Advertisement

Small scale and spin effects on free transverse vibration of size-dependent nano-scale beams

  • M. R. Ilkhani
  • R. NazemnezhadEmail author
  • Sh. Hosseini-Hashemi
Technical Paper

Abstract

This study aims to investigate the transverse vibration of size-dependent nano-beam which spins about its longitudinal axis. To this end, nano-beams are modeled based on the Euler–Bernoulli and Timoshenko theories. To consider the size dependency of the nano-beams, the nonlocal elasticity theory is used. By using an exact analytical solution, the governing equations of motions are solved. Comprehensive results are presented to show the effects of various boundary conditions, nonlocal scale parameter, rotational speed, and geometrical parameters on natural frequencies and critical speeds of spinning nano-beam. As spinning nano-beams are the main part of any rotary nano-machines, conclusions of present analysis promote researcher’s information about the vibrational behavior of spinning nano-beams.

Keywords

Free vibration Rotating nano-beam Spinning nano-beam Nonlocal elasticity Critical speed 

Notes

References

  1. 1.
    Han J, Globus A, Jaffe R, Deardorff G (1997) Molecular dynamics simulations of carbon nanotube-based gears. Nanotechnology 8(3):95Google Scholar
  2. 2.
    Srivastava D (1997) A phenomenological model of the rotation dynamics of carbon nanotube gears with laser electric fields. Nanotechnology 8(4):186Google Scholar
  3. 3.
    Fennimore A, Yuzvinsky T, Han W-Q, Fuhrer M, Cumings J, Zettl A (2003) Rotational actuators based on carbon nanotubes. Nature 424(6947):408–410Google Scholar
  4. 4.
    Zhang S, Liu WK, Ruoff RS (2004) Atomistic simulations of double-walled carbon nanotubes (DWCNTs) as rotational bearings. Nano Lett 4(2):293–297Google Scholar
  5. 5.
    Tu Z, Hu X (2005) Molecular motor constructed from a double-walled carbon nanotube driven by axially varying voltage. Phys Rev B 72(3):033404Google Scholar
  6. 6.
    Lohrasebi A, Rafii-Tabar H (2008) Computational modeling of an ion-driven nanomotor. J Mol Graph Model 27(2):116–123Google Scholar
  7. 7.
    Takagi Y, Uda T, Ohno T (2008) Carbon nanotube motors driven by carbon nanotube. J Chem Phys 128(19):194704Google Scholar
  8. 8.
    Lohrasebi A, Jamali Y (2011) Computational modeling of a rotary nanopump. J Mol Graph Model 29(8):1025–1029Google Scholar
  9. 9.
    Cook EH, Buehler MJ, Spakovszky ZS (2013) Mechanism of friction in rotating carbon nanotube bearings. J Mech Phys Solids 61(2):652–673Google Scholar
  10. 10.
    Cai K, Cai H, Ren L, Shi J, Qin Q-H (2016) Over-speeding rotational transmission of a carbon nanotube-based bearing. J Phys Chem C 120(10):5797–5803Google Scholar
  11. 11.
    Cai K, Yin H, Wei N, Chen Z, Shi J (2015) A stable high-speed rotational transmission system based on nanotubes. Appl Phys Lett 106(2):021909Google Scholar
  12. 12.
    Cai K, Yu J, Liu L, Shi J, Qin QH (2016) Rotation measurements of a thermally driven rotary nanomotor with a spring wing. Phys Chem Chem Phys 18(32):22478–22486Google Scholar
  13. 13.
    Cai K, Yu J, Wan J, Yin H, Shi J, Qin QH (2016) Configuration jumps of rotor in a nanomotor from carbon nanostructures. Carbon 101:168–176Google Scholar
  14. 14.
    Wen H, He M-F, Huang Y, Chen J (2018) Free vibration analysis of single-walled carbon nanotubes based on the nonlocal higher-order cylindrical beam model. Acta Acust United Acust 104(2):284–294Google Scholar
  15. 15.
    Li X-F, Tang G-J, Shen Z-B, Lee KY (2015) Resonance frequency and mass identification of zeptogram-scale nanosensor based on the nonlocal beam theory. Ultrasonics 55:75–84Google Scholar
  16. 16.
    Li X-F, Wang B-L (2009) Vibrational modes of Timoshenko beams at small scales. Appl Phys Lett 94(10):101903Google Scholar
  17. 17.
    Reddy J (2007) Nonlocal theories for bending, buckling and vibration of beams. Int J Eng Sci 45(2):288–307zbMATHGoogle Scholar
  18. 18.
    Zhang Y, Wang C, Tan V (2009) Assessment of Timoshenko beam models for vibrational behavior of single-walled carbon nanotubes using molecular dynamics. Adv Appl Math Mech 1(1):89–106MathSciNetGoogle Scholar
  19. 19.
    Arash B, Wang Q (2012) A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Comput Mater Sci 51(1):303–313Google Scholar
  20. 20.
    Hosseini-Hashemi S, Nahas I, Fakher M, Nazemnezhad R (2014) Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity. Acta Mech 225(6):1555–1564MathSciNetzbMATHGoogle Scholar
  21. 21.
    Yu YJ, Tian X-G, Liu J (2017) Size-dependent damping of a nanobeam using nonlocal thermoelasticity: extension of Zener, Lifshitz, and Roukes’ damping model. Acta Mech 228(4):1287–1302MathSciNetzbMATHGoogle Scholar
  22. 22.
    Mohammadi M, Safarabadi M, Rastgoo A, Farajpour A (2016) Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment. Acta Mech 227(8):2207–2232MathSciNetzbMATHGoogle Scholar
  23. 23.
    Rafiee R, Moghadam RM (2014) On the modeling of carbon nanotubes: a critical review. Compos B Eng 56:435–449Google Scholar
  24. 24.
    Li X-F, Tang G-J, Shen Z-B, Lee KY (2017) Size-dependent resonance frequencies of longitudinal vibration of a nonlocal Love nanobar with a tip nanoparticle. Math Mech Solids 22(6):1529–1542MathSciNetzbMATHGoogle Scholar
  25. 25.
    Li XF, Shen ZB, Lee KY (2017) Axial wave propagation and vibration of nonlocal nanorods with radial deformation and inertia. ZAMM J Appl Math Mech 97(5):602–616MathSciNetGoogle Scholar
  26. 26.
    Huang Y, Luo Q-Z, Li X-F (2013) Transverse waves propagating in carbon nanotubes via a higher-order nonlocal beam model. Compos Struct 95:328–336Google Scholar
  27. 27.
    Murmu T, Adhikari S (2010) Scale-dependent vibration analysis of prestressed carbon nanotubes undergoing rotation. J Appl Phys 108(12):123507Google Scholar
  28. 28.
    Narendar S, Gopalakrishnan S (2011) Nonlocal wave propagation in rotating nanotube. Res Phys 1(1):17–25Google Scholar
  29. 29.
    Pradhan S, Murmu T (2010) Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever. Physica E 42(7):1944–1949Google Scholar
  30. 30.
    Narendar S (2012) Differential quadrature based nonlocal flapwise bending vibration analysis of rotating nanotube with consideration of transverse shear deformation and rotary inertia. Appl Math Comput 219(3):1232–1243MathSciNetzbMATHGoogle Scholar
  31. 31.
    Aranda-Ruiz J, Loya J, Fernández-Sáez J (2012) Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory. Compos Struct 94(9):2990–3001Google Scholar
  32. 32.
    Shafiei N, Kazemi M, Fatahi L (2015) Transverse vibration of rotary tapered microbeam based on modified couple stress theory and generalized differential quadrature element method. Mech Adv Mater StructGoogle Scholar
  33. 33.
    Shafiei N, Kazemi M, Ghadiri M (2016) On size-dependent vibration of rotary axially functionally graded microbeam. Int J Eng Sci 101:29–44zbMATHGoogle Scholar
  34. 34.
    Shafiei N, Kazemi M, Ghadiri M (2016) Comparison of modeling of the rotating tapered axially functionally graded Timoshenko and Euler–Bernoulli microbeams. Physica E 83:74–87zbMATHGoogle Scholar
  35. 35.
    Shafiei N, Kazemi M, Ghadiri M (2016) Nonlinear vibration behavior of a rotating nanobeam under thermal stress using Eringen’s nonlocal elasticity and DQM. Appl Phys A Mater 122(8):1–18Google Scholar
  36. 36.
    Hosseini-Hashemi S, Ilkhani M (2016) Nonlocal modeling for dynamic stability of spinning nanotube under axial load. Meccanica 1–15Google Scholar
  37. 37.
    Hosseini-Hashemi S, Ilkhani M (2016) Exact solution for free vibrations of spinning nanotube based on nonlocal first order shear deformation shell theory. Compos Struct 157:1–11Google Scholar
  38. 38.
    Hosseini-Hashemi S, Ilkhani M, Fadaee M (2013) Accurate natural frequencies and critical speeds of a rotating functionally graded moderately thick cylindrical shell. Int J Eng Sci 76:9–20Google Scholar
  39. 39.
    Ilkhani M, Hosseini-Hashemi S (2016) Size dependent vibro-buckling of rotating beam based on modified couple stress theory. Compos Struct 143:75–83Google Scholar
  40. 40.
    Li C (2014) A nonlocal analytical approach for torsion of cylindrical nanostructures and the existence of higher-order stress and geometric boundaries. Compos Struct 118:607–621Google Scholar
  41. 41.
    Lim CW (2010) On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: equilibrium, governing equation and static deflection. Appl Math Mech Eng 31(1):37–54MathSciNetzbMATHGoogle Scholar
  42. 42.
    Lim C, Yang Y (2010) Wave propagation in carbon nanotubes: nonlocal elasticity-induced stiffness and velocity enhancement effects. J Mech Mater Struct 5(3):459–476Google Scholar
  43. 43.
    Hu Y-G, Liew KM, Wang Q, He X, Yakobson B (2008) Nonlocal shell model for elastic wave propagation in single-and double-walled carbon nanotubes. J Mech Phys Solids 56(12):3475–3485zbMATHGoogle Scholar
  44. 44.
    Sudak L (2003) Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics. J Appl Phys 94(11):7281–7287Google Scholar
  45. 45.
    Li C, Yao L, Chen W, Li S (2015) Comments on nonlocal effects in nano-cantilever beams. Int J Eng Sci 87:47–57Google Scholar
  46. 46.
    Li C, Li S, Yao L, Zhu Z (2015) Nonlocal theoretical approaches and atomistic simulations for longitudinal free vibration of nanorods/nanotubes and verification of different nonlocal models. Appl Math Model 39(15):4570–4585MathSciNetGoogle Scholar
  47. 47.
    Shen J, Li C (2017) A semi-continuum-based bending analysis for extreme-thin micro/nano-beams and new proposal for nonlocal differential constitution. Compos Struct 172:210–220Google Scholar
  48. 48.
    Choi S, Pierre C, Ulsoy A (1992) Consistent modeling of rotating Timoshenko shafts subject to axial loads. J Vib Acoust 114(2):249–259Google Scholar
  49. 49.
    Zhu X, Li L (2017) Closed form solution for a nonlocal strain gradient rod in tension. Int J Eng Sci 119:16–28MathSciNetzbMATHGoogle Scholar
  50. 50.
    Zhu X, Li L (2017) On longitudinal dynamics of nanorods. Int J Eng Sci 120:129–145Google Scholar
  51. 51.
    Hosseini-Hashemi S, Nazemnezhad R, Rokni H (2015) Nonlocal nonlinear free vibration of nanobeams with surface effects. Eur J Mech A Solids 52:44–53MathSciNetzbMATHGoogle Scholar
  52. 52.
    Nazemnezhad R, Zare M, Hosseini-Hashemi S (2018) Effect of nonlocal elasticity on vibration analysis of multi-layer graphene sheets using sandwich model. Eur J Mech A Solids 70:75–85MathSciNetzbMATHGoogle Scholar
  53. 53.
    Nazemnezhad R, Zare M (2016) Nonlocal Reddy beam model for free vibration analysis of multilayer nanoribbons incorporating interlayer shear effect. Eur J Mech A Solids 55:234–242MathSciNetzbMATHGoogle Scholar
  54. 54.
    Nazemnezhad R (2015) Nonlocal Timoshenko beam model for considering shear effect of van der Waals interactions on free vibration of multilayer graphene nanoribbons. Compos Struct 133:522–528Google Scholar
  55. 55.
    Nazemnezhad R, Hosseini-Hashemi S (2014) Free vibration analysis of multi-layer graphene nanoribbons incorporating interlayer shear effect via molecular dynamics simulations and nonlocal elasticity. Phys Lett A 378(44):3225–3232MathSciNetGoogle Scholar
  56. 56.
    Huang L, Han Q, Liang Y (2012) Calibration of nonlocal scale effect parameter for bending single-layered graphene sheet under molecular dynamics. Nano 7(05):1250033Google Scholar
  57. 57.
    Duan W, Wang C, Zhang Y (2007) Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics. J Appl Phys 101(2):024305Google Scholar
  58. 58.
    Hosseini-Hashemi S, Fakher M, Nazemnezhad R (2017) Longitudinal vibrations of aluminum nanobeams by applying elastic moduli of bulk and surface: molecular dynamics simulation and continuum model. Mater Res Express 4(8):085036Google Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Composite group, Engineering DepartmentThe University of Nottingham, University ParkNottinghamUK
  2. 2.School of EngineeringDamghan UniversityDamghanIran
  3. 3.Impact Research Laboratory, Department of Mechanical EngineeringIran University of Science and TechnologyTehranIran
  4. 4.Center of Excellence in Railway TransportationIran University of Science and TechnologyTehranIran

Personalised recommendations