. Liew, Appl. Math. Model. 49, 691 (2017)MathSciNetCrossRefGoogle Scholar
  25. 25.
    R. Ansari, S. Ajori, B. Motevalli, Superlattices Microstruct. 51, 274 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    E. Allahyari, M. Fadaee, Compos. Part B Eng. 85, 259 (2016)CrossRefGoogle Scholar
  27. 27.
    A.C. Eringen, J. Appl. Phys. 54, 4703 (1983)ADSCrossRefGoogle Scholar
  28. 28.
    S. Hosseini-Hashemi, M. Es’Haghi, H.R.D. Taher, M. Fadaie, J. Sound Vib. 329, 3382 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    M. Fadaee, Meccanica 50, 2325 (2015)MathSciNetCrossRefGoogle Scholar
  30. 30.
    M.R. Talabi, A.R. Saidi, Appl. Math. Model. 37, 7664 (2013)MathSciNetCrossRefGoogle Scholar
  31. 31.
    J.N. Reddy, Int. J. Solids Struct. 20, 881 (1984)CrossRefGoogle Scholar
  32. 32.
    J.N. Reddy, Energy Principles and Variational Methods in Applied Mechanics (John Wiley & Sons, Inc., 2017)Google Scholar
  33. 33.
    J.N. Reddy, Int. J. Numer. Methods Eng. 47, 663 (2000)CrossRefGoogle Scholar
  34. 34.
    M. Es’haghi, S.H. Hashemi, M. Fadaee, Int. J. Mech. Sci. 53, 585 (2011)CrossRefGoogle Scholar
  35. 35.
    S. Hosseini-Hashemi, M. Es’haghi, H.R.D. Taher, Compos. Struct. 92, 1333 (2010)CrossRefGoogle Scholar
  36. 36.
    M.R. Spiegel, Mathematical Handbook of Formulas and Tables (McGraw-Hill, Inc., 1968)Google Scholar
  37. 37.
    T. Irie, G. Yamada, S. Aomura, J. Appl. Mech. 47, 652 (1980)ADSCrossRefGoogle Scholar
  38. 38.
    N. Ding, X. Chen, C.-M.L. Wu, Sci. Rep. 6, 31499 (2016)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringK. N. Toosi University of TechnologyTehranIran
  2. 2.School of Mechanical EngineeringIran University of Science and TechnologyTehranIran

Personalised recommendations