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

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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.

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References

  1. F. Ebrahimi, M.R. Barati, A. Dabbagh, Waves Random Complex Media 28, 215 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  2. F. Ebrahimi, A. Rastgoo, Thin-Walled Struct. 46, 1402 (2008)

    Article  Google Scholar 

  3. H.S.Shen, Compos. Struct. 91, 375 (2009)

    Article  Google Scholar 

  4. Y. Huang, X.F. Li, J. Sound Vib. 329, 2291 (2010)

    Article  ADS  Google Scholar 

  5. A.E. Alshorbagy, M.A. Eltaher, F.F. Mahmoud, Appl. Math. Modell. 35, 412 (2011)

    Article  Google Scholar 

  6. M. Simşek, T. Kocatürk, S.D. Akbaş, Compos. Struct. 94, 2358 (2012)

    Article  Google Scholar 

  7. H.T. Thai, D.H. Choi, Compos. Part B 43, 2335 (2012)

    Article  Google Scholar 

  8. F. Ebrahimi, Mech. Adv. Mater. Struct. 20, 854 (2013)

    Article  Google Scholar 

  9. S.E. Ghiasian, Y. Kiani, M. Sadighi, M.R. Eslami, Int. J. Mech. Sci. 81, 137 (2014)

    Article  Google Scholar 

  10. M. Simşek, Compos. Struct. 133, 968 (2015)

    Article  Google Scholar 

  11. S.E. Ghiasian, Y. Kiani, M.R. Eslami, Eur. J. Mech. A/Solids 54, 232 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  12. M.R. Jafarinezhad, M.R. Eslami, Compos. Struct. 168, 758 (2017)

    Article  Google Scholar 

  13. M. Gharibi, M. Zamani Nejad, A. Hadi, J. Comput. Appl. Mech. 48, 89 (2017)

    Google Scholar 

  14. Y. Tang, T. Yang, Compos. Struct. 185, 393 (2018)

    Article  Google Scholar 

  15. A. Menasria, A. Bouhadra, A. Tounsi, A.A. Bousahla, S.R. Mahmoud, Steel Compos. Struct. 25, 157 (2017)

    Google Scholar 

  16. M. Zamani Nejad, M. Jabbari, A. Hadi, J. Comput. Appl. Mech. 48, 357 (2017)

    Google Scholar 

  17. A. Mahi, A. Tounsi, Appl. Math. Modell. 39, 2489 (2018)

    Article  Google Scholar 

  18. A. Attia, A.A. Bousahla, A. Tounsi, S.R. Mahmoud, A.S Alwabli, Struct. Eng. Mech. 65, 453 (2018)

    Google Scholar 

  19. A. Zargaripoora, A. Daneshmehra, I.I. Hosseinia, A. Rajabpoora, J. Comput. Appl. Mech. 49, 86 (2018)

    Google Scholar 

  20. A.C. Eringen, Int. J. Eng. Sci. 10, 425 (1972)

    Article  Google Scholar 

  21. S.C. Pradhan, T. Murmu, Physica E 42, 1293 (2010)

    Article  ADS  Google Scholar 

  22. R. Ansari, B. Arash, H. Rouhi, Compos. Struct. 93, 2419 (2011)

    Article  Google Scholar 

  23. F.F. Mahmoud, M.A. Eltaher, A.E. Alshorbagy, E.I. Meletis, J. Mech. Sci. Technol. 26, 3555 (2012)

    Article  Google Scholar 

  24. M.A. Eltaher, A.E. Alshorbagy, F.F. Mahmoud, Appl. Math. Modell. 37, 4787 (2013)

    Article  Google Scholar 

  25. E.O. Alzahrani, A.M. Zenkour, M. Sobhy, Compos. Struct. 105, 163 (2013)

    Article  Google Scholar 

  26. F. Ebrahimi, E. Salari, J. Mech. Sci. Technol. 29, 3797 (2015)

    Article  Google Scholar 

  27. A.M. Zenkour, Physica E 79, 87 (2016)

    Article  ADS  Google Scholar 

  28. A. Ghorbanpour Arani, M. Jamali, A.H. Ghorbanpour-Arani, R. Kolahchi, M. Mosayyebi, Proc. Inst. Mech. Eng. Part C 231, 387 (2017)

    Article  Google Scholar 

  29. F. Ebrahimi, M. Karimiasl, Mech. Adv. Mater. Struct. 25, 943 (2018)

    Article  Google Scholar 

  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. F. Ebrahimi, A. Dabbagh, Appl. Phys. A 124, 301 (2018)

    Article  ADS  Google Scholar 

  32. F. Ebrahimi, A. Dabbagh, Eur. Phys. J. Plus 133, 97 (2018)

    Article  Google Scholar 

  33. S.K. Jalali, M.H. Naei, J. Comput. Appl. Mech. 45, 61 (2014)

    Google Scholar 

  34. A. Zemri, M.S.A. Houari, A.A. Bousahla, A. Tounsi, Struct. Eng. Mech. 54, 693 (2015)

    Article  Google Scholar 

  35. M. Ahouel, M.S.A. Houari, E.A. Bedia, A. Tounsi, Steel Compos. Struct. 20, 963 (2016)

    Article  Google Scholar 

  36. M. Yazid, H. Heireche, A. Tounsi, A.A. Bousahla, M.S.A. Houari, Smart Struct. Syst. 21, 15 (2018)

    Google Scholar 

  37. M. Ajri, M.M.S. Fakhrabadi, J. Comput. Appl. Mech. 49, 44 (2018)

    Google Scholar 

  38. N.A. Fleck, J.W. Hutchinson, J. Mech. Phys. Solids 41, 1825 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  39. J.S. Stölken, A.G. Evans, Acta Mater. 46, 5109 (1998)

    Article  Google Scholar 

  40. D.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, J. Mech. Phys. Solids 51, 1477 (2003)

    Article  ADS  Google Scholar 

  41. C.W. Lim, G. Zhang, J.N. Reddy, J. Mech. Phys. Solids 78, 298 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  42. L. Li, Y. Hu, Int. J. Eng. Sci. 97, 84 (2015)

    Article  Google Scholar 

  43. A. Farajpour, M.H. Yazdi, A. Rastgoo, M. Mohammadi, Acta Mech. 227, 1849 (2016)

    Article  MathSciNet  Google Scholar 

  44. X.J. Xu, X.C. Wang, M.L. Zheng, Z. Ma, Compos. Struct. 160, 366 (2017)

    Article  Google Scholar 

  45. S. Sahmani, M.M. Aghdam, Compos. Struct. 178, 97 (2017)

    Article  Google Scholar 

  46. F. Ebrahimi, M.R. Barati, J. Braz. Soc. Mech. Sci. Eng. 40, 428 (2018)

    Article  Google Scholar 

  47. M.A. Eltaher, S.A. Emam, F.F. Mahmoud, Appl. Math. Comput. 218, 7406 (2012)

    MathSciNet  Google Scholar 

  48. S. Natarajan, S. Chakraborty, M. Thangavel, S. Bordas, T. Rabczuk, Comput. Mater. Sci. 65, 74 (2012)

    Article  Google Scholar 

  49. O. Rahmani, O. Pedram, Int. J. Eng. Sci. 77, 55 (2014)

    Article  Google Scholar 

  50. R. Nazemnezhad, S. Hosseini-Hashemi, Compos. Struct. 110, 192 (2014)

    Article  Google Scholar 

  51. F. Ebrahimi, E. Salari, Compos. Struct. 128, 363 (2015)

    Article  Google Scholar 

  52. L. Li, Y. Hu, L. Ling, Compos. Struct. 133, 1079 (2015)

    Article  Google Scholar 

  53. F. Ebrahimi, M.R. Barati, J. Therm. Stresses 39, 1210 (2016)

    Article  Google Scholar 

  54. M. Zamani Nejad, A. Hadi, A. Rastgoo, Int. J. Eng. Sci. 103, 1 (2016)

    Article  Google Scholar 

  55. F. Ebrahimi, M.R. Barati, A. Dabbagh, Appl. Phys. A 122, 949 (2016)

    Article  ADS  Google Scholar 

  56. F. Ebrahimi, A. Dabbagh, M.R. Barati, Eur. Phys. J. Plus 131, 433 (2016)

    Article  Google Scholar 

  57. M.R. Barati, A. Zenkour, Compos. Struct. 168, 885 (2017)

    Article  Google Scholar 

  58. S. Srividhya, P. Raghu, A. Rajagopal, J.N. Reddy, Int. J. Eng. Sci. 125, 1 (2018)

    Article  Google Scholar 

  59. S.A. Yahia, H.A. Atmane, M.S.A. Houari, A. Tounsi, Struct. Eng. Mech. 53, 1143 (2015)

    Article  Google Scholar 

  60. B. Karami, M. Janghorban, A. Tounsi, Thin-Walled Struct. 129, 251 (2018)

    Article  Google Scholar 

  61. M.S.A. Houari, A. Tounsi, A. Bessaim, S.R. Mahmoud, Steel Compos. Struct. 22, 257 (2016)

    Article  Google Scholar 

  62. A. Kaci, M.S.A. Houari, A.A. Bousahla, A. Tounsi, S.R. Mahmoud, Struct. Eng. Mech. 65, 621 (2018)

    Google Scholar 

  63. A. Tounsi, M.S.A. Houari, S. Benyoucef, Aerospace Sci. Technol. 24, 209 (2013)

    Article  Google Scholar 

  64. B. Bouderba, M.S.A. Houari, A. Tounsi, Steel Compos. Struct. 14, 85 (2013)

    Article  Google Scholar 

  65. A.A. Bousahla, M.S.A. Houari, A. Tounsi, E.A. Adda Bedia, Int. J. Comput. Methods 11, 1350082 (2014)

    Article  MathSciNet  Google Scholar 

  66. H. Hebali, A. Tounsi, M.S.A. Houari, A. Bessaim, E.A.A. Bedia, J. Eng. Mech. 140, 374 (2014)

    Article  Google Scholar 

  67. M.A.A. Meziane, H.H. Abdelaziz, A. Tounsi, J. Sandw. Struct. Mater. 16, 293 (2014)

    Article  Google Scholar 

  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 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran

    Farzad Ebrahimi

  2. School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Ali Dabbagh

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  1. Farzad Ebrahimi
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  2. Ali Dabbagh
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Correspondence to Farzad Ebrahimi.

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Ebrahimi, F., Dabbagh, A. Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams. Eur. Phys. J. Plus 134, 112 (2019). https://doi.org/10.1140/epjp/i2019-12464-x

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