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Free transverse vibration analysis of spinning Timoshenko–Ehrenfest nano-beams through two-phase local/nonlocal elasticity theory

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Abstract

The present research aims to study the free transverse vibration of spinning nano-beams. Indeed, this research has conducted a numerical analysis through the generalized differential quadrature method, Timoshenko–Ehrenfest theory and the two-phase local/nonlocal elasticity theory as a size-dependent theory. First, comprehensive results have been validated, and then the effects of the local phase fraction coefficient and nonlocal factor on the natural frequencies and critical speed have been discussed.

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References

  1. S.A. Faghidian, Int. J. Eng. Sci. 129, 96 (2018)

    MathSciNet  Google Scholar 

  2. S.A. Faghidian, Eur. J. Mech. A. Solids 70, 115 (2018)

    ADS  MathSciNet  Google Scholar 

  3. S.A. Faghidian, K.K. Żurand, E. Pan, Int. J. Eng. Sci. 182, 103786 (2023)

    Google Scholar 

  4. S.A. Faghidian, K.K. Żur, I. Elishakoff, Commun. Nonlinear Sci. Numer. Simul. 117, 106928 (2023)

    Google Scholar 

  5. S.A. Faghidian, I. Elishakoff, Eng. Anal. Bound. Elem. 152, 14 (2023)

    Google Scholar 

  6. A. Apuzzo, R. Barretta, F. Fabbrocino, S.A. Faghidian, R. Luciano, F. Marotti De Sciarra, J. Appl. Comput. Mech. 5(2), 402 (2019)

    Google Scholar 

  7. S. Behdad, M. Arefi, Eur. J. Mech. A. Solids 94, 104558 (2022)

    ADS  Google Scholar 

  8. P.L. Bian, H. Qing, T. Yu, Compos. Struct. 295, 115769 (2022)

    Google Scholar 

  9. S. Behdad, M. Fakher, S. Hosseini-Hashemi, Mech. Mater. 153, 103633 (2021)

    Google Scholar 

  10. M. Fakher, S. Hosseini-Hashemi, J. Vib. Control 27(3–4), 378 (2021)

    MathSciNet  Google Scholar 

  11. M. Fakher, S. Behdad, A. Naderi, S. Hosseini-Hashemi, Int. J. Mech. Sci. 171, 105381 (2020)

    Google Scholar 

  12. S. Hosseini-Hashemi, S. Behdad, M. Fakher, Eur. Phys. J. Plus 135, 1 (2020)

    Google Scholar 

  13. A. Naderi, S. Behdad, M. Fakher, S. Hosseini-Hashemi, Mech. Syst. Signal Process. 145, 106931 (2020)

    Google Scholar 

  14. D. Scorza, R. Luciano, S. Vantadori, Compos. Struct. 280, 114957 (2022)

    Google Scholar 

  15. S. Wang, W. Kang, W. Yang, Z. Zhang, Q. Li, M. Liu, X. Wang, Eur. J. Mech. A. Solids 94, 104554 (2022)

    ADS  Google Scholar 

  16. P. Zhang, H. Qing, J. Vib. Control 28(23–24), 3808 (2022)

    MathSciNet  Google Scholar 

  17. M. Gökhan-Günay, J. Vib. Acoust. 145(3), 031009 (2023)

    Google Scholar 

  18. M.S. Vaccaro, H.M. Sedighi, Eng. Comput. 39(1), 827 (2023)

    Google Scholar 

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

    Google Scholar 

  20. Y.B. Wang, X.W. Zhu, H.H. Dai, Aip Adv. (2016). https://doi.org/10.1063/1.4961695

    Article  PubMed  PubMed Central  Google Scholar 

  21. X. Zhu, Y. Wang, H.H. Dai, Int. J. Eng. Sci. 116, 130 (2017)

    Google Scholar 

  22. S.A. Faghidian, I. Elishakoff, Meccanica 58(1), 97 (2023)

    MathSciNet  Google Scholar 

  23. M. Fakher, S. Hosseini-Hashemi, Eng. Comput. 1 (2022)

  24. H.M. Numanoğlu, H. Ersoy, B. Akgöz, Ö. Civalek, Math. Methods Appl. Sci. 45(5), 2592 (2022)

    ADS  MathSciNet  Google Scholar 

  25. Y. Ren, H. Qing, Compos. Struct. 300, 116129 (2022)

    Google Scholar 

  26. P. Zhang, H. Qing, Compos. Struct. 265, 113770 (2021)

    Google Scholar 

  27. Y. Wang, K. Huang, X. Zhu, Z. Lou, Math. Mech. Solids 24(3), 559 (2019)

    MathSciNet  Google Scholar 

  28. M.S. Vaccaro, F.P. Pinnola, F.M. de Sciarra, M. Canadija, R. Barretta, Proc. Inst. Mech. Eng. N: J. Nanomater. Nanoeng. Nanosyst. 235(1–2), 52 (2021)

    Google Scholar 

  29. Y. Lei, S. Adhikari, M.I. Friswell, Int. J. Eng. Sci. 66, 1 (2013)

    Google Scholar 

  30. X.F. Li, B.L. Wang, Appl. Phys. Lett. 94(10) (2009)

  31. R. Nazemnezhad, Compos. Struct. 133, 522 (2015)

    Google Scholar 

  32. Y.Y. Zhang, C.M. Wang, V.B.C. Tan, Adv. Appl. Math. Mech. 1(1), 89 (2009)

    MathSciNet  Google Scholar 

  33. M. Azimi, S.S. Mirjavadi, N. Shafiei, A.M.S. Hamouda, Appl. Phys. A 123, 1 (2017)

    Google Scholar 

  34. N. Shafiei, M. Kazemi, M. Ghadiri, Phys. E: Low-Dimens. Syst. Nanostruct. 83, 74 (2016)

    ADS  Google Scholar 

  35. K. Cai, H. Yin, N. Wei, Z. Chen, J. Shi, Appl. Phys. Lett. 106(2) (2015)

  36. S. Guo, Y. He, D. Liu, J. Lei, Z. Li, Microsyst. Technol. 24, 963 (2018)

    Google Scholar 

  37. M.R. Ilkhani, S.H. Hosseini-Hashemi, Compos. Struct. 143, 75 (2016)

    Google Scholar 

  38. M. Mohammadi, M. Safarabadi, A. Rastgoo, A. Farajpour, Acta Mech. 227, 2207 (2016)

    MathSciNet  Google Scholar 

  39. S. Narendar, Appl. Math. Comput. 219(3), 1232 (2012)

    MathSciNet  Google Scholar 

  40. N. Shafiei, M. Kazemi, M. Ghadiri, Appl. Phys. A 122, 1 (2016)

    Google Scholar 

  41. X. Yan, Appl. Phys. A 128(8), 641 (2022)

    ADS  Google Scholar 

  42. J. Aranda-Ruiz, J. Loya, J. Fernández-Sáez, Compos. Struct. 94(9), 2990 (2012)

    Google Scholar 

  43. K. Cai, J. Yu, L. Liu, J. Shi, Q.H. Qin, Phys. Chem. Chem. Phys. 18(32), 22478 (2016)

    PubMed  Google Scholar 

  44. A.M. Fennimore, T.D. Yuzvinsky, W.Q. Han, M.S. Fuhrer, J. Cumings, A. Zettl, Nature 424(6947), 408 (2003)

    ADS  PubMed  Google Scholar 

  45. S. Hosseini-Hashemi, M.R. Ilkhani, M. Fadaee, Int. J. Mech. Sci. 76, 9 (2013)

    Google Scholar 

  46. T. Murmu, S. Adhikari, J. Appl. Phys. 108(12) (2010)

  47. S. Narendar, S. Gopalakrishnan, Results Phys. 1(1), 17 (2011)

    ADS  Google Scholar 

  48. S.C. Pradhan, T. Murmu, Phys. E: Low-Dimens. Syst. Nanostruct. 42(7), 1944 (2010)

    ADS  Google Scholar 

  49. D. Srivastava, Nanotechnology 8(4), 186 (1997)

    ADS  Google Scholar 

  50. M.R. Ilkhani, R. Nazemnezhad, S. Hosseini-Hashemi, J. Braz. Soc. Mech. Sci. 41, 1 (2019)

    Google Scholar 

  51. S.A. Faghidian, Int. J. Mech. Sci. 111, 65 (2016)

    Google Scholar 

  52. S.S. Rao, Vibration of continuous systems (Wiley, 2019)

    Google Scholar 

  53. S.A. Faghidian, J. Press. Vessel. Technol. 139(3), 031205 (2017)

    Google Scholar 

  54. G.H. Farrahi, S.A. Faghidian, D.J. Smith, Int. J. Press. Vessel. 86(11), 777 (2009)

    Google Scholar 

  55. S.A. Faghidian, J. Press. Vessel. Technol. 139(4), 041202 (2017)

    Google Scholar 

  56. P. Polyanin, A.V. Manzhirov, Handbook of integral equations (Chapman and Hall/CRC, 2008)

    Google Scholar 

  57. T.Y. Wu, G.R. Liu, Int. J. Numer. Methods Eng. 50(8), 1907 (2001)

    Google Scholar 

  58. C.W. Bert, M. Malik, Differential quadrature method in computational mechanics: a review (1996)

  59. Y. Wang, Y.B. Zhao, G. Wei, J. Comput. Appl. Math. 159(2), 387 (2003)

    ADS  MathSciNet  Google Scholar 

  60. J.R. Quan, C.T. Chang, Comput. Chem. Eng. 13(7), 779 (1989)

    Google Scholar 

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Authors and Affiliations

  1. School of Engineering, Damghan University, Damghan, Iran

    Reza Nazemnezhad & Roozbeh Ashrafian

Authors
  1. Reza Nazemnezhad
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  2. Roozbeh Ashrafian
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Contributions

The first author: conceptualization, methodology, writing the paper (review and editing). The second author: software (designing computer programs; implementation of the computer code and supporting algorithms), validation, formal analysis, writing the paper (original draft preparation).

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Correspondence to Reza Nazemnezhad or Roozbeh Ashrafian.

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Appendix

Appendix

$$\left\{\begin{array}{l}{a}_{10}=\frac{-1}{{\left({x}_{1}-{x}_{ns}\right)}^{2}}+\frac{-{l}_{1}^{\left(1\right)}({x}_{1})}{\left({x}_{1}-{x}_{ns}\right)},\\ {b}_{10}=\frac{1}{\left({x}_{1}-{x}_{ns}\right)}-{a}_{10}\left({x}_{1}+{x}_{ns}\right),\\ {c}_{10}=1-{a}_{10}{{x}_{1}}^{2}-{b}_{10}{x}_{1},\end{array}\right.$$
$$\left\{\begin{array}{l}{a}_{11}=\frac{1}{{x}_{1}-{x}_{ns}},\\ {b}_{11}=\frac{{-(x}_{1}+{x}_{ns})}{{x}_{1}-{x}_{ns}},\\ {c}_{11}=\frac{{x}_{1}{x}_{ns}}{{x}_{1}-{x}_{ns}},\end{array}\right.$$
$$\left\{\begin{array}{l}{a}_{ns0}=\frac{-1}{{\left({x}_{1}-{x}_{ns}\right)}^{2}}+\frac{-{l}_{ns}^{\left(1\right)}({x}_{1})}{\left({x}_{1}-{x}_{ns}\right)},\\ {b}_{ns0}=\frac{-1}{\left({x}_{1}-{x}_{ns}\right)}-{a}_{ns0}\left({x}_{1}+{x}_{ns}\right),\\ {c}_{ns0}=1-{a}_{ns0}{{x}_{ns}}^{2}-{b}_{ns0}{x}_{ns},\end{array}\right.$$
$$\left\{\begin{array}{l}{a}_{ns1}=\frac{-1}{{x}_{1}-{x}_{ns}},\\ {b}_{ns1}=\frac{{x}_{1}+{x}_{ns}}{{x}_{1}-{x}_{ns}},\\ {c}_{ns1}=\frac{{-x}_{1}{x}_{ns}}{{x}_{1}-{x}_{ns}}.\end{array}\right.$$

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Nazemnezhad, R., Ashrafian, R. Free transverse vibration analysis of spinning Timoshenko–Ehrenfest nano-beams through two-phase local/nonlocal elasticity theory. Appl. Phys. A 130, 199 (2024). https://doi.org/10.1007/s00339-024-07350-9

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