Skip to main content
SpringerLink
Log in

A novel porosity-dependent homogenization procedure for wave dispersion in nonlocal strain gradient inhomogeneous nanobeams

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

Present research aims to consider the reciprocal impacts of Young moduli and mass density while investigating the wave propagation behaviors of functionally graded (FG) nanobeams via a nonlocal strain gradient based shear deformable beam theory for the first time. The porosity influences are regarded within the framework of a newly developed method. The motion equations are obtained by extending the dynamic form of the principle of virtual work for a higher-order beam model. Thereafter, the constitutive relations are modified based on the nonlocal strain gradient theory in order to account for the effects of small scale. At the end, the dispersion curves are achieved by solving the problem with an analytical method. The results show that there is a remarkable difference between the results of this homogenization method and those of former simple methods that were utilized to capture porosity effects. Also, it is proven that the presented methodology is efficient enough to estimate the dynamic behaviors of FG nanobeams.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Google Scholar 

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

    Google Scholar 

  3. V. Birman, L.W. Byrd, Appl. Mech. Rev. 60, 195 (2007)

    Article  ADS  Google Scholar 

  4. M. Koizumi, Composites Part B 28, 1 (1997)

    Article  Google Scholar 

  5. X. Zhao, Y. Lee, K.M. Liew, J. Sound Vib. 319, 918 (2009)

    Article  ADS  Google Scholar 

  6. M. Talha, B. Singh, Appl. Math. Model. 34, 3991 (2010)

    Article  MathSciNet  Google Scholar 

  7. L.-L. Ke et al., Int. J. Eng. Sci. 50, 256 (2012)

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. H.-S. Shen, H. Wang, Composites Part B 60, 167 (2014)

    Article  Google Scholar 

  10. G. Romano, A. Barretta, R. Barretta, Eur. J. Mech.-A/Solids 35, 47 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  11. R. Barretta, Int. J. Solids Struct. 49, 3038 (2012)

    Article  Google Scholar 

  12. R. Barretta, J. Elastic. 112, 233 (2013)

    Article  Google Scholar 

  13. R. Barretta, Acta Mech. 224, 2955 (2013)

    Article  MathSciNet  Google Scholar 

  14. R. Barretta, Acta Mech. 225, 2075 (2014)

    Article  MathSciNet  Google Scholar 

  15. P. Chu et al., Acta Mech. 226, 2235 (2015)

    Article  MathSciNet  Google Scholar 

  16. K. Mercan, Ç. Demir, Ö. Civalek Curved Layered Struct. (2016) https://doi.org/10.1515/cls-2016-0007

    Article  MathSciNet  Google Scholar 

  17. G.-L. She, F.-G. Yuan, Y.-R. Ren, Compos. Struct. 170, 111 (2017)

    Article  Google Scholar 

  18. M. Taczała, R. Buczkowski, M. Kleiber, Composites Part B 109, 238 (2017)

    Article  Google Scholar 

  19. G. Sheng, X. Wang, Eur. J. Mech.-A/Solids 71, 224 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  20. K. Darilmaz, E. Orakdöğen, K. Girgin, Acta Mech. 229, 1387 (2018)

    Article  MathSciNet  Google Scholar 

  21. F. Ebrahimi, M. Zia, Acta Astronaut. 116, 117 (2015)

    Article  Google Scholar 

  22. D. Chen, J. Yang, S. Kitipornchai, Int. J. Mech. Sci. 108, 14 (2016)

    Article  Google Scholar 

  23. F. Ebrahimi, M. Hashemi, Proc. Inst. Mech. Eng., Part G 230, 1903 (2016)

    Article  Google Scholar 

  24. H.A. Atmane, A. Tounsi, F. Bernard, Int. J. Mech. Mater. Design 13, 71 (2017)

    Article  Google Scholar 

  25. F. Ebrahimi, A. Jafari, Mech. Adv. Mater. Struct. 25, 212 (2018)

    Article  Google Scholar 

  26. M. Heshmati, F. Daneshmand Proc. Inst. Mech. Eng., Part L (2018) https://doi.org/10.1177/1464420718780902

    Article  Google Scholar 

  27. J. Zhao et al., Composites Part B 156, 406 (2019)

    Article  Google Scholar 

  28. J. Zhao et al., Composites Part B 159, 20 (2019)

    Article  Google Scholar 

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

    Article  Google Scholar 

  30. H.-T. Thai, Int. J. Eng. Sci. 52, 56 (2012)

    Article  Google Scholar 

  31. M. Ghafarian, A. Ariaei, J. Appl. Phys. 120, 054301 (2016)

    Article  ADS  Google Scholar 

  32. A. Pourasghar, M. Homauni, S. Kamarian, Polym. Compos. 37, 3175 (2016)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  35. F. Mahmoud et al., J. Mech. Sci. Technol. 26, 3555 (2012)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. J. Fernández-Sáez et al., Int. J. Eng. Sci. 99, 107 (2016)

    Article  Google Scholar 

  41. J. Fernández-Sáez, R. Zaera, Int. J. Eng. Sci. 119, 232 (2017)

    Article  Google Scholar 

  42. Bakhshi Khaniki, Charact. Appl. Nanomater. 1(No 2) (2018) https://doi.org/10.24294/can.v1i2.202

  43. N. Fleck, J. Hutchinson, J. Mech. Phys. Solids 41, 1825 (1993)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  46. A. Farajpour et al., Acta Mech. 227, 1849 (2016)

    Article  MathSciNet  Google Scholar 

  47. X.-J. Xu et al., Compos. Struct. 160, 366 (2017)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  50. A. Apuzzo et al., Int. J. Eng. Sci. 133, 99 (2018)

    Article  MathSciNet  Google Scholar 

  51. R. Barretta, F.M. de Sciarra, Int. J. Eng. Sci. 130, 187 (2018)

    Article  Google Scholar 

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

    MathSciNet  Google Scholar 

  53. S. Natarajan et al., Comput. Mater. Sci. 65, 74 (2012)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  57. R. Barretta et al., Composites Part B 100, 208 (2016)

    Article  Google Scholar 

  58. M. Čanajija, R. Barretta, F.M. de Sciarra, Compos. Struct. 135, 286 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  60. M. Simşek, Int. J. Eng. Sci. 105, 12 (2016)

    Article  Google Scholar 

  61. F. Ebrahimi, M.R. Barati, Arab. J. Sci. Eng. 42, 1715 (2017)

    Article  MathSciNet  Google Scholar 

  62. S.S. Mirjavadi et al., Appl. Phys. A 123, 315 (2017)

    Article  ADS  Google Scholar 

  63. H. Shahverdi, M.R. Barati, Int. J. Eng. Sci. 120, 82 (2017)

    Article  Google Scholar 

  64. F. Ebrahimi, M.R. Barati, P. Haghi, J. Vib. Control 24, 3809 (2018)

    Article  MathSciNet  Google Scholar 

  65. B. Karami, D. Shahsavari, M. Janghorban, Mech. Adv. Mater. Struct. 25, 1047 (2018)

    Article  Google Scholar 

  66. M. Malikan, F. Tornabene, R. Dimitri, Mater. Res. Express 5, 095006 (2018)

    Article  ADS  Google Scholar 

  67. M. Hosseini, M. Mahinzare, M. Ghadiri, J. Intell. Mater. Syst. Struct. 29, 2885 (2019)

    Article  Google Scholar 

  68. S.S. Mirjavadi et al., J. Braz. Soc. Mech. Sci. Eng. 40, 352 (2018)

    Article  Google Scholar 

  69. G.-L. She et al., Eur. Phys. J. Plus 133, 368 (2018)

    Article  Google Scholar 

  70. N. Radić, Composites Part B 153, 465 (2018)

    Article  Google Scholar 

  71. S. Sahmani, M.M. Aghdam, T. Rabczuk, Compos. Struct. 186, 68 (2018)

    Article  Google Scholar 

  72. A.P. Roberts, E.J. Garboczi, Acta Mater. 49, 189 (2001)

    Article  Google Scholar 

  73. M.A. Eltaher et al., J. Braz. Soc. Mech. Sci. Eng. 40, 141 (2018)

    Article  Google Scholar 

  74. F.W. Zok, C.G. Levi, Adv. Eng. Mater. 3, 15 (2001)

    Article  Google Scholar 

  75. M. Touratier, Int. J. Eng. Sci. 29, 901 (1991)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Farzad Ebrahimi & Ali Seyfi

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

    Ali Dabbagh

Authors
  1. Farzad Ebrahimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Seyfi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ali Dabbagh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farzad Ebrahimi.

Additional information

Publisher’s Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ebrahimi, F., Seyfi, A. & Dabbagh, A. A novel porosity-dependent homogenization procedure for wave dispersion in nonlocal strain gradient inhomogeneous nanobeams. Eur. Phys. J. Plus 134, 226 (2019). https://doi.org/10.1140/epjp/i2019-12547-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2019-12547-8

Search

Navigation