Abstract
This paper studies terahertz wave propagation in a fluid-conveying single-walled carbon nanotube (SWCNT) under temperature and magnetic fields. The SWCNT is modelled as a Timoshenko beam based on the theory of nonlocal elasticity, where the nanoscale effects are only included in bending moment and shear force through a nonlocal parameter. The governing equations of motion are derived based on nonlocal Timoshenko beam theory. A wave analysis is carried out to get the equations of the dispersion characteristics of wave propagation. Numerical results confirm the validity of the present model by comparing the results in reduced cases with those reported in the published literature. The dispersion curves of wave propagation show that the initial stress plays a very important role on the shear and flexural frequencies of a fluid-conveying SWCNT. Meanwhile, the influences of the nonlocal parameter, fluid velocity, flow density, temperature change and magnetic field on the critical stress of a fluid-conveying SWCNT are discussed. This study may be useful for the design of smart nanodevices for the delivery of drugs to cells, carrying gases, and other applications of nanobeam devices.
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References
Arghavan S., Singh A.V.: On the vibrations of single-walled carbon nanotubes. J. Sound Vib. 330, 3102–3122 (2011)
Arash, B., Wang, Q.: Detection of gas atoms with carbon nanotubes. Sci. Rep. 3 (2013). doi:10.1038/srep01782
Mahar B., Laslau C., Yip R., Yu S.: Development of carbon nanotube-based sensors—a review. IEEE Sens. J. 7, 266–284 (2007)
Joshi A.Y., Harsha S.P., Sharma S.C.: Vibration signature analysis of single walled carbon nanotube based nanomechanical sensors. Phys. E 42, 2115–2123 (2010)
Khademolhosseini F., Phani A.S., Nojeh A., Rajapakse N.: Nonlocal continuum modeling and molecular dynamics simulation of torsional vibration of carbon nanotubes. IEEE Trans. Nanotechnol. 11, 34–43 (2012)
Yan J.W., Liew K.M., He L.H.: Ultra-sensitive analysis of a cantilevered single-walled carbon nanocone-based mass detector. Nanotechnology 24, 125703 (2013)
Zhang S., Liu W.K., Ruoff R.S.: Atomistic simulations of double-walled carbon nanotubes (DWCNTs) as rotational bearings. Nano Lett. 4, 293–297 (2004)
Schoen P.A.E., Walther J.H., Arcidiacono S., Poulikakos D., Koumoutsakos P.: Nanoparticle traffic on helical tracks? Thermophoretic mass transport through carbon nanotubes. Nano Lett. 6, 1910–1917 (2006)
Soltani P., Pashaei O., Taherian Mohammad M., Farshidianfar A.: Free vibration of a carbon nanotube-based mass sensor. Adv. Mater. Res. 403–408, 1163–1167 (2012)
Chang W.-J., Lee H.-L.: Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model. Phys. Lett. A 373, 982–985 (2009)
Ghavanloo E., Rafiei M., Daneshmand F.: In-plane vibration analysis of curved carbon nanotubes conveying fluid embedded in viscoelastic medium. Phys. Lett. A 375, 1994–1999 (2011)
Wang Y.-Z., Cui H.-T., Li F.-M., Kishimoto K.: Effects of viscous fluid on wave propagation in carbon nanotubes. Phys. Lett. A 375, 2448–2451 (2011)
Wang X.Y., Chen W.: The coupled vibration of fluid-filled multiwalled carbon nanotubes with intertube deformation. J. Appl. Phys. 108, 114307–114313 (2010)
Decher G.: Fuzzy nanoassemblies: toward layered polymeric multicomposites. Science 277, 1232–1237 (1997)
Narendar S., Gopalakrishnan S.: Temperature effects on wave propagation in nanoplates. Compos. Part B Eng. 43, 1275–1281 (2012)
Eringen A.C.: Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10, 425–435 (1972)
Eringen A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)
Reddy J.N.: Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45, 288–307 (2007)
Ghavanloo E., Fazelzadeh S.A.: Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid. Phys. E 44, 17–24 (2011)
Narendar S., Gopalakrishnan S.: Terahertz wave characteristics of a single-walled carbon nanotube containing a fluid flow using the nonlocal Timoshenko beam model. Phys. E 42, 1706–1712 (2010)
Kiani K.: Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model. Appl. Math. Model. 37, 1836–1850 (2013)
Lim C.W., Yang Q., Zhang J.B.: Thermal buckling of nanorod based on non-local elasticity theory. Int. J. Non-Linear Mech. 47, 496–505 (2012)
Wang H., Dong K., Men F., Yan Y.J., Wang X.: Influences of longitudinal magnetic field on wave propagation in carbon nanotubes embedded in elastic matrix. Appl. Math. Model. 34, 878–889 (2010)
Chang T.P.: Thermal–mechanical vibration and instability of a fluid-conveying single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory. Appl. Math. Model. 36, 1964–1973 (2012)
Zimmermann J., Pavone P., Cuniberti G.: Vibrational modes and low-temperature thermal properties of graphene and carbon nanotubes: minimal force-constant model. Phys. Rev. B 78, 045410 (2008)
Ansari R., Gholami R., Sahmani S.: On the dynamic stability of embedded single-walled carbon nanotubes including thermal environment effects. Sci. Iran. 19, 919–925 (2012)
Narendar S., Gupta S.S., Gopalakrishnan S.: Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory. Appl. Math. Model. 36, 4529–4538 (2012)
Wang L., Ni Q., Li M., Qian Q.: The thermal effect on vibration and instability of carbon nanotubes conveying fluid. Phys. E 40, 3179–3182 (2008)
Murmu T., McCarthy M.A., Adhikari S.: Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach. J. Sound Vib. 331, 5069–5086 (2012)
Murmu T., McCarthy M.A., Adhikari S.: In-plane magnetic field affected transverse vibration of embedded single-layer graphene sheets using equivalent nonlocal elasticity approach. Compos. Struct. 96, 57–63 (2012)
Benzair A., Tounsi A., Besseghier A., Heireche H., Moulay N., Boumia L.: The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. J. Phys. D Appl. Phys. 41, 225404 (2008)
Heireche H., Tounsi A., Benzair A.: Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading. Nanotechnology 19, 185703 (2008)
Chen X., Kong T., Wang X.: Effects of initial stress on wave propagation in multi-walled carbon nanotubes. Phys. Scr. 78, 015601 (2008)
Song J., Shen J., Li X.F.: Effects of initial axial stress on waves propagating in carbon nanotubes using a generalized nonlocal model. Comput. Mater. Sci. 49, 518–523 (2010)
Murmu T., Adhikari S.: Nonlocal elasticity based vibration of initially pre-stressed coupled nanobeam systems. Eur. J. Mech. A/Solids 34, 52–62 (2012)
Cai H., Wang X.: Effects of initial stress on transverse wave propagation in carbon nanotubes based on Timoshenko laminated beam models. Nanotechnology 17, 45–53 (2006)
Selim M.M.: Torsional vibration of carbon nanotubes under initial compression stress. Braz. J. Phys. 40, 283–287 (2010)
Selim M.M., Abe S., Harigaya K.: Effects of initial compression stress on wave propagation in carbon nanotubes. Eur. Phys. J. B 69, 523–528 (2009)
Selim M.M.: Dispersion of dilatation wave propagation in single-wall carbon nanotubes under initial stress using nonlocal scale effects. J. Comput. Theor. Nanosci. 10, 2547–2554 (2013)
Soltani P., Taherian M.M., Farshidianfar A.: Vibration and instability of a viscous-fluid-conveying single-walled carbon nanotube embedded in a visco-elastic medium. J. Phys. D Appl. Phys. 43, 425401 (2010)
Yang J., Ke L.L., Kitipornchai S.: Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. Phys. E 42, 1727–1735 (2010)
Kaya M.O., Ozgumus O.O.: Energy expressions and free vibration analysis of a rotating uniform Timoshenko beam featuring bending—torsion coupling. J. Vib. Control 16, 915–934 (2010)
Banerjee J.R.: Frequency equation and mode shape formulae for composite Timoshenko beams. Compos. Struct. 51, 381–388 (2001)
Zhang Y.Q., Liu X., Zhao J.H.: Influence of temperature change on column buckling of multiwalled carbon nanotubes. Phys. Lett. A 372, 1676–1681 (2008)
Heireche H., Tounsi A., Benzair A., Mechab I.: Sound wave propagation in single-walled carbon nanotubes with initial axial stress. J. Appl. Phys. 104, 014301–014309 (2008)
Heireche H., Tounsi A., Benzair A., Maachou M., Adda Bedia E.A.: Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity. Phys. E 40, 2791–2799 (2008)
Kiani K.: Transverse wave propagation in elastically confined single-walled carbon nanotubes subjected to longitudinal magnetic fields using nonlocal elasticity models. Phys. E 45, 86–96 (2012)
Wang C.M., Zhang Y.Y., He X.Q.: Vibration of nonlocal Timoshenko beams. Nanotechnology 18, 105401 (2007)
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Wang, B., Deng, Z., Ouyang, H. et al. Terahertz wave propagation in a fluid-conveying single-walled carbon nanotube with initial stress subjected to temperature and magnetic fields. Acta Mech 226, 3031–3043 (2015). https://doi.org/10.1007/s00707-015-1367-6
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DOI: https://doi.org/10.1007/s00707-015-1367-6