Advances in nano research

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Exact solution for dynamic response of size dependent torsional vibration of CNT subjected to linear and harmonic loadings

  • Hosseini, Seyyed A.H. (Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University) ;
  • Khosravi, Farshad (Department of Aerospace Engineering, K.N. Toosi University of Technology)
  • Received : 2019.03.03
  • Accepted : 2019.10.12
  • Published : 2020.01.25
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Abstract

Rotating systems concern with torsional vibration, and it should be considered in vibration analysis. To do this, the time-dependent torsional vibrations in a single-walled carbon nanotube (SWCNT) under the linear and harmonic external torque, are investigated in this paper. Eringen's nonlocal elasticity theory is considered to demonstrate the nonlocality and constitutive relations. Hamilton's principle is established to derive the governing equation of motion and consequently related boundary conditions. An analytical method, called the Galerkin method, is utilized to discretize the driven differential equations. Linear and harmonic torsional loads, along with determined amplitude, are applied to the SWCNT as the external torques. SWCNT is considered under the clamped-clamped end supports. In free vibration, analysis of small scale effect reveals the capability of natural frequencies in different modes, and this results desirably are in coincidence with another study. The forced torsional vibration in the time domain, especially for carbon nanotubes, has not been done before in the previous works. The previous forced studies were devoted to the transverse vibrations. It should be emphasized that the dynamical analysis of torsion is novel, workable, and at the beginning of the path. The variations of nonlocal parameter, CNT's thickness, and the influence of excitation frequency on time-dependent angular displacement and nondimensional angular displacement are investigated in the context.

Keywords

References

  1. Adams, F.C. and Barbante, C. (2013), "Nanoscience, nanotechnology and spectrometry", Spectrochimica Acta Part B: Atomic Spectroscopy, 86, 3-13. https://doi.org/10.1016/j.sab.2013.04.008
  2. Adeli, M.M., Hadi, A., Hosseini, M. and Gorgani, H.H. (2017), "Torsional vibration of nano-cone based on nonlocal strain gradient elasticity theory", Eur. Phys. J. Plus, 132(9), 393. https://doi.org/10.1140/epjp/i2017-11688-0
  3. Ahouel, M., Houari, M.S.A., Bedia, E. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., Int. J., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  4. Alizade Hamidi, B., Hosseini, S.A.H., Hassannejad, R. and Khosravi, F. (2019), "An exact solution on gold microbeam with thermoelastic damping via generalized Green-Naghdi and modified couple stress theories", J. Thermal Stresses, 43(2), 154-174. https://doi.org/10.1080/01495739.2019.1666694
  5. Angeli, E., Buzio, R., Firpo, G., Magrassi, R., Mussi, V., Repetto, L. and Valbusa, U. (2008), "Nanotechnology applications in medicine", Tumori J., 94(2), 206-215. https://doi.org/10.1177/030089160809400213
  6. Apuzzo, A., Barretta, R., Canadija, M., Feo, L., Luciano, R. and de Sciarra, F.M. (2017), "A closed-form model for torsion of nanobeams with an enhanced nonlocal formulation", Compos. Part B: Eng., 108, 315-324. https://doi.org/10.1016/j.compositesb.2016.09.012
  7. Arda, M. and Aydogdu, M. (2014), "Torsional statics and dynamics of nanotubes embedded in an elastic medium", Compos. Struct., 114, 80-91. https://doi.org/10.1016/j.compstruct.2014.03.053
  8. Assadi, A. (2013), "Size dependent forced vibration of nanoplates with consideration of surface effects", Appl. Mathe. Model., 37(5), 3575-3588. https://doi.org/10.1016/j.apm.2012.07.049
  9. Aydogdu, M. (2009a), "Axial vibration of the nanorods with the nonlocal continuum rod model", Physica E: Low-dimens. Syst. Nanostruct., 41(5), 861-864. https://doi.org/10.1016/j.physe.2009.01.007
  10. Aydogdu, M. (2009b), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low-dimens. Syst. Nanostruct., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  11. Aydogdu, M. and Elishakoff, I. (2014), "On the vibration of nanorods restrained by a linear spring in-span", Mech. Res. Commun., 57, 90-96. https://doi.org/10.1016/j.mechrescom.2014.03.003
  12. Aydogdu, M. and Filiz, S. (2011), "Modeling carbon nanotubebased mass sensors using axial vibration and nonlocal elasticity", Physica E: Low-dimens. Syst. Nanostruct., 43(6), 1229-1234. https://doi.org/10.1016/j.physe.2011.02.006
  13. Baruah, S. and Dutta, J. (2009), "Nanotechnology applications in pollution sensing and degradation in agriculture: a review", Environ. Chem. Lett., 7(3), 191-204. https://doi.org/10.1007/s10311-009-0228-8
  14. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Brazil. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  15. Dai, H., Hafner, J.H., Rinzler, A.G., Colbert, D.T. and Smalley, R.E. (1996), "Nanotubes as nanoprobes in scanning probe microscopy", Nature, 384(6605), 147. https://doi.org/10.1038/384147a0
  16. Ditta, A. (2012), "How helpful is nanotechnology in agriculture?", Adv. Natural Sci.: Nanosci. Nanotechnol., 3(3), 033002. https://doi.org/10.1088/2043-6262/3/3/033002
  17. Dresselhaus, M.S., Dresselhaus, G., Sugihara, K., Spain, I.L. and Goldberg, H.A. (2013), Graphite Fibers and Filaments, Springer Science & Business Media
  18. Duncan, T.V. (2011), "Applications of nanotechnology in food packaging and food safety: barrier materials, antimicrobials and sensors", J. Colloid Interf. Sci., 363(1), 1-24. https://doi.org/10.1016/j.jcis.2011.07.017
  19. Eatemadi, A., Daraee, H., Karimkhanloo, H., Kouhi, M., Zarghami, N., Akbarzadeh, A., Abasi, M., Hanifehpour, Y. and Joo, S.W. (2014), "Carbon nanotubes: properties, synthesis, purification, and medical applications", Nanoscale Res. Lett., 9(1), 393. https://doi.org/10.1186/1556-276X-9-393
  20. Ebrahimi, F. and Barati, M.R. (2017), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092
  21. El-Borgi, S., Rajendran, P., Friswell, M., Trabelssi, M. and Reddy, J. (2018), "Torsional vibration of size-dependent viscoelastic rods using nonlocal strain and velocity gradient theory", Compos. Struct., 186, 274-292. https://doi.org/10.1016/j.compstruct.2017.12.002
  22. Eltaher, M., Alshorbagy, A.E. and Mahmoud, F. (2013), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appli. Mathe. Model., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
  23. 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
  24. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  25. Farajpour, M.R., Rastgoo, A., Farajpour, A. and Mohammadi, M. (2016), "Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory", Micro Nano Lett., 11(6), 302-307. https://doi.org/10.1049/mnl.2016.0081
  26. Fatahi-Vajari, A. and Imam, A. (2016), "Torsional vibration of single-walled carbon nanotubes using doublet mechanics", Zeitschrift fur angewandte Mathematik und Physik, 67(4), 81. https://doi.org/10.1007/s00033-016-0675-6
  27. Feynman, R.P. (1959). "Plenty of Room at the Bottom", APS Annual Meeting.
  28. Gates, T., Odegard, G., Frankland, S. and Clancy, T. (2005), "Computational materials: multi-scale modeling and simulation of nanostructured materials", Compos. Sci. Technol., 65(15-16), 2416-2434. https://doi.org/10.1016/j.compscitech.2005.06.009
  29. Gheshlaghi, B. and Hasheminejad, S.M. (2010), "Size dependent torsional vibration of nanotubes", Physica E: Low-dimens. Syst. Nanostruct., 43(1), 45-48. https://doi.org/10.1016/j.physe.2010.06.015
  30. Gooding, J.J. (2005), "Nanostructuring electrodes with carbon nanotubes: A review on electrochemistry and applications for sensing", Electrochimica Acta, 50(15), 3049-3060. https://doi.org/10.1016/j.electacta.2004.08.052
  31. Gopalakrishnan, K., Birgisson, B., Taylor, P. and Attoh-Okine, N.O. (2011), Nanotechnology in Civil Infrastructure: A Paradigm Shift, Springer.
  32. Hao, M., Guo, X. and Wang, Q. (2010), "Small-scale effect on torsional buckling of multi-walled carbon nanotubes", Eur. J. Mech.-A/Solids, 29(1), 49-55. https://doi.org/10.1016/j.euromechsol.2009.05.008
  33. Hayati, H., Hosseini, S.A. and Rahmani, O. (2016), "Coupled twist-bending static and dynamic behavior of a curved singlewalled carbon nanotube based on nonlocal theory", Microsyst. Technol., 23, 2393-2401. https://doi.org/10.1007/s00542-016-2933-0
  34. Hosseini, S. and Rahmani, O. (2016a), "Surface effects on buckling of double nanobeam system based on nonlocal Timoshenko model", Int. J. Struct. Stabil. Dyn., 16(10), 1550077. https://doi.org/10.1142/S0219455415500777
  35. Hosseini, S.A.H. and Rahmani, O. (2016b), "Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory", Meccanica, 52(6), 1441-1457. https://doi.org/10.1007/s11012-016-0491-2
  36. Hosseini, S.A.H. and Rahmani, O. (2016c), "Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model", Appl. Phys. A, 122(3), 169. https://doi.org/10.1007/s00339-016-9696-4
  37. Hosseini, S.A.H. and Rahmani, O. (2016d), "Thermomechanical vibration of curved functionally graded nanobeam based on nonlocal elasticity", J. Thermal Stress., 39(10), 1252-1267. https://doi.org/10.1080/01495739.2016.1215731
  38. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58. https://doi.org/10.1038/354056a0
  39. Jiang, K., Li, Q. and Fan, S. (2002), "Nanotechnology: Spinning continuous carbon nanotube yarns", Nature, 419(6909), 801. https://doi.org/10.1038/419801a
  40. Katz, E. and Willner, I. (2004), "Biomolecule-functionalized carbon nanotubes: applications in nanobioelectronics", Chem. Phys. Chem., 5(8), 1084-1104. https://doi.org/10.1002/cphc.200400193
  41. Kazemnia Kakhki, E., Hosseini, S.M. and Tahani, M. (2016), "An analytical solution for thermoelastic damping in a micro-beam based on generalized theory of thermoelasticity and modified couple stress theory", Appl. Mathe. Model., 40(4), 3164-3174. https://doi.org/10.1016/j.apm.2015.10.019
  42. Ke, L.-L., Wang, Y.-S. and Wang, Z.-D. (2012), "Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory", Composi. Struct., 94(6), 2038-2047. https://doi.org/10.1016/j.compstruct.2012.01.023
  43. Ke, L.-L., Wang, Y.-S., Yang, J. and Kitipornchai, S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory", Acta Mechanica Sinica, 30(4), 516-525. https://doi.org/10.1007/s10409-014-0072-3
  44. Kiani, K. (2014), "Forced vibrations of a current-carrying nanowire in a longitudinal magnetic field accounting for both surface energy and size effects", Physica E: Low-dimens. Syst. Nanostruct., 63, 27-35. https://doi.org/10.1016/j.physe.2014.04.009
  45. Krishnan, A., Dujardin, E., Ebbesen, T., Yianilos, P. and Treacy, M. (1998), "Young's modulus of single-walled nanotubes", Physical review B, 58, 14013. https://doi.org/10.1103/PhysRevB.58.14013
  46. Lee, S.C. (1998), "Biotechnology for nanotechnology", Trends Biotechnol., 16(6), 239-240. https://doi.org/10.1016/S0167-7799(98)01187-1
  47. Li, J., Lu, Y., Ye, Q., Cinke, M., Han, J. and Meyyappan, M. (2003), "Carbon nanotube sensors for gas and organic vapor detection", Nano Lett., 3(7), 929-933. https://doi.org/10.1021/nl034220x
  48. Lieber, C.M. (2003), "Nanoscale science and technology: building a big future from small things", MRS bulletin. 28(7), 486-491. https://doi.org/10.1557/mrs2003.144
  49. Lim, C., Islam, M. and Zhang, G. (2015), "A nonlocal finite element method for torsional statics and dynamics of circular nanostructures", Int. J. Mech. Sci., 94, 232-243. https://doi.org/10.1016/j.ijmecsci.2015.03.002
  50. Mehralian, F., Beni, Y.T. and Zeverdejani, M.K. (2017), "Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes", Physica B: Condensed Matter, 514, 61-69. https://doi.org/10.1016/j.physb.2017.03.030
  51. Mukhopadhyay, S.S. (2014), "Nanotechnology in agriculture: prospects and constraints", Nanotechnol. Sci. Appl., 7, 63. https://doi.org/10.2147/nsa.s39409
  52. Murmu, T. and Adhikari, S. (2010), "Nonlocal effects in the longitudinal vibration of double-nanorod systems", Physica E: Low-dimens. Syst. Nanostruct., 43(1), 415-422. https://doi.org/10.1016/j.physe.2010.08.023
  53. Murmu, T. and Pradhan, S. (2009a), "Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model", Physica E: Low-dimens. Syst. Nanostruct., 41(8), 1628-1633. https://doi.org/10.1016/j.physe.2009.05.013
  54. Murmu, T. and Pradhan, S. (2009b), "Small-scale effect on the vibration of nonuniform nanocantilever based on nonlocal elasticity theory", Physica E: Low-dimens. Syst. Nanostruct., 41(8), 1451-1456. https://doi.org/10.1016/j.physe.2009.04.015
  55. Nazemnezhad, R. and Fahimi, P. (2017), "Free torsional vibration of cracked nanobeams incorporating surface energy effects", Appl. Mathe. Mech., 38(2), 217-230. https://doi.org/10.1007/s10483-017-2167-9
  56. Pradhan, S. and Kumar, A. (2011), "Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method", Compos. Struct., 93(2), 774-779. https://doi.org/10.1016/j.compstruct.2010.08.004
  57. Rahmani, O., Hosseini, S.A.H. and Parhizkari, M. (2016), "Buckling of double functionally-graded nanobeam system under axial load based on nonlocal theory: an analytical approach", Microsyst. Technol., 23, 2739-2751. https://doi.org/10.1007/s00542-016-3127-5
  58. Rao, S.S. (2019), Vibration of Continuous Systems, Wiley
  59. Reddy, J. (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
  60. Roco, M.C. (2003), "Nanotechnology: convergence with modern biology and medicine", Current Opinion Biotechnol., 14(3), 337-346. https://doi.org/10.1016/S0958-1669(03)00068-5
  61. Salvetat, J.-P., Bonard, J.-M., Thomson, N., Kulik, A., Forro, L., Benoit, W. and Zuppiroli, L. (1999), "Mechanical properties of carbon nanotubes", Appl. Physics A, 69(3), 255-260. https://doi.org/10.1007/s003390050999
  62. Sanchez, F. and Sobolev, K. (2010), "Nanotechnology in concrete- a review", Constr. Build. Mater., 24(11), 2060-2071. https://doi.org/10.1016/j.conbuildmat.2010.03.014
  63. Scott, N. and Chen, H. (2013), "Nanoscale science and engineering for agriculture and food systems", Indust. Biotechnol., 9(1), 17-18. https://doi.org/10.1089/ind.2013.1555
  64. Sharabiani, P.A. and Yazdi, M.R.H. (2013), "Nonlinear free vibrations of functionally graded nanobeams with surface effects", Compos. Part B: Eng., 45(1), 581-586. https://doi.org/10.1016/j.compositesb.2012.04.064
  65. Simsek, M. (2011), "Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle", Computat. Mater. Sci., 50(7), 2112-2123. https://doi.org/10.1016/j.commatsci.2011.02.017
  66. Simsek, M. (2014), "Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory", Compos. Part B: Eng., 56, 621-628. https://doi.org/10.1016/j.compositesb.2013.08.082
  67. Tounsi, A., Benguediab, S., Adda, B., Semmah, A. and Zidour, M. (2013a), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001
  68. Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013b), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  69. Wang, G.-F. and Feng, X.-Q. (2009), "Timoshenko beam model for buckling and vibration of nanowires with surface effects", J. Phys. D: Appl. Phys., 42(15), 155411. https://doi.org/10.1088/0022-3727/42/15/155411
  70. Wang, G.-F. and Feng, X.-Q. (2010), "Effect of surface stresses on the vibration and buckling of piezoelectric nanowires", EPL (Europhysics Letters), 91(5), 56007. https://doi.org/10.1209/0295-5075/91/56007
  71. Wang, Y., Li, Z., Wang, J., Li, J. and Lin, Y. (2011), "Graphene and graphene oxide: biofunctionalization and applications in biotechnology", Trends Biotechnol., 29(5), 205-212. https://doi.org/10.1016/j.tibtech.2011.01.008
  72. West, J.L. and Halas, N.J. (2000), "Applications of nanotechnology to biotechnology: Commentary", Current Opinion Biotechnol., 11(2), 215-217. https://doi.org/10.1016/S0958-1669(00)00082-3
  73. Wilkinson, J. (2003), "Nanotechnology applications in medicine", Medical Device Technol., 14(5), 29-31.
  74. Zakeri, M. and Shayanmehr, M. (2013), "On the mechanical properties of chiral carbon nanotubes", J. Ultrafine Grained Nanostruct. Mater., 46(1), 1-9. https://doi.org/10.7508/JUFGNSM.2013.01.001
  75. Zarepour, M., Hosseini, S.A. and Kokaba, M.R. (2016), "Electrothermo-mechanical nonlinear free vibration of nanobeam resting on the winkler-pasternak foundations based on nonlocal elasticity using differential transform method", Microsyst. Technol., 23, 2641-2648. https://doi.org/10.1007/s00542-016-2935-y
  76. Zhang, L., Lei, Z. and Liew, K. (2015), "Free vibration analysis of functionally graded carbon nanotube-reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method", Compos. Struct., 120, 189-199. https://doi.org/10.1016/j.compstruct.2014.10.009