References
- P.M. Ajayan and O.Z. Zhou. Applications of carbon nanotubes. Topics Appl. Phys., 80:391–425, 2001. http://dx.doi.org/10.1007/3-540-39947-X14.
- R. Ansari, R. Gholami and S. Ajori. Torsional vibration analysis of carbon nanotubes based on the strain gradient theory and molecular dynamic simulations. J. Vib. Acoust., 135(5):051016, 2013. http://dx.doi.org/10.1115/1.4024208.
- A.G. Arani, M.R. Bagheri, R. Kolahchi and Z.K. Maraghi. Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory. J. Mech. Sci. Tech., 27:2645–2658, 2013. http://dx.doi.org/10.1007/s12206-013-0709-3.
- A.G. Arani and M.A. Roudbari. Nonlocal piezoelastic surface effect on the vibration of visco-Pasternak coupled boron nitride nanotube system under a moving nanoparticle. Thin Solid Films, 542:232–241, 2013. http://dx.doi.org/10.1016/j.tsf.2013.06.025.
- A.G. Arani, M.S. Zarei, M. Mohammadimehr, A. Arefmanesh and M.R. Mozdianfard. The thermal effect on buckling analysis of a DWCNT embedded on the Pasternak foundation. Phys. E, 43(9):1642–1648, 2011. http://dx.doi.org/10.1016/j.physe.2011.05.014.
- M. Arda and M. Aydogdu. Torsional statics and dynamics of nanotubes embedded in an elastic medium. Compos. Struct., 114:80–91, 2014. http://dx.doi.org/10.1016/j.compstruct.2014.03.053.
- R.C. Batra and A. Sears. Continuum models of multi-walled carbon nanotubes. Int. J. Solids Struct., 44(22–23):7577–7596, 2007. http://dx.doi.org/10.1016/j.ijsolstr.2007.04.029.
- A.C. Eringen. Nonlocal polar elastic continua. Int. J. Eng. Sci., 10:1–16, 1972. doi: 10.1016/0020-7225(72)90070-5
- A.C. Eringen. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys., 54:4703–4710, 1983. http://dx.doi.org/10.1063/1.332803.
- A.C. Eringen. Nonlocal Continuum Field Theories. New York: Springer Verlag, 2002.
- R.F. Gibson, E.O. Ayorinde and Y-F. Wen. Vibrations of carbon nanotubes and their composites: a review. Compos. Sci. Tech., 67(1):1–28, 2007. http://dx.doi.org/10.1016/j.compscitech.2006.03.031.
- S. Govindjee and J.L. Sackman. On the use of continuum mechanics to estimate the properties of nanotubes. Solid State Commun., 110(4):227–230, 1999. http://dx.doi.org/10.1016/S0038-1098(98)00626-7.
- I.A. Guz, A.A. Rodger, A.N. Guz and J.J. Rushchitsky. Developing the mechanical models for nanomaterials. Compos. A, 38(4):1234–1250, 2007. http://dx.doi.org/10.1016/j.compositesa.2006.04.012.
- Q. Han and G. Lu. Torsional buckling of a double-walled carbon nanotube embedded in an elastic medium. Eur. J. Mech. A/solids, 22(6):875–883, 2003. http://dx.doi.org/10.1016/j.euromechsol.2003.07.001.
- M.J. Hao, X.M. Guo and Q. Wang. Small-scale effect on torsional buckling of multiwalled carbon nanotubes. Eur. J. Mech. A/Solids, 29(1):49–55, 2010. http://dx.doi.org/10.1016/j.euromechsol.2009.05.008.
- S. Iijima. Helical microtubes of graphitic carbon. Nature, 354:56–58, 1991. doi: 10.1038/354056a0
- F. Khademolhosseini, A.S. Phani, A. Nojeh and N. Rajapakse. Nonlocal continuum modeling and molecular dynamics simulation of torsional vibration of carbon nanotubes. IEEE Transact. Nanotechn., 11(1):34–43, 2012. http://dx.doi.org/10.1109/TNANO.2011.2111380.
- M. Mohammadimehr, A.R. Saidi, A.G. Arani, A. Arefmanesh and Q. Han. Torsional buckling of a DWCNT embedded on Winkler and Pasternak foundations using nonlocal theory. J. Mech. Sci. Tech., 24(6):1289–1299, 2010. http://dx.doi.org/10.1007/s12206-010-0331-6.
- T. Murmu, S. Adhikari and C.Y. Wang. Torsional vibration of carbon nanotubebuckyball systems based on nonlocal elasticity theory. Phys. E, 43(6):1276–1280, 2011. http://dx.doi.org/10.1016/j.physe.2011.02.017.
- T. Murmu and S.C. Pardhan. Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Phys. E, 41(7):1232–1239, 2009. http://dx.doi.org/10.1016/j.physe.2009.02.004.
- M.B. Nardelli, C. Brabec and A. Maiti. Lip-lip interactions and the growth of multiwalled carbon nanotubes. Phys. Rev. Lett., 80(2):313–316, 1998. http://dx.doi.org/10.1103/PhysRevLett.80.313.
- T. Natsuki, T. Tsuchiya, Q.Q. Ni and M. Endo. Torsional elastic instability of double walled carbon nanotubes. Carbon, 48(15):4362–4368, 2010. http://dx.doi.org/10.1016/j.carbon.2010.07.050.
- D. Qian, G.J. Wagner, W.K. Liu, M.F. Yu and R.S. Ruoff. Mechanics of carbon nanotubes. Appl. Mech. Rev., 55(6):495–533, 2002. http://dx.doi.org/10.1115/1.1490129.
- P. Soltani, M.M. Taherian and A. Farshidianfar. Vibration and instability of a viscous-fluid-conveying single-walled carbon nanotube embedded in a visco-elastic medium. J. Phys. D: Appl. Phys., 43(42):425401, 2010. http://dx.doi.org/10.1088/0022-3727/43/42/425401.
- C. Sun and K. Liu. Combined torsional buckling of multi-walled carbon nanotubes coupling with axial loading and radial pressures. Int. J. Solids Struct., 45(78):2128–2139, 2008. http://dx.doi.org/10.1016/j.ijsolstr.2007.11.009.
- X. Wang, G.X. Lu and Y.J. Lu. Buckling of embedded multi-walled carbon nanotubes under combined torsion and axial loading. Int. J. Solids Struct., 44(1):336–351, 2007. http://dx.doi.org/10.1016/j.ijsolstr.2006.04.031.
- H.K. Yang and X. Wang. Bending stability of multi-wall carbon nanotubes embedded in an elastic medium. Model. Simulat. Mater. Sci. Eng., 14(1):99–116, 2006. http://dx.doi.org/10.1088/0965-0393/14/1/008.
- H.K. Yang and X. Wang. Torsional buckling of multi-wall carbon nanotubes embedded in an elastic medium. Compos. Struct., 77(2):182–189, 2007. http://dx.doi.org/10.1016/j.compstruct.2005.06.013.
- J. Yoon, C.Q. Ru and A. Mioduchowski. Vibration of an embedded multiwall carbon nanotube. Compos. Sci. Tech., 63(11):1533–1542, 2003. http://dx.doi.org/10.1016/S0266-3538(03)00058-7.
- W. Yu, N. Xiang-Gui, W. Xiu-Xi and W. Heng-An. Effect of temperature on deformation of carbon nanotube under compression. Chinese Phys., 12(9):1007–1010, 2003. http://dx.doi.org/10.1088/1009-1963/12/9/315.
- A.M. Zenkour. Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium. Phys. E, 79:87–97, 2016. http://dx.doi.org/10.1016/j.physe.2015.12.003.
- A.M. Zenkour. Vibration analysis of a single-layered graphene sheet embedded in visco-Pasternak’s medium using nonlocal elasticity theory. J. Vibroeng., 18(4):2319–2330, 2016. http://dx.doi.org/10.21595/jve.2016.16585.
- Y.-X. Zhen, B. Fang and Y. Tang. Thermal-mechanical vibration and instability analysis of fluid-conveying double walled carbon nanotubes embedded in visco-elastic medium. Phys. E, 44(2):379–385, 2011. http://dx.doi.org/10.1016/j.physe.2011.09.004.