TY - JOUR TT - Longitudinal Vibration of CNTs Viscously Damped in Span AU - Arda, Mustafa AU - Aydogdu, Metin PY - 2017 DA - July DO - 10.24107/ijeas.305348 JF - International Journal of Engineering and Applied Sciences JO - IJEAS PB - Akdeniz University WT - DergiPark SN - 1309-0267 SP - 22 EP - 38 VL - 9 IS - 2 KW - longitudinal vibration KW - viscously damped KW - carbon nanotubes N2 - In this study, longitudinalvibration of a carbon nanotube with an attached damper has been investigatedusing the nonlocal stress gradient elasticity theory. Equations of motions havebeen solved analytically and frequencies of clamped-clamped and clamped-free nanotubeshave been obtained explicitly in terms of damping coefficient, nonlocalparameter, the attachment point of damper and nanotube length. The nonlocaleffects have important effects on the dynamics of a CNT with an attacheddamper. CR - [1] Iijima S. Helical microtubules of graphitic carbon, Nature, 354, 56–8, 1991. doi:10.1038/354056a0 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [9] Eringen AC. Nonlocal polar elastic continua, International Journal of Engineering Science, 10, 1–16, 1972. doi:10.1016/0020-7225(72)90070-5 CR - [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 CR - [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 CR - [12] Aydogdu M. Longitudinal wave propagation in multiwalled carbon nanotubes, Composite Structures, 107, 578–84, 2014. doi:10.1016/j.compstruct.2013.08.031 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [22] Martin MJ, Houston BH. Gas damping of carbon nanotube oscillators, Applied Physics Letters, 91, 103116, 2007. doi:10.1063/1.2779973 CR - [23] Aydogdu M. On the vibration of aligned carbon nanotube reinforced composite beams, Advances in Nano Research, 2, 199–210, 2014 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [35] Yüksel Ş, Dalli U. Longitudinally vibrating elastic rods with locally and non-locally reacting viscous dampers, Shock and Vibration, 12, 109–18, 2005 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 CR - [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 UR - https://doi.org/10.24107/ijeas.305348 L1 - https://dergipark.org.tr/en/download/article-file/292850 ER -