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Three-dimensional dynamics of beam-like nanorotors on the basis of newly developed nonlocal shear deformable mode shapes

  • Keivan Kiani
  • Soroush Soltani
Regular Article
  • 5 Downloads

Abstract.

The longitudinal, chordwise, and flapwise vibrations of nanorotors are going to be examined via nonlocal Euler-Bernoulli and Timoshenko beam models. By exploiting Hamilton’s principle on the basis of the nonlocal constitutive relations, the novel-nonlocal equations of motion that display three-dimensional vibrations of the beam-like nanorotors are constructed and solved for natural frequencies using the Galerkin-based assumed mode methodology. For capturing the frequencies more accurately, the newly developed-size-dependent mode shapes are employed in which the true nonlocal boundary conditions at the free end are satisfied exactly. Accounting for dynamic couplings of the longitudinal and chordwise vibrations, the roles of the angular velocity, nonlocality, length of the nanorotor, and radius of the nanoshaft on the longitudinal, chordwise, and flapwise frequencies are displayed and discussed. Further, the critical angular velocity of the nanorotor by considering the nonlocality is derived and its influential factors are displayed. The crucial role of the shear deformation on the obtained results is also explained methodically.

References

  1. 1.
    K.E. Drexler, Nanosystems: Molecular Machinery, Manufacturing, and Computation (John Wiley & Sons, Inc, 1992)Google Scholar
  2. 2.
    D.H. Robertson, B.I. Dunlap, D.W. Brenner, J.W. Mintmire, C.T. White, MRS Online Proc. Libr. Arch. 349, 283 (1994)CrossRefGoogle Scholar
  3. 3.
    S. Fournier-Bidoz, A.C. Arsenault, I. Manners, G.A. Ozin, Chem. Commun. 4, 441 (2005)CrossRefGoogle Scholar
  4. 4.
    P.H. Jones, F. Palmisano, F. Bonaccorso, P.G. Gucciardi, G. Calogero, A.C. Ferrari, O.M. Marago, ACS Nano 3, 3077 (2009)CrossRefGoogle Scholar
  5. 5.
    T. Mirkovic, N.S. Zacharia, G.D. Scholes, G.A. Ozin, Small 6, 159 (2010)CrossRefGoogle Scholar
  6. 6.
    A.C. Eringen, Int. J. Eng. Sci. 10, 1 (1972)CrossRefGoogle Scholar
  7. 7.
    A.C. Eringen, J. Appl. Phys. 54, 4703 (1983)ADSCrossRefGoogle Scholar
  8. 8.
    A.C. Eringen, Nonlocal Continuum Field Theories (Springer Science & Business Media, 2002)Google Scholar
  9. 9.
    J.N. Reddy, Int. J. Eng. Sci. 45, 288 (2007)CrossRefGoogle Scholar
  10. 10.
    C.M. Wang, Y.Y. Zhang, X.Q. He, Nanotechnology 18, 105401 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    B. Arash, Q. Wang, Comput. Mater. Sci. 51, 303 (2012)CrossRefGoogle Scholar
  12. 12.
    Q. Wang, J. Appl. Phys. 98, 124301 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    W.H. Duan, C.M. Wang, Nanotechnology 18, 385704 (2007)ADSCrossRefGoogle Scholar
  14. 14.
    L.E. Shen, H.S. Shen, C.L. Zhang, Comput. Mater. Sci. 48, 680 (2010)CrossRefGoogle Scholar
  15. 15.
    K. Kiani, Physica E 44, 229 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    R. Barretta, M. Brcic, M. Canadija, R. Luciano, F.M. de Sciarra, Eur. J. Mech. A Solids 65, 1 (2017)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    R. Barretta, F.M. de Sciarra, Adv. Mater. Sci. Eng. 2013, 360935 (2013)CrossRefGoogle Scholar
  18. 18.
    M. Canadija, R. Barretta, F.M. de Sciarra, Compos. Struct. 135, 286 (2016)CrossRefGoogle Scholar
  19. 19.
    K. Kiani, Physica E 83, 151 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    K. Kiani, Compos. Struct. 139, 151 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    G. Romano, R. Barretta, M. Diaco, F.M. de Sciarra, Int. J. Mech. Sci. 121, 151 (2017)CrossRefGoogle Scholar
  22. 22.
    R. Barretta, M. Canadija, L. Feo, R. Luciano, F.M. de Sciarra, R. Penna, Composites Part B: Eng. 142, 273 (2018)CrossRefGoogle Scholar
  23. 23.
    T. Murmu, S. Adhikari, J. Appl. Phys. 108, 123507 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    S.C. Pradhan, T. Murmu, Physica E 42, 1944 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    S. Narendar, Appl. Math. Comput. 219, 1232 (2012)MathSciNetGoogle Scholar
  26. 26.
    A. Pourasghar, M. Homauni, S. Kamarian, Polym. Compos. 37, 3175 (2016)CrossRefGoogle Scholar
  27. 27.
    S. Narendar, S. Gopalakrishnan, Results Phys. 1, 17 (2011)ADSCrossRefGoogle Scholar
  28. 28.
    F. Ebrahimi, M.R. Barati, P. Haghi, J. Therm. Stresses 40, 535 (2017)CrossRefGoogle Scholar
  29. 29.
    M. Safarabadi, M. Mohammadi, A. Farajpour, M. Goodarzi, J. Solid Mech. 7, 299 (2015)Google Scholar
  30. 30.
    M. Ghadiri, S.H.S. Hosseini, N. Shafiei, Mech. Adv. Mater. Struct. 23, 1414 (2016)CrossRefGoogle Scholar
  31. 31.
    M. Ghadiri, N. Shafiei, H. Safarpour, Microsyst. Technol. 23, 1045 (2017)CrossRefGoogle Scholar
  32. 32.
    M. Mohammadi, M. Safarabadi, A. Rastgoo, A. Farajpour, Acta Mech. 227, 2207 (2016)MathSciNetCrossRefGoogle Scholar
  33. 33.
    N. Shafiei, M. Kazemi, M. Ghadiri, Appl. Phys. A 122, 1 (2016)CrossRefGoogle Scholar
  34. 34.
    K. Kiani, J. Therm. Stresses 39, 1483 (2016)CrossRefGoogle Scholar
  35. 35.
    K. Kiani, Acta Mech. Sin. 32, 813 (2016)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    K. Kiani, Int. J. Mech. Sci. 106, 39 (2016)CrossRefGoogle Scholar
  37. 37.
    K. Kiani, J. Phys. D: Appl. Phys. 49, 275306 (2016)ADSCrossRefGoogle Scholar
  38. 38.
    K. Kiani, Microsyst. Technol. 23, 4853 (2017)CrossRefGoogle Scholar
  39. 39.
    P. Lu, H.P. Lee, C. Lu, P.Q. Zhang, J. Appl. Phys. 99, 073510 (2006)ADSCrossRefGoogle Scholar
  40. 40.
    S.S. Gupta, R.C. Batra, Comput. Mater. Sci. 43, 715 (2008)CrossRefGoogle Scholar
  41. 41.
    S.S. Gupta, F.G. Bosco, R.C. Batra, Comput. Mater. Sci. 47, 1049 (2010)CrossRefGoogle Scholar
  42. 42.
    H.H. Yoo, S.H. Shin, J. Sound Vib. 212, 807 (1998)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Civil EngineeringK.N. Toosi University of TechnologyTehranIran

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