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Original Articles

Calibration of nonlocal generalized helical beam model for free vibration analysis of coiled carbon nanotubes via molecular dynamics simulations

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Pages 1624-1648 | Received 30 Oct 2021, Accepted 02 Feb 2022, Published online: 03 Mar 2022

References

  • S. Iijima, Helical microtubules of graphitic carbon, Nature, vol. 354, no. 6348, pp. 56–58, 1991. DOI: 10.1038/354056a0.
  • L. Liu, F. Liu, and J. Zhao, Curved carbon nanotubes: From unique geometries to novel properties and peculiar applications, Nano Res., vol. 7, no. 5, pp. 626–657, 2014. DOI: 10.1007/s12274-014-0431-1.
  • J. Xie, K. Mukhopadyay, J. Yadev, and V. Varadan, Catalytic chemical vapor deposition synthesis and electron microscopy observation of coiled carbon nanotubes, Smart Mater. Struct., vol. 12, no. 5, pp. 744–748, 2003. DOI: 10.1088/0964-1726/12/5/010.
  • A. Volodin, D. Buntinx, M. Ahlskog, A. Fonseca, J. B. Nagy, and C. Van Haesendonck, Coiled Carbon Nanotubes as Self-Sensing Mechanical Resonators, Nano Lett., vol. 4, no. 9, pp. 1775–1779, 2004. DOI: 10.1021/nl0491576.
  • D. J. Bell, Y. Sun, L. Zhang, L. X. Dong, B. J. Nelson, and D. Grutzmacher, Three-dimensional nanosprings for electromechanical sensors. In: The 13th International Conference on Solid-State Sensors, Actuators and Microsystems, 2005. pp. 15–18. Vol. 11.
  • K. Hernadi, L. Thiên-Nga, and L. Forró, Growth and Microstructure of Catalytically Produced Coiled Carbon Nanotubes, J. Phys. Chem. B., vol. 105, no. 50, pp. 12464–12468, 2001. DOI: 10.1021/jp011208p.
  • K. T. Lau, M. Lu, and D. Hui, Coiled carbon nanotubes: Synthesis and their potential applications in advanced composite structures, Compos. Part B: Eng., vol. 37, no. 6, pp. 437–448, 2006. DOI: 10.1016/j.compositesb.2006.02.008.
  • J. H. Chang, and W. Park, Nano elastic memory using carbon nanocoils, J. Nano Bio Tech., vol. 3, no. 1, pp. 30–35, 2006.
  • K. Akagi, R. Tamura, M. Tsukada, S. Itoh, and S. Ihara, Electronic structure of helically coiled cage of graphitic carbon, Phys. Rev. Lett., vol. 74, no. 12, pp. 2307–2310, 1995.
  • A. F. da Fonseca, and D. S. Galvão, Mechanical properties of nanosprings, Phys. Rev. Lett., vol. 92, no. 17, pp. 175502, 2004.
  • L. Liu, H. Gao, J. Zhao, and J. Lu, Superelasticity of carbon nanocoils from atomistic quantum simulations, Nanoscale Res. Lett., vol. 5, no. 3, pp. 478–483, 2010.
  • S. H. Ghaderi, and E. Hajiesmaili, Nonlinear analysis of coiled carbon nanotubes using the molecular dynamics finite element method, Mater. Sci. Eng.: A., vol. 582, pp. 225–234, 2013. DOI: 10.1016/j.msea.2013.05.060.
  • J. Wang, T. Kemper, T. Liang, and S. B. Sinnott, Predicted mechanical properties of a coiled carbon nanotube, Carbon, vol. 50, no. 3, pp. 968–976, 2012. DOI: 10.1016/j.carbon.2011.09.060.
  • J. Wu, J. He, G. M. Odegard, S. Nagao, Q. Zheng, and Z. Zhang, Giant stretchability and reversibility of tightly wound helical carbon nanotubes, J. Am. Chem. Soc., vol. 135, no. 37, pp. 13775–13785, 2013.
  • A. Sharifian, V. Fadaei Naeini, M. Baniassadi, J. Wu, and M. Baghani, Role of chemical doping in large deformation behavior of spiral carbon-based nanostructures: Unraveling geometry-dependent chemical doping effects, J. Phys. Chem. C., vol. 123, no. 31, pp. 19208–19219, 2019. DOI: 10.1021/acs.jpcc.9b04894.
  • N. Khani, M. Yildiz, and B. Koc, Elastic properties of coiled carbon nanotube reinforced nanocomposite: A finite element study, Mater. Design, vol. 109, pp. 123–132, 2016. DOI: 10.1016/j.matdes.2016.06.126.
  • A. Kianfar, M. M. Seyyed Fakhrabadi, and M. M. Mashhadi, Prediction of mechanical and thermal properties of polymer nanocomposites reinforced by coiled carbon nanotubes for possible application as impact absorbent, Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., vol. 234, no. 4, pp. 882–902, 2019.
  • E. Yarali, M. Baniassadi, and M. Baghani, Numerical homogenization of coiled carbon nanotube reinforced shape memory polymer nanocomposites, Smart Mater. Struct., vol. 28, no. 3, pp. 035026, 2019. DOI: 10.1088/1361-665X/ab02b6.
  • M. M. S. Fakhrabadi, A. Amini, F. Reshadi, N. Khani, and A. Rastgoo, Investigation of buckling and vibration properties of hetero-junctioned and coiled carbon nanotubes, Comput. Mater. Sci., vol. 73, pp. 93–112, 2013. DOI: 10.1016/j.commatsci.2013.02.020.
  • F. Darvishi, and O. Rahmani, Investigation of the free longitudinal vibration of single-walled coiled carbon nanotubes (SWCCNTs) using molecular dynamics simulation, Amirkabir J. Mec. Eng., vol. 51, no. 3, pp. 91–100, 2019.
  • W. H. Wittrick, On elastic wave propagation in helical springs, Int. J. Mech. Sci., vol. 8, no. 1, pp. 25–47, 1966. DOI: 10.1016/0020-7403(66)90061-0.
  • K. Washizu, Some considerations on a naturally curved and twisted slender beam, J. Math. Phys., vol. 43, no. 1–4, pp. 111–116, 1964. DOI: 10.1002/sapm1964431111.
  • J. E. Mottershead, Finite elements for dynamical analysis of helical rods, Int. J. Mech. Sci., vol. 22, no. 5, pp. 267–283, 1980. DOI: 10.1016/0020-7403(80)90028-4.
  • D. Pearson, The transfer matrix method for the vibration of compressed helical springs, J. Mech. Eng. Sci., vol. 24, no. 4, pp. 163–171, 1982. DOI: 10.1243/JMES_JOUR_1982_024_033_02.
  • V. Yildirim, Investigation of parameters affecting free vibration frequency of helical springs, Int. J. Numer. Meth. Engng., vol. 39, no. 1, pp. 99–114, 1996. DOI: 10.1002/(SICI)1097-0207(19960115)39:1<99::AID-NME850>3.0.CO;2-M.
  • V. Yıldırım, On the linearized disturbance dynamic equations for buckling and free vibration of cylindrical helical coil springs under combined compression and torsion, Meccanica, vol. 47, no. 4, pp. 1015–1033, 2012. DOI: 10.1007/s11012-011-9492-3.
  • V. Yildirim, Axial static load dependence free vibration analysis of helical springs based on the theory of spatially curved bars, Lat. Am. J. Solids Struct., vol. 13, no. 15, pp. 2852–2875, 2016., DOI: 10.1590/1679-78253123.
  • J. Lee, and D. J. Thompson, Dynamic stiffness formulation, free vibration and wave motion of helical springs, J. Sound Vib., vol. 239, no. 2, pp. 297–320, 2001. DOI: 10.1006/jsvi.2000.3169.
  • J. Lee, Free vibration analysis of cylindrical helical springs by the pseudospectral method, J. Sound Vib., vol. 302, no. 1–2, pp. 185–196, 2007. DOI: 10.1016/j.jsv.2006.11.008.
  • A. M. Yu, and C. Yang, Formulation and evaluation of an analytical study for cylindrical helical springs, Acta Mech. Solida Sin., vol. 23, no. 1, pp. 85–94, 2010. DOI: 10.1016/S0894-9166(10)60010-9.
  • S. Z. Mohammadi, and M. Farid, Free vibration analysis of helically coiled carbon nanotubes considering nonlocal effect using curved beam elements, Int. J. Mult. Comp. Eng., vol. 17, no. 1, pp. 83–97, 2019. DOI: 10.1615/IntJMultCompEng.2019015907.
  • F. Darvishi, and O. Rahmani, On the free vibration of doubly clamped single-walled coiled carbon nanotubes: A novel size dependent continuum model, J. Solid Mech., vol. 13, no. 2, pp. 114–133, 2021.
  • A. E. H. Love, The Mathematical Theory of Elasticity, 3rd ed., Cambridge University Press, Cambridge, 1920.
  • S. P. Timoshenko, and J. N. Goodier, Theory of Elasticity, McGraw-HilI, New York, 1951.
  • M. H. Sadd, Chapter 9: Extension, torsion, and flexure of elastic cylinders. In: M. H. Sadd (Ed.) Elasticity, 2nd ed., Academic Press, Boston, 2009. pp. 215–256
  • V. Yıldırım, Exact determination of the global tip deflection of both close-coiled and open-coiled cylindrical helical compression springs having arbitrary doubly-symmetric cross-sections, Int. J. Mech. Sci., vol. 115–116, pp. 280–298, 2016. DOI: 10.1016/j.ijmecsci.2016.06.022.
  • A. M. Wahl, Mechanical Springs, McGraw-Hill, New York, 1963.
  • C. W. Lim, C. M. Wang, and S. Kitipornchai, Timoshenko curved beam bending solutions in terms of Euler-Bernoulli solutions, Arch. Appl. Mech., vol. 67, no. 3, pp. 179–190, 1997. DOI: 10.1007/s004190050110.
  • A. C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., vol. 54, no. 9, pp. 4703–4710, 1983. DOI: 10.1063/1.332803.
  • J.-G. Kim, J.-K. Lee, and H. J. Yoon, On the effect of shear coefficients in free vibration analysis of curved beams, J. Mech. Sci. Technol., vol. 28, no. 8, pp. 3181–3187, 2014. DOI: 10.1007/s12206-014-0727-9.
  • J. R. Hutchinson, Shear coefficients for timoshenko beam theory, J. Appl. Mech., vol. 68, no. 1, pp. 87–92, 2001. DOI: 10.1115/1.1349417.
  • H. Du, M. K. Lim, and R. M. Lin, Application of generalized differential quadrature to vibration analysis, J. Sound Vib., vol. 181, no. 2, pp. 279–293, 1995. DOI: 10.1006/jsvi.1995.0140.
  • C. Shu, and B. E. Richards, Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations, Int. J. Numer. Meth. Fluids, vol. 15, no. 7, pp. 791–798, 1992. DOI: 10.1002/fld.1650150704.
  • C. Chuang, Y.-C. Fan, and B.-Y. Jin, Dual space approach to the classification of toroidal carbon nanotubes, J. Chem. Inf. Model, vol. 49, no. 7, pp. 1679–1686, 2009. DOI: 10.1021/ci900124z.
  • S. Plimpton, A. Thompson, and P. Crozier, Lammps molecular dynamics simulator, http://lammps.sandia.gov/.
  • H. J. W. Müller-Kirsten, Basics of Statistical Physics, World Scientific, Singapore, 2012.
  • H. Rafii-Tabar, Modelling the nano-scale phenomena in condensed matter physics via computer-based numerical simulations, Phys. Rep., vol. 325, no. 6, pp. 239–310, 2000. DOI: 10.1016/S0370-1573(99)00087-3.
  • Y. Y. Zhang, C. M. Wang, and V. B. C. Tan, Assessment of timoshenko beam models for vibrational behavior of single-walled carbon nanotubes using molecular dynamics, Adv. Appl. Math. Mech., vol. 1, no. 1, pp. 89–106, 2009.
  • B. Arash, and R. Ansari, Evaluation of nonlocal parameter in the vibrations of single-walled carbon nanotubes with initial strain, Phys. E., vol. 42, no. 8, pp. 2058–2064, 2010. DOI: 10.1016/j.physe.2010.03.028.
  • Y. Jin, and F. G. Yuan, Simulation of elastic properties of single-walled carbon nanotubes, Compos. Sci. Technol., vol. 63, no. 11, pp. 1507–1515, 2003. DOI: 10.1016/S0266-3538(03)00074-5.
  • Y.-G. Hu, K. M. Liew, and Q. Wang, Nonlocal continuum model and molecular dynamics for free vibration of single-walled carbon nanotubes, J. Nanosci. Nanotechnol., vol. 11, no. 12, pp. 10401–10407, 2011.
  • R. Ansari, H. Rouhi, and S. Sahmani, Calibration of the analytical nonlocal shell model for vibrations of double-walled carbon nanotubes with arbitrary boundary conditions using molecular dynamics, Int. J. Mech. Sci., vol. 53, no. 9, pp. 786–792, 2011. DOI: 10.1016/j.ijmecsci.2011.06.010.

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