Advances in nano research

  • 제4권4호
  • /
  • Pages.265-279
  • /
  • 2016
  • /
  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Forced vibration of nanorods using nonlocal elasticity

  • Aydogdu, Metin (Department of Mechanical Engineering, Trakya University) ;
  • Arda, Mustafa (Department of Mechanical Engineering, Trakya University)
  • 투고 : 2016.05.14
  • 심사 : 2016.08.24
  • 발행 : 2016.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

Present study interests with the longitudinal forced vibration of nanorods. The nonlocal elasticity theory of Eringen is used in modeling of nanorods. Uniform, linear and sinusoidal axial loads are considered. Dynamic displacements are obtained for nanorods with different geometrical properties, boundary conditions and nonlocal parameters. The nonlocal effect increases dynamic displacement and frequency when compared with local elasticity theory. Present results can be useful for modeling of the axial nanomotors and nanoelectromechanical systems.

키워드

참고문헌

  1. Ansari, R., Gholami, R., Hosseini, K. and Sahmani, S. (2011), "A sixth-order compact finite difference method for vibrational analysis of nanobeams embedded in an elastic medium based on nonlocal beam theory", Math. Comput. Model., 54(11-12), 2577-2586. https://doi.org/10.1016/j.mcm.2011.06.030
  2. Arash, B. and Wang, Q. (2012), "A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes", Comput. Mater. Sci., 51(1), 303-313. https://doi.org/10.1016/j.commatsci.2011.07.040
  3. Arda, M. and Aydogdu, M. (2016), "Torsional wave propagation in multiwalled carbon nanotubes using nonlocal elasticity", Appl. Phys. A., 122(3), 219.
  4. Aydogdu, M. (2009a), "A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration", Phys. E Low-Dimens. Syst. Nanostruct., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  5. Aydogdu, M. (2012a), "Longitudinal wave propagation in nanorods using a general nonlocal unimodal rod theory and calibration of nonlocal parameter with lattice dynamics", Int. J. Eng. Sci., 5617-28.
  6. Aydogdu, M. (2014), "Longitudinal wave propagation in multiwalled carbon nanotubes", Compos. Struct., 107, 578-584. https://doi.org/10.1016/j.compstruct.2013.08.031
  7. Aydogdu, M. (2009b), "Axial vibration of the nanorods with the nonlocal continuum rod model", Phys. E Low-dimensional Syst Nanostructures, 41(5), 861-864. https://doi.org/10.1016/j.physe.2009.01.007
  8. Aydogdu, M. (2012b), "Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity", Mech. Res. Commun., 4334-40.
  9. Aydogdu, M. and Arda, M. (2014), "Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity", Int. J. Mech. Mater. Des., doi: 10.1007/s10999-014-9292-8
  10. Danesh, M., Farajpour, A. and Mohammadi, M. (2012), "Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method", Mech. Res. Commun., 39(1), 23-27. https://doi.org/10.1016/j.mechrescom.2011.09.004
  11. Demir, C., Civalek, O. and Akgoz, B. (2010), "Free vibration analysis of carbon nanotubes based on shear deformable beam theory by discrete singular convolution technique", Math. Comput. Appl., 15(1), 57-65.
  12. Duan, W.H., Wang, C.M. and Zhang, Y.Y. (2007), "Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics", J. Appl. Phys., 101(2), 24305. https://doi.org/10.1063/1.2423140
  13. Ece, M.C. and Aydogdu, M. (2007), "Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes", Acta Mech., 190(1-4), 185-195. https://doi.org/10.1007/s00707-006-0417-5
  14. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803
  15. Eringen, A.C. (2007), Nonlocal Continuum Field Theories, Springer, New York
  16. Hu, Y.G., Liew, K.M., Wang, Q., He, X.Q. and Yakobson, B.I. (2008), "Nonlocal shell model for elastic wave propagation in single-and double-walled carbon nanotubes", J. Mech. Phys. Solid., 56(12), 3475-3485. https://doi.org/10.1016/j.jmps.2008.08.010
  17. Huang, Z.X. (2012), "Nonlocal effects of longitudinal vibration in nanorod with internal long range interactions", Int. J. Solid. Struct., 49(1516), 2150-2154. https://doi.org/10.1016/j.ijsolstr.2012.04.020
  18. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354, 56-58. https://doi.org/10.1038/354056a0
  19. Karaoglu, P. and Aydogdu, M. (2010), "On the forced vibration of carbon nanotubes via a non-local Euler--Bernoulli beam model", Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., 224(2), 497-503. https://doi.org/10.1243/09544062JMES1707
  20. Kiani, K. (2010), "A meshless approach for free transverse vibration of embedded single-walled nanotubes with arbitrary boundary conditions accounting for nonlocal effect", Int. J. Mech. Sci., 52(10), 1343-1356. https://doi.org/10.1016/j.ijmecsci.2010.06.010
  21. Kiani, K. (2014), "Nonlocal continuous models for forced vibration analysis of two-and three-dimensional ensembles of single-walled carbon nanotubes", Phys. E Low-dimens. Syst. Nanostruct., 60229-245.
  22. Kiani, K. (2010), "Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique", Phys. E Low-dimens. Syst. Nanostruct., 43(1) 387-397. https://doi.org/10.1016/j.physe.2010.08.022
  23. Kiani, K. (2014), "Nonlocal discrete and continuous modeling of free vibration of stocky ensembles of vertically aligned singlewalled carbon nanotubes", Curr. Appl. Phys., 14(8), 1116-1139. https://doi.org/10.1016/j.cap.2014.05.018
  24. Kiani, K. (2014), "In and out of plane dynamic flexural behaviors of two dimensional ensembles of vertically aligned singlewalled carbon nanotubes", Physica B: Condens. Matter., 449, 164-180. https://doi.org/10.1016/j.physb.2014.04.044
  25. Kiani, K. (2014), "Free dynamic analysis of functionally graded tapered nanorods via a newly developed nonlocal surface energybased integrodifferential model", Compos. Struct., 139, 151-166.
  26. Kiani, K. (2010), "Nonlocal integro differential modeling of vibration of elastically supported nanorods", Phys. E Low-dimens. Syst. Nanostruct., 83, 151-163.
  27. Murmu, T. and Pradhan, S.C. (2009), "Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Comput. Mater. Sci., 46(4), 854-859. https://doi.org/10.1016/j.commatsci.2009.04.019
  28. Murmu, T. and Adhikari, S. (2010), "Non local effects in the longitudinal vibration of doublenanorod systems", Physica E, 43(1), 415-422. https://doi.org/10.1016/j.physe.2010.08.023
  29. Narendar, S. (2011), "Terahertz wave propagation in uniform nanorods: A nonlocal continuum mechanics formulation including the effect of lateral inertia", Phys. E Low-dimens. Syst. Nanostruct., 43(4), 1015-1020. https://doi.org/10.1016/j.physe.2010.12.004
  30. Narendar, S. and Gopalakrishnan, S. (2010), "Nonlocal scale effects on ultrasonic wave characteristics of nanorods", Phys. E Low-dimens. Syst. Nanostruct., 42(5), 1601-1604. https://doi.org/10.1016/j.physe.2010.01.002
  31. Narendar, S. and Gopalakrishnan, S. (2011), "Axial wave propagation in coupled nanorod system with nonlocal small scale effects", Compos. Part B-Eng, 42(7), 2013-2023 https://doi.org/10.1016/j.compositesb.2011.05.021
  32. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41(3), 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  33. Reddy, J.N.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  34. Sudak, L.J. (2003), "Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics", J. Appl. Phys., 94(11), 7281. https://doi.org/10.1063/1.1625437
  35. Simsek, M. (2011), "Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle", Comput. Mater. Sci., 50(7), 2112-2123. https://doi.org/10.1016/j.commatsci.2011.02.017
  36. Simsek, M. (2010), "Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory", Phys. E Low-dimens. Syst. Nanostruct., 43(1), 182-191. https://doi.org/10.1016/j.physe.2010.07.003
  37. Truax, S., Lee, S.W., Muoth, M. and Hierold, C. (2014), "Axially tunable carbon nanotube resonators using co-integrated microactuators", Nano Lett., 14(11), 6092-6. https://doi.org/10.1021/nl501853w
  38. Wang, L. and Hu, H. (2005), "Flexural wave propagation in single-walled carbon nanotubes", Phys. Rev. B, 71(19), 195412. https://doi.org/10.1103/PhysRevB.71.195412
  39. Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98(12), 124301. https://doi.org/10.1063/1.2141648
  40. Wang, Q. and Liew, K.M. (2007), "Application of nonlocal continuum mechanics to static analysis of micro-and nano-structures", Phys. Lett. A, 363(3), 236-242. https://doi.org/10.1016/j.physleta.2006.10.093
  41. Wang, Q. and Varadan, V.K. (2006), "Wave characteristics of carbon nanotubes", Int. J. Solid. Struct., 43(2), 254-265. https://doi.org/10.1016/j.ijsolstr.2005.02.047
  42. Wang, Q. and Wang, C.M. (2007), "The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes", Nanotechnol., 18(7), 75702. https://doi.org/10.1088/0957-4484/18/7/075702

피인용 문헌

  1. Nonlinear longitudinal forced vibration of a rod undergoing finite strain 2017, https://doi.org/10.1177/0954406217716957
  2. Dynamic stability of harmonically excited nanobeams including axial inertia pp.1741-2986, 2018, https://doi.org/10.1177/1077546318802430
  3. Comparing magnitudes of surface energy stress in synchronous and asynchronous bending/buckling analysis of slanting double-layer METE nanoplates vol.125, pp.2, 2019, https://doi.org/10.1007/s00339-019-2429-8
  4. Torsional dynamics of coaxial nanotubes with different lengths in viscoelastic medium vol.25, pp.10, 2016, https://doi.org/10.1007/s00542-019-04446-8
  5. Nonlocal vibration analysis of Ti-6Al-4V/ZrO2 functionally graded nanobeam on elastic matrix vol.13, pp.4, 2020, https://doi.org/10.1007/s12517-020-5168-4
  6. Forced Axial Vibration of a Single-Walled Carbon Nanotube Embedded in Elastic Medium under Various Moving Forces vol.63, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.63.112
  7. A two-unknown nonlocal shear and normal deformations theory for buckling analysis of nanorods vol.42, pp.7, 2020, https://doi.org/10.1007/s40430-020-02451-x
  8. Instability analysis of bi-axial micro-scanner under electromagnetic actuation including small scale and damping effects vol.26, pp.8, 2020, https://doi.org/10.1007/s00542-020-04802-z
  9. Vibrations of the Euler-Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics vol.42, pp.4, 2016, https://doi.org/10.2478/sgem-2019-0049