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Vibration of carbon nanotubes with defects: order reduction methods. (English) Zbl 1402.82015
Summary: Order reduction methods are widely used to reduce computational effort when calculating the impact of defects on the vibrational properties of nearly periodic structures in engineering applications, such as a gas-turbine bladed disc. However, despite obvious similarities these techniques have not yet been adapted for use in analysing atomic structures with inevitable defects. Two order reduction techniques, modal domain analysis and modified modal domain analysis, are successfully used in this paper to examine the changes in vibrational frequencies, mode shapes and mode localization caused by defects in carbon nanotubes. The defects considered are isotope defects and Stone-Wales defects, though the methods described can be extended to other defects.
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
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[1] Fan, Y.; Goldsmith, BR; Collins, PG, Identifying and counting point defects in carbon nanotubes, Nat. Mater., 4, 906-911, (2005)
[2] Cleland, AN, Advanced Texts in Physics, Foundations of nanomechanics, (2003), Springer
[3] Charlier, J-C; Blase, X.; Roche, S., Electronic and transport properties of nanotubes, Rev. Mod. Phys., 79, 677-732, (2007)
[4] Dresselhaus, MS; Dresselhaus, G.; Avouris, P., Carbon nanotubes, (2001), Springer
[5] Collet, M.; Ouisse, M.; Ruzzene, M.; Ichchou, MN, Floquet-Bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems, Int. J. Solids Struct., 48, 2837-2848, (2011)
[6] Ping, S., Springer Series in Materials Science, Introduction to wave scattering, localization and mesoscopic phenomena, (2006), Springer
[7] Jorio, A.; Saito, R.; Dresselhaus, G.; Dresselhaus, MS, Raman spectroscopy in graphene related systems, (2011), Wiley-VCH Verlag GmbH & Co. KGaA
[8] Stone, AJ; Wales, DJ, Theoretical studies of icosahedral C 60 and some related species, Chem. Phys. Lett., 128, 501-503, (1986)
[9] Chen, LJ; Zhao, Q.; Gong, ZQ, The effects of different defects on vibration properties of single-walled carbon nanotubes, Adv. Mater. Res., 225-226, 1133-1136, (2011)
[10] Georgantzinos, SK; Giannopoulos, GI; Anifantis, NK, The effect of atom vacancy defect on the vibrational behavior of single-walled carbon nanotubes: a structural mechanics approach, Adv. Mech. Eng., 6, 291645, (2014)
[11] Li, C.; Chou, T-W, A structural mechanics approach for the analysis of carbon nanotubes, Int. J. Solids Struct., 40, 2487-2499, (2003) · Zbl 1032.74606
[12] Sinha, A., Reduced-order model of a bladed rotor with geometric mistuning, J. Turbomach., 131, 31007, (2009)
[13] Yang, M-T; Griffine, JH, A reduced order model of mistuning using a subset of nominal system modes, J. Eng. Gas Turbines Power, 123, 893-900, (1999)
[14] Sinha, A., Vibration of nearly periodic structures and mistuned bladed rotors, (2017), Cambridge University Press · Zbl 1364.74004
[15] Leimkuhler, B.; Matthews, C., Molecular dynamics, (2015), Springer International Publishing
[16] Sinha, A., Vibration of mechanical systems, (2010), Cambridge University Press · Zbl 1218.70001
[17] Kunc, K.; Martin, RM, Ab initio force constants of GaAs: a new approach to calculation of phonons and dielectric properties, Phys. Rev. Lett., 48, 406-409, (1982)
[18] Sánchez-Portal, D.; Artacho, E.; Soler, JM; Rubio, A.; Ordejón, P., \(Ab initio\) structural, elastic, and vibrational properties of carbon nanotubes, Phys. Rev. B, 59, 12 678-12 688, (1999)
[19] Lindsay, L.; Broido, DA, Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene, Phys. Rev. B, 81, 205441, (2010)
[20] Tersoff, J., New empirical approach for the structure and energy of covalent systems, Phys. Rev. B, 37, 6991-7000, (1988)
[21] Tersoff, J., Modeling solid-state chemistry: interatomic potentials for multicomponent systems, Phys. Rev. B, 39, 5566-5568, (1989)
[22] Brenner, DW; Shenderova, OA; Harrison, JA; Stuart, SJ; Ni, B.; Sinnott, SB, A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, J. Phys. Condens. Matter., 14, 783-802, (2002)
[23] Stuart, SJ; Tutein, AB; Harrison, JA, A reactive potential for hydrocarbons with intermolecular interactions, J. Chem. Phys., 112, 6472-6486, (2000)
[24] Plimpton, S., Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys., 117, 1-19, (1995) · Zbl 0830.65120
[25] Khalil, HK, Nonlinear systems, (2002), Prentice Hall
[26] Phani, AS; Woodhouse, J.; Fleck, NA, Wave propagation in two-dimensional periodic lattices, J. Acoust. Soc. Am., 119, 1995-2005, (2006)
[27] Friedberg, SH; Insel, AJ; Spence, LE, Linear algebra, (2003), Pearson/Prentice Hall
[28] Sinha, A.; Bhartiya, Y., Modeling geometric mistuning of a bladed rotor: modified modal domain analysis, IUTAM symposium on emerging trends in rotor dynamics, 177-184, (2010), Springer
[29] Liang, YC; Lee, HP; Lim, SP; Lin, WZ; Lee, KH; Wu, CG, Proper orthogonal decomposition and its applications—part I: theory, J. Sound Vibr., 252, 527-544, (2002) · Zbl 1237.65040
[30] Chatterjee, A., An introduction to the proper orthogonal decomposition, Curr. Sci., 78, 808-817, (2000)
[31] Ma, J.; Alfè, D.; Michaelides, A.; Wang, E., Stone-Wales defects in graphene and other planar \(sp\)\^{2}-bonded materials, Phys. Rev. B, 80, 033407, (2009)
[32] Rumble, JR, CRC handbook of chemistry and physics, (2017), CRC Press
[33] Humphrey, W.; Dalke, A.; Schulten, K., VMD: visual molecular dynamics, J. Mol. Graphics., 14, 33-38, (1996)
[34] Pastor, M.; Binda, M.; Harčarik, T., Modal assurance criterion, Proc. Eng., 48, 543-548, (2012)
[35] Allen, PB; Kelner, J., Evolution of a vibrational wave packet on a disordered chain, Am. J. Phys., 66, 497-506, (1998)
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