Longitudinal Vibration of CNTs Viscously Damped in Span

Year 2017, Volume: 9 Issue: 2, 22 - 38, 14.04.2017

Mustafa Arda , Metin Aydogdu

https://doi.org/10.24107/ijeas.305348

Cited By: 8

Abstract

In this study, longitudinal
vibration of a carbon nanotube with an attached damper has been investigated
using the nonlocal stress gradient elasticity theory. Equations of motions have
been solved analytically and frequencies of clamped-clamped and clamped-free nanotubes
have been obtained explicitly in terms of damping coefficient, nonlocal
parameter, the attachment point of damper and nanotube length. The nonlocal
effects have important effects on the dynamics of a CNT with an attached
damper.

Keywords

longitudinal vibration, viscously damped, carbon nanotubes

References

• [1] Iijima S. Helical microtubules of graphitic carbon, Nature, 354, 56–8, 1991. doi:10.1038/354056a0
• [2] He H, Pham-Huy LA, Dramou P, Xiao D, Zuo P, Pham-Huy C. Carbon nanotubes: Applications in pharmacy and medicine, BioMed Research International, 2013, 2013. doi:10.1155/2013/578290
• [3] Marchesan S, Kostarelos K, Bianco A, Prato M. The winding road for carbon nanotubes in nanomedicine, Materials Today, 18, 12–9, 2015. doi:10.1016/j.mattod.2014.07.009
• [4] Bourlon B, Glattli DC, Miko C, Forró L, Bachtold A. Carbon Nanotube Based Bearing for Rotational Motions, Nano Letters, 4, 709–12, 2004. doi:10.1021/nl035217g
• [5] Kimoto Y, Mori H, Mikami T, Akita S, Nakayama Y, Higashi K, et al. Molecular Dynamics Study of Double-Walled Carbon Nanotubes for Nano-Mechanical Manipulation, Japanese Journal of Applied Physics, 44, 1641, 2005. doi:10.1143/JJAP.44.1641
• [6] Von Oppen F, Guinea F, Mariani E. Synthetic electric fields and phonon damping in carbon nanotubes and graphene, Physical Review B - Condensed Matter and Materials Physics, 80, 1–11, 2009. doi:10.1103/PhysRevB.80.075420
• [7] Falk K, Sedlmeier F, Joly L, Netz RR, Bocquet L. Molecular origin of fast water transport in carbon nanotube membranes: Superlubricity versus curvature dependent friction, Nano Letters, 10, 4067–73, 2010. doi:10.1021/nl1021046
• [8] Miyako E, Kono K, Yuba E, Hosokawa C, Nagai H, Hagihara Y. Carbon nanotube-liposome supramolecular nanotrains for intelligent molecular-transport systems., Nature Communications, 3, 1226, 2012. doi:10.1038/ncomms2233
• [9] Eringen AC. Nonlocal polar elastic continua, International Journal of Engineering Science, 10, 1–16, 1972. doi:10.1016/0020-7225(72)90070-5
• [10] Eringen AC. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 4703–10, 1983. doi:10.1063/1.332803
• [11] Khademolhosseini F, Phani AS, Nojeh A, Rajapakse N. Nonlocal continuum modeling and molecular dynamics simulation of torsional vibration of carbon nanotubes, IEEE Transactions on Nanotechnology, 11, 34–43, 2012. doi:10.1109/TNANO.2011.2111380
• [12] Aydogdu M. Longitudinal wave propagation in multiwalled carbon nanotubes, Composite Structures, 107, 578–84, 2014. doi:10.1016/j.compstruct.2013.08.031
• [13] Chen C, Ma M, Zhe Liu J, Zheng Q, Xu Z. Viscous damping of nanobeam resonators: Humidity, thermal noise, and a paddling effect, Journal of Applied Physics, 110, 2011. doi:10.1063/1.3619854
• [14] Wang CYY, Li CFF, Adhikari S. Axisymmetric vibration of single-walled carbon nanotubes in water, Physics Letters A, 374, 2467–74, 2010. doi:10.1016/j.physleta.2010.04.002
• [15] Rinaldi S, Prabhakar S, Vengallatore S, Païdoussis MP. Dynamics of microscale pipes containing internal fluid flow: Damping, frequency shift, and stability, Journal of Sound and Vibration, 329, 1081–8, 2010. doi:10.1016/j.jsv.2009.10.025
• [16] Ghavanloo E, Daneshmand F, Rafiei M. Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation, Physica E: Low-Dimensional Systems and Nanostructures, 42, 2218–24, 2010. doi:10.1016/j.physe.2010.04.024
• [17] Ghavanloo E, Daneshmand F, Amabili M. Vibration analysis of a single microtubule surrounded by cytoplasm, Physica E: Low-Dimensional Systems and Nanostructures, 43, 192–8, 2010. doi:10.1016/j.physe.2010.07.016
• [18] Ghavanloo E, Rafiei M, Daneshmand F. In-plane vibration analysis of curved carbon nanotubes conveying fluid embedded in viscoelastic medium, Physics Letters A, 375, 1994–9, 2011. doi:10.1016/j.physleta.2011.03.025
• [19] Ghavanloo E, Fazelzadeh SA. Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid, Physica E: Low-Dimensional Systems and Nanostructures, 44, 17–24, 2011. doi:10.1016/j.physe.2011.06.024
• [20] Yun K, Choi J, Kim S-K, Song O. Flow-induced vibration and stability analysis of multi-wall carbon nanotubes, Journal of Mechanical Science and Technology, 26, 3911–20, 2012. doi:10.1007/s12206-012-0888-3
• [21] Zeighampour H, Tadi Beni Y. Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory, Physica E: Low-Dimensional Systems and Nanostructures, 61, 28–39, 2014. doi:10.1016/j.physe.2014.03.011
• [22] Martin MJ, Houston BH. Gas damping of carbon nanotube oscillators, Applied Physics Letters, 91, 103116, 2007. doi:10.1063/1.2779973
• [23] Aydogdu M. On the vibration of aligned carbon nanotube reinforced composite beams, Advances in Nano Research, 2, 199–210, 2014
• [24] Chemi A, Heireche H, Zidour M, Rakrak K, Bousahla AA. Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity, Advances in Nano Research, 3, 193–206, 2015. doi:10.12989/anr.2015.3.4.193
• [25] Aydogdu M, Arda M. Forced vibration of nanorods using nonlocal elasticity, Advances in Nano Research, 4, 265–79, 2016. doi:10.12989/anr.2016.4.4.265
• [26] Soltani P, Taherian MM, Farshidianfar A. Vibration and instability of a viscous-fluid-conveying single-walled carbon nanotube embedded in a visco-elastic medium, Journal of Physics D: Applied Physics, 43, 425401, 2010. doi:10.1088/0022-3727/43/42/425401
• [27] Zhen Y-X, Fang B, Tang Y. Thermal–mechanical vibration and instability analysis of fluid-conveying double walled carbon nanotubes embedded in visco-elastic medium, Physica E: Low-Dimensional Systems and Nanostructures, 44, 379–85, 2011. doi:10.1016/j.physe.2011.09.004
• [28] Hoseinzadeh MS, Khadem SE. Thermoelastic vibration and damping analysis of double-walled carbon nanotubes based on shell theory, Physica E: Low-Dimensional Systems and Nanostructures, 43, 1146–54, 2011. doi:10.1016/j.physe.2011.01.013
• [29] Hoseinzadeh MS, Khadem SE. A nonlocal shell theory model for evaluation of thermoelastic damping in the vibration of a double-walled carbon nanotube, Physica E: Low-Dimensional Systems and Nanostructures, 57, 6–11, 2014. doi:10.1016/j.physe.2013.10.009
• [30] Hajnayeb A, Khadem SE, Zamanian M. Thermoelastic damping of a double-walled carbon nanotube under electrostatic force, Micro & Nano Letters, 6, 698, 2011. doi:10.1049/mnl.2011.0193
• [31] Schmid DR, Stiller PL, Strunk C, Hüttel a K. Magnetic damping of a carbon nanotube nano-electromechanical resonator, New Journal of Physics, 14, 83024, 2012. doi:10.1088/1367-2630/14/8/083024
• [32] Chang W-J, Lee H-L. Vibration analysis of viscoelastic carbon nanotubes, Micro & Nano Letters, 7, 1308–12, 2012. doi:10.1049/mnl.2012.0612
• [33] Hizal NA, Gürgöze M. LUMPED PARAMETER REPRESENTATION OF A LONGITUDINALLY VIBRATING ELASTIC ROD VISCOUSLY DAMPED IN-SPAN, Journal of Sound and Vibration, 216, 328–36, 1998. doi:10.1006/jsvi.1998.1685
• [34] Yüksel Ş, Gürgöze M. Continuous and discrete models for longitudinally vibrating elastic rods viscously damped in-span, Journal of Sound and Vibration, 257, 996–1006, 2002. doi:10.1006/jsvi.5032
• [35] Yüksel Ş, Dalli U. Longitudinally vibrating elastic rods with locally and non-locally reacting viscous dampers, Shock and Vibration, 12, 109–18, 2005
• [36] Zhou Z, Qian D, Yu M-F. A Computational Study on the Transversal Visco-Elastic Properties of Single Walled Carbon Nanotubes and Their Relation to the Damping Mechanism, Journal of Computational and Theoretical Nanoscience, 8, 820–30, 2010
• [37] Jeong B, Cho H, Yu M-F, Vakakis AF, McFarland DM, Bergman LA. Modeling and Measurement of Geometrically Nonlinear Damping in a Microcantilever–Nanotube System, ACS Nano, 7, 8547–53, 2013. doi:10.1021/nn402479d
• [38] Adhikari S, Murmu T, McCarthy MA. Dynamic finite element analysis of axially vibrating nonlocal rods, Finite Elements in Analysis and Design, 63, 42–50, 2013. doi:10.1016/j.finel.2012.08.001
• [39] Lei Y, Adhikari S, Murmu T, Friswell MI. Asymptotic frequencies of various damped nonlocal beams and plates, Mechanics Research Communications, 62, 94–101, 2014. doi:10.1016/j.mechrescom.2014.08.002
• [40] Ghorbanpour Arani A, Amir S, Dashti P, Yousefi M. Flow-induced vibration of double bonded visco-CNTs under magnetic fields considering surface effect, Computational Materials Science, 86, 144–54, 2014. doi:10.1016/j.commatsci.2014.01.047
• [41] Karličić D, Cajić M, Murmu T, Adhikari S. Nonlocal longitudinal vibration of viscoelastic coupled double-nanorod systems, European Journal of Mechanics - A/Solids, 49, 183–96, 2015. doi:10.1016/j.euromechsol.2014.07.005
• [42] Erol H, Gürgöze M. Longitudinal vibrations of a double-rod system coupled by springs and dampers, Journal of Sound and Vibration, 276, 419–30, 2004. doi:10.1016/j.jsv.2003.10.043
• [43] Buchoux J, Aimé J-P, Boisgard R, Nguyen C V, Buchaillot L, Marsaudon S. Investigation of the carbon nanotube AFM tip contacts: free sliding versus pinned contact., Nanotechnology, 20, 475701/8pp, 2009. doi:10.1088/0957-4484/20/47/475701
• [44] Eichler A., Moser J., Chaste J., Zdrojek M., Wilson-RaeI., Bachtold A. Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene, Nat Nano, 6, 339–42, 2011
• [45] Li J, Bi K, Chen M, Chen Y. The oscillatory damped behavior of double wall carbon nanotube oscillators in gaseous environment, Science in China, Series E: Technological Sciences, 52, 916–21, 2009. doi:10.1007/s11431-009-0073-9
• [46] Barnard AW, Sazonova V, van der Zande AM, McEuen PL. Fluctuation broadening in carbon nanotube resonators., Proceedings of the National Academy of Sciences of the United States of America, 109, 19093–6, 2012. doi:10.1073/pnas.1216407109
• [47] Hüttel AK, Steele GA, Witkamp B, Poot M, Kouwenhoven LP, Van Der Zant HSJ. Carbon nanotubes as ultrahigh quality factor mechanical resonators, Nano Letters, 9, 2547–52, 2009. doi:10.1021/nl900612h
• [48] Aydogdu M, Elishakoff I. On the vibration of nanorods restrained by a linear spring in-span, Mechanics Research Communications, 57, 90–6, 2014. doi:10.1016/j.mechrescom.2014.03.003