Parametric vibration analysis of single-walled carbon nanotubes based on Sanders shell theory |
Khadimallah, Mohamed A.
(Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department)
Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir) Ayed, Hamdi (Department of Civil Engineering, College of Engineering, King Khalid University) Tounsi, Abdelouahed (YFL (Yonsei Frontier Lab), Yonsei University) |
1 | Brischotto, S. (2015), "A continuum shell model including van der Waals interaction for free vibrations of double-walled carbon nanotubes", CMES, 104, 305-327. https://doi.org/10.3970/cmes.2015.104.305. DOI |
2 | Budiansky, B. and Sanders, J.L. (1963), On the Best First-Order Linear Shell Theory, Progress in Applied Mechanics, Prager Anniversary Volume, Japan. |
3 | Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer Science and Business Media, New York, USA. |
4 | Flugge, W. (1962), Handbook of Engineering Mechanics, McGraw-Hill, New York, USA. |
5 | Flugge, S. (1973), Stresses in Shells, Springer, Berlin, Germany. |
6 | Gao, Y. and An, L. (2010), "A nonlocal elastic anisotropic shell model for microtubule buckling behaviors in cytoplasm", Physica E Low Dimens. Syst. Nanostruct., 42(9), 2406-2415. https://doi.org/10.1016/j.physe.2010.05.022. DOI |
7 | Ghavanloo, E., Daneshmand, F. and Rafiei, M. (2010), "Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscous elastic Winkler foundation", Physica E Low Dimens. Syst. Nanostruct., 42, 2218-2224. https://doi.org/10.1016/j.physe.2010.04.024. DOI |
8 | Gibson, R.F., Ayorinde, E.O. and Wen, Y.F. (2007), "Vibrations of carbon nanotubes and their composites: a review", Compos. Sci. Technol., 67(1), 1-28. https://doi.org/10.1016/j.compscitech.2006.03.031. DOI |
9 | Gupta, S.S., Bosco, F.G. and Batra, R.C. (2010), "Wall thickness and elastic moduli of single-walled carbon nanotubes from frequencies of axial, torsional and inextensional modes of vibration", Comput. Mater. Sci., 47(4), 1049-1059. https://doi.org/10.1016/j.commatsci.2009.12.007. DOI |
10 | Usuki, T. and Yogo, K. (2009), "Beam equations for multi-walled carbon nanotubes derived from Flugge shell theory", Proc. Math. Phys. Eng. Sci., 465(2104), 1199-1226. https://doi.org/10.1098/rspa.2008.0394. DOI |
11 | Wang, Q. and Varadan, V.K. (2006), "Vibration of carbon nanotubes studied using nonlocal continuum mechanics", Smart Mater. Struct., 15(2), 659. https://doi.org/10.1088/0964-1726/16/1/022. DOI |
12 | Wang, J. and Gao, Y. (2016), "Nonlocal orthotropic shell model applied on wave propagation in microtubules", Appl. Math. Model., 40(11-12), 5731-5744. https://doi.org/10.1016/j.apm.2016.01.013. DOI |
13 | Xu, K.U., Aifantis, E.C. and Yan, Y.H. (2008), "Vibrations of double-walled carbon nanotubes with different boundary conditions between inner and outer tubes", J. Appl. Mech., 75(2), 021013-1. https://doi.org/10.1115/1.2793133. DOI |
14 | Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with SiO2 nano-particles", Wind Struct., Int. J., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043 DOI |
15 | Yang, J., Ke, L.L. and Kitipornchai, S. (2010), "Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", Physica E Low Dimens. Syst. Nanostruct., 42(5), 1727-1735. https://doi.org/10.1016/j.physe.2010.01.035. DOI |
16 | Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., Int. J., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015. DOI |
17 | Yoon, J., Ru, C.Q. and Mioduchowski, A. (2002), "Noncoaxial resonance of an isolated multiwall carbon nanotube", Phys. Rev. B, 66(23), 2334021-2334024. https://doi.org/10.1103/PhysRevB.66.233402. DOI |
18 | Hu, Y.G., Liew, K.M., Wang, Q., He, X.Q. and Yakobson, B.I. (2008), "Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes", J. Mech. Phys. Solids, 56, 3475-3485. https://doi.org/10.1016/j.jmps.2008.08.010. DOI |
19 | He, X.Q., Kitipornchai, S. and Liew, K.M. (2005), "Buckling analysis of multi-walled carbon nanotubes: A continuum model accounting for van der Waals interaction", J. Mech. Phys. Solids, 53, 303-326. https://doi.org/10.1016/j.jmps.2004.08.003. DOI |
20 | Heydarpour, Y., Aghdam, M.M. and Malekzadeh, P. (2014), "Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells", Compos. Struct., 117, 187-200. https://doi.org/10.1016/j.compstruct.2014.06.023. DOI |
21 | Hussain, M., Naeem., M.N., Shahzad, A. and He, M. (2017), "Vibrational behavior of single-walled carbon nanotubes based on cylindrical shell model using wave propagation approach", AIP Adv., 7(4), 045114. https://doi.org/10.1063/1.4979112. DOI |
22 | Ke, L.L., Xiang, Y., Yang, J. and Kitipornchai, S. (2009), "Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory", Comput. Mater. Sci., 47(2), 409-417. https://doi.org/10.1016/j.commatsci.2009.09.002. DOI |
23 | Kroner, E. (1967), "Elasticity theory of materials with long range cohesive forces", Int. J. Solids Struct., 3(5), 731-742. https://doi.org/10.1016/0020-7683(67)90049-2. DOI |
24 | Lee, H.L. and Chang, W.J. (2008), "Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory", J. Appl. Phys., 103(2), 024302. https://doi.org/10.1063/1.2822099. DOI |
25 | Zou, R.D. and Foster, C.G. (1995), "Simple solution for buckling of orthotropic circular cylindrical shells", Thin-Wall. Struct., 22(3), 143-158. https://doi.org/10.1016/0263-8231(94)00026-V. DOI |
26 | Manevitch, L.I., Smirnov, V.V., Strozzi, M. and Pellicano, F. (2017), "Nonlinear optical vibrations of single-walled carbon nanotubes", Int. J. Non Linear Mech., 94, 351-361. http://dx.doi.org/10.1016/j.ijnonlinmec.2016.10.010 DOI |
27 | Loy, C.T., Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells" Int. J. Mech. Sci., 41, 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X. DOI |
28 | Zhang, X.M., Liu, G.R. and Lam, K.Y. (2001), "Vibration analysis of thin cylindrical shells using wave propagation approach", J. Sound Vib., 239(3), 397-403. DOI |
29 | Akbas, S.D. (2017a), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stab. Dyn., 17(3), 1750033. https://doi.org/10.1142/S021945541750033X. DOI |
30 | Akbas, S.D. (2017b), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009. DOI |
31 | Naeem, M.N. and Sharma, C.B. (2000), "Prediction of natural frequencies for thin circular cylindrical shells", Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci., 214(10), 1313-1328. https://doi.org/10.1243/0954406001523290. DOI |
32 | Narendar, S. (2011), "Terahertz wave propagation in uniform nanorods: A nonlocal continuum mechanics formulation including the effect of lateral inertia", Physica E Low Dimens. Syst. Nanostruct., 43, 1015-1020. https://doi.org/10.1016/j.physe.2010.12.004 DOI |
33 | Natsuki, T., Qing, Q.N. and Morinobu, E. (2007), "Wave propagation in single-walled and double-walled carbon nanotubes filled with fluids", J. Appl. Phys., 101(3), 034319-034319-5. https://doi.org/10.1063/1.2432025. DOI |
34 | Paliwal, D.N., Kanagasabapathy, H. and Gupta, K.M. (1995), "The large deflection of an orthotropic cylindrical shell on a Pasternak foundation", Compos. Struct., 31(1), 31-37. https://doi.org/10.1016/0263-8223(94)00068-9. DOI |
35 | Akbas, S.D. (2018c), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., Int. J., 6(3), 219-242. https://doi.org/10.12989/anr.2018.6.3.219. DOI |
36 | Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41, 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0. DOI |
37 | Pradhan, S.C. and Phadikar, J.K. (2009), "Nonlocal elasticity theory for vibration of nanoplates", J. Sound Vib., 325(1-2), 206-223. https://doi.org/10.1016/j.jsv.2009.03.007. DOI |
38 | Rouhi, H., Ansari, R. and Arash, B. (2012), "Vibration analysis of double-walled carbon nanotubes based on the non-local donnell shell via a new numerical approach", Int. J. Mech. Sci., 37, 91-105. https://doi.org/10.1016/S0020-7225(02)00210-0. DOI |
39 | Akbas, S.D. (2018a), "Forced vibration analysis of cracked nanobeams", J. Braz. Soc. Mech. Sci. Eng., 40(8), 392. https://doi.org/10.1007/s40430-018-1315-1. DOI |
40 | Akbas, S.D. (2018b), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., Int. J., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.039. DOI |
41 | Akbas, S.D. (2019), "Axially forced vibration analysis of cracked a nanorod", J. Comput. Appl. Mech., 50(1), 63-68. https://doi.org/10.22059/jcamech.2019.281285.392. DOI |
42 | Benguediab, S., Tounsi, A., Ziadour, M. and Semmah, A. (2014), "Chirality and scale effects on mechanical and buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B Eng, 57, 21-24. https://doi.org/10.1016/j.compositesb.2013.08.020. DOI |
43 | Ansari, R. and Rouhi, H. (2013), "Nonlocal analytical Flügge shell model for the vibrations of double-walled carbon nanotubes with different end conditions", Int. J. Appl. Mech., 80(2), 021006. https://doi.org/10.1142/S179329201250018X. DOI |
44 | Ansari, R., Rouhi, S. and Aryayi, M. (2013), "Nanoscale finite element models for vibrations of single-walled carbon nanotubes: atomistic versus continuum", Appl. Math. Mech., 34(10), 1187-1200. https://doi.org/10.1007/s10483-013-1738-6. DOI |
45 | Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, Int. J., 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567. DOI |
46 | Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with nano-fiber reinforced polymer (NFRP)", Comput. Concrete, Int. J., 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053. DOI |
47 | Strozzi, M and Pellicano, F. (2019), "Nonlinear resonance interaction between conjugate circumferential flexural modes in single-walled carbon nanotubes", Shock Vib., 2019, 3241698. https://doi.org/10.1155/2019/3241698. DOI |
48 | Safeer, M., Taj, M. and Abbas, S.S. (2019), "Effect of viscoelastic medium on wave propagation along protein microtubules", AIP Adv., 9(4), 045108. https://doi.org/10.1016/0263-8223(94)00068-9. DOI |
49 | Simsek, M. (2010), "Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory", Physica E Low Dimens. Syst. Nanostruct., 43, 182-191. https://doi.org/10.12989/scs.2011.11.1.059. DOI |
50 | Strozzi, M. and Pellicano, F. (2018), "Linear vibrations of triplewalled carbon nanotubes", Math. Mech. Solids, 23(11), 1456-1481. http://dx.doi.org/10.1177/1081286517727331. DOI |
51 | Swain, A., Roy, T. and Nanda, B.K. (2013), "Vibration behavior of single-walled carbon nanotube using finite element", Int. J. Theor. Appl. Res. Mech. Eng., 2, 129-133. |
52 | Strozzi, M., Smirnov, V.V., Manevitch, L.I. and Pellicano, F. (2018), "Nonlinear vibrations and energy exchange of single-walled carbon nanotubes: Radial breathing modes", Compos. Struct., 184, 613-632. http://dx.doi.org/10.1016/j.compstruct.2017.09.108. DOI |
53 | Strozzi, M., Smirnov, V.V., Manevitch, L.I. and Pellicano, F. (2020), "Nonlinear normal modes, resonances and energy exchange in single-walled carbon nanotubes", Int. J. Non Linear Mech., 120, 103398. https://doi.org/10.1016/j.ijnonlinmec.2019.103398. DOI |
54 | Sudak, L.J. (2003), "Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics", J. Appl. Phys., 94(11), 7281-7287. https://doi.org/10.1063/1.1625437. DOI |