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Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams

  • Farzad EbrahimiEmail author
  • Ali Dabbagh
Regular Article
  • 34 Downloads

Abstract.

In this article, the wave dispersion analysis of heterogeneous functionally graded (FG) nanosize beams is undertaken in the framework of a nonlocal strain gradient higher-order beam theory. Shear deformation effects are completely included free from any additional shear correction coefficient by the means of a refined sinusoidal beam theorem. Furthermore, the small scale effects are covered based on the nonlocal strain gradient elasticity theory. This is proven that the aforementioned theory is powerful enough to guesstimate the behavior of the nanostructures better than formerly presented ones. In fact, both stiffness-softening and -hardening characteristics of nanosize elements are coupled together in this theory. On the other hand, the equivalent material properties are achieved utilizing the rule of mixture. The motion equations are derived extending the dynamic version of the principle of virtual work. Thereafter, the size-dependent partial differential equations of the problem are solved based on an exponential solution function to reach the circular wave frequency. Next, some graphical examples are presented to investigate the influences of various parameters on the wave propagation behaviors of FG nanobeams.

References

  1. 1.
    F. Ebrahimi, M.R. Barati, A. Dabbagh, Waves Random Complex Media 28, 215 (2018)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    F. Ebrahimi, A. Rastgoo, Thin-Walled Struct. 46, 1402 (2008)CrossRefGoogle Scholar
  3. 3.
    H.S.Shen, Compos. Struct. 91, 375 (2009)CrossRefGoogle Scholar
  4. 4.
    Y. Huang, X.F. Li, J. Sound Vib. 329, 2291 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    A.E. Alshorbagy, M.A. Eltaher, F.F. Mahmoud, Appl. Math. Modell. 35, 412 (2011)CrossRefGoogle Scholar
  6. 6.
    M. Simşek, T. Kocatürk, S.D. Akbaş, Compos. Struct. 94, 2358 (2012)CrossRefGoogle Scholar
  7. 7.
    H.T. Thai, D.H. Choi, Compos. Part B 43, 2335 (2012)CrossRefGoogle Scholar
  8. 8.
    F. Ebrahimi, Mech. Adv. Mater. Struct. 20, 854 (2013)CrossRefGoogle Scholar
  9. 9.
    S.E. Ghiasian, Y. Kiani, M. Sadighi, M.R. Eslami, Int. J. Mech. Sci. 81, 137 (2014)CrossRefGoogle Scholar
  10. 10.
    M. Simşek, Compos. Struct. 133, 968 (2015)CrossRefGoogle Scholar
  11. 11.
    S.E. Ghiasian, Y. Kiani, M.R. Eslami, Eur. J. Mech. A/Solids 54, 232 (2015)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    M.R. Jafarinezhad, M.R. Eslami, Compos. Struct. 168, 758 (2017)CrossRefGoogle Scholar
  13. 13.
    M. Gharibi, M. Zamani Nejad, A. Hadi, J. Comput. Appl. Mech. 48, 89 (2017)Google Scholar
  14. 14.
    Y. Tang, T. Yang, Compos. Struct. 185, 393 (2018)CrossRefGoogle Scholar
  15. 15.
    A. Menasria, A. Bouhadra, A. Tounsi, A.A. Bousahla, S.R. Mahmoud, Steel Compos. Struct. 25, 157 (2017)Google Scholar
  16. 16.
    M. Zamani Nejad, M. Jabbari, A. Hadi, J. Comput. Appl. Mech. 48, 357 (2017)Google Scholar
  17. 17.
    A. Mahi, A. Tounsi, Appl. Math. Modell. 39, 2489 (2018)CrossRefGoogle Scholar
  18. 18.
    A. Attia, A.A. Bousahla, A. Tounsi, S.R. Mahmoud, A.S Alwabli, Struct. Eng. Mech. 65, 453 (2018)Google Scholar
  19. 19.
    A. Zargaripoora, A. Daneshmehra, I.I. Hosseinia, A. Rajabpoora, J. Comput. Appl. Mech. 49, 86 (2018)Google Scholar
  20. 20.
    A.C. Eringen, Int. J. Eng. Sci. 10, 425 (1972)CrossRefGoogle Scholar
  21. 21.
    S.C. Pradhan, T. Murmu, Physica E 42, 1293 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    R. Ansari, B. Arash, H. Rouhi, Compos. Struct. 93, 2419 (2011)CrossRefGoogle Scholar
  23. 23.
    F.F. Mahmoud, M.A. Eltaher, A.E. Alshorbagy, E.I. Meletis, J. Mech. Sci. Technol. 26, 3555 (2012)CrossRefGoogle Scholar
  24. 24.
    M.A. Eltaher, A.E. Alshorbagy, F.F. Mahmoud, Appl. Math. Modell. 37, 4787 (2013)CrossRefGoogle Scholar
  25. 25.
    E.O. Alzahrani, A.M. Zenkour, M. Sobhy, Compos. Struct. 105, 163 (2013)CrossRefGoogle Scholar
  26. 26.
    F. Ebrahimi, E. Salari, J. Mech. Sci. Technol. 29, 3797 (2015)CrossRefGoogle Scholar
  27. 27.
    A.M. Zenkour, Physica E 79, 87 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    A. Ghorbanpour Arani, M. Jamali, A.H. Ghorbanpour-Arani, R. Kolahchi, M. Mosayyebi, Proc. Inst. Mech. Eng. Part C 231, 387 (2017)CrossRefGoogle Scholar
  29. 29.
    F. Ebrahimi, M. Karimiasl, Mech. Adv. Mater. Struct. 25, 943 (2018)CrossRefGoogle Scholar
  30. 30.
    M.R. Farajpour, A.R. Shahidi, A. Hadi, A. Farajpour, Mech. Adv. Mater. Struct. (2018)  https://doi.org/10.1080/15376494.2018.1432820
  31. 31.
    F. Ebrahimi, A. Dabbagh, Appl. Phys. A 124, 301 (2018)ADSCrossRefGoogle Scholar
  32. 32.
    F. Ebrahimi, A. Dabbagh, Eur. Phys. J. Plus 133, 97 (2018)CrossRefGoogle Scholar
  33. 33.
    S.K. Jalali, M.H. Naei, J. Comput. Appl. Mech. 45, 61 (2014)Google Scholar
  34. 34.
    A. Zemri, M.S.A. Houari, A.A. Bousahla, A. Tounsi, Struct. Eng. Mech. 54, 693 (2015)CrossRefGoogle Scholar
  35. 35.
    M. Ahouel, M.S.A. Houari, E.A. Bedia, A. Tounsi, Steel Compos. Struct. 20, 963 (2016)CrossRefGoogle Scholar
  36. 36.
    M. Yazid, H. Heireche, A. Tounsi, A.A. Bousahla, M.S.A. Houari, Smart Struct. Syst. 21, 15 (2018)Google Scholar
  37. 37.
    M. Ajri, M.M.S. Fakhrabadi, J. Comput. Appl. Mech. 49, 44 (2018)Google Scholar
  38. 38.
    N.A. Fleck, J.W. Hutchinson, J. Mech. Phys. Solids 41, 1825 (1993)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    J.S. Stölken, A.G. Evans, Acta Mater. 46, 5109 (1998)CrossRefGoogle Scholar
  40. 40.
    D.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, J. Mech. Phys. Solids 51, 1477 (2003)ADSCrossRefGoogle Scholar
  41. 41.
    C.W. Lim, G. Zhang, J.N. Reddy, J. Mech. Phys. Solids 78, 298 (2015)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    L. Li, Y. Hu, Int. J. Eng. Sci. 97, 84 (2015)CrossRefGoogle Scholar
  43. 43.
    A. Farajpour, M.H. Yazdi, A. Rastgoo, M. Mohammadi, Acta Mech. 227, 1849 (2016)MathSciNetCrossRefGoogle Scholar
  44. 44.
    X.J. Xu, X.C. Wang, M.L. Zheng, Z. Ma, Compos. Struct. 160, 366 (2017)CrossRefGoogle Scholar
  45. 45.
    S. Sahmani, M.M. Aghdam, Compos. Struct. 178, 97 (2017)CrossRefGoogle Scholar
  46. 46.
    F. Ebrahimi, M.R. Barati, J. Braz. Soc. Mech. Sci. Eng. 40, 428 (2018)CrossRefGoogle Scholar
  47. 47.
    M.A. Eltaher, S.A. Emam, F.F. Mahmoud, Appl. Math. Comput. 218, 7406 (2012)MathSciNetGoogle Scholar
  48. 48.
    S. Natarajan, S. Chakraborty, M. Thangavel, S. Bordas, T. Rabczuk, Comput. Mater. Sci. 65, 74 (2012)CrossRefGoogle Scholar
  49. 49.
    O. Rahmani, O. Pedram, Int. J. Eng. Sci. 77, 55 (2014)CrossRefGoogle Scholar
  50. 50.
    R. Nazemnezhad, S. Hosseini-Hashemi, Compos. Struct. 110, 192 (2014)CrossRefGoogle Scholar
  51. 51.
    F. Ebrahimi, E. Salari, Compos. Struct. 128, 363 (2015)CrossRefGoogle Scholar
  52. 52.
    L. Li, Y. Hu, L. Ling, Compos. Struct. 133, 1079 (2015)CrossRefGoogle Scholar
  53. 53.
    F. Ebrahimi, M.R. Barati, J. Therm. Stresses 39, 1210 (2016)CrossRefGoogle Scholar
  54. 54.
    M. Zamani Nejad, A. Hadi, A. Rastgoo, Int. J. Eng. Sci. 103, 1 (2016)CrossRefGoogle Scholar
  55. 55.
    F. Ebrahimi, M.R. Barati, A. Dabbagh, Appl. Phys. A 122, 949 (2016)ADSCrossRefGoogle Scholar
  56. 56.
    F. Ebrahimi, A. Dabbagh, M.R. Barati, Eur. Phys. J. Plus 131, 433 (2016)CrossRefGoogle Scholar
  57. 57.
    M.R. Barati, A. Zenkour, Compos. Struct. 168, 885 (2017)CrossRefGoogle Scholar
  58. 58.
    S. Srividhya, P. Raghu, A. Rajagopal, J.N. Reddy, Int. J. Eng. Sci. 125, 1 (2018)CrossRefGoogle Scholar
  59. 59.
    S.A. Yahia, H.A. Atmane, M.S.A. Houari, A. Tounsi, Struct. Eng. Mech. 53, 1143 (2015)CrossRefGoogle Scholar
  60. 60.
    B. Karami, M. Janghorban, A. Tounsi, Thin-Walled Struct. 129, 251 (2018)CrossRefGoogle Scholar
  61. 61.
    M.S.A. Houari, A. Tounsi, A. Bessaim, S.R. Mahmoud, Steel Compos. Struct. 22, 257 (2016)CrossRefGoogle Scholar
  62. 62.
    A. Kaci, M.S.A. Houari, A.A. Bousahla, A. Tounsi, S.R. Mahmoud, Struct. Eng. Mech. 65, 621 (2018)Google Scholar
  63. 63.
    A. Tounsi, M.S.A. Houari, S. Benyoucef, Aerospace Sci. Technol. 24, 209 (2013)CrossRefGoogle Scholar
  64. 64.
    B. Bouderba, M.S.A. Houari, A. Tounsi, Steel Compos. Struct. 14, 85 (2013)CrossRefGoogle Scholar
  65. 65.
    A.A. Bousahla, M.S.A. Houari, A. Tounsi, E.A. Adda Bedia, Int. J. Comput. Methods 11, 1350082 (2014)MathSciNetCrossRefGoogle Scholar
  66. 66.
    H. Hebali, A. Tounsi, M.S.A. Houari, A. Bessaim, E.A.A. Bedia, J. Eng. Mech. 140, 374 (2014)CrossRefGoogle Scholar
  67. 67.
    M.A.A. Meziane, H.H. Abdelaziz, A. Tounsi, J. Sandw. Struct. Mater. 16, 293 (2014)CrossRefGoogle Scholar
  68. 68.
    H.H. Abdelaziz, M.A.A. Meziane, A.A. Bousahla, A. Tounsi, S.R. Mahmoud, A.S. Alwabli, Steel Compos. Struct. 25, 693 (2017)Google Scholar

Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

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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