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http://dx.doi.org/10.12989/anr.2017.5.2.179

Free vibration analysis of double walled carbon nanotubes embedded in an elastic medium with initial imperfection  

Ehyaei, Javad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
Daman, Mohsen (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
Publication Information
Advances in nano research / v.5, no.2, 2017 , pp. 179-192 More about this Journal
Abstract
The transverse vibration of double walled carbon nanotube (DWCNT) embedded in elastic medium with an initial imperfection is considered. In this paper, Timoshenko beam theory is employed. However the nonlocal theory is used for modeling the nano scale of nanotube. In addition, the governing Equations of motion are obtained utilizing the Hamilton's principle and simply-simply boundary conditions are assumed. Furthermore, the Navier method is used for determining the natural frequencies of DWCNT. Hence, some parameters such as nonlocality, curvature amplitude, Winkler and Pasternak elastic foundations and length of the curved DWCNT are analyzed and discussed. The results show that, the curvature amplitude causes to increase natural frequency. However, nonlocal coefficient and elastic foundations have important role in vibration behavior of DWCNT with imperfection.
Keywords
free vibration; double walled carbon nanotubes initial imperfection; elastic foundation;
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1 Akgoz, B. and Civalek, O. (2014), "A new trigonometric beam model for buckling of strain gradientmicrobeams", Int. J. Mech. Sci., 81, 88-94.   DOI
2 Chang, W.J. and Lee, H.L. (2009), "Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model", Phys. Lett. A, 373(10), 982-985.   DOI
3 Civalek, O, and Akgoz, B. (2009), "Static analysis of single walled carbon nanotubes (SWCNT) based on Eringen's nonlocal elasticity theory", Int. J. Eng. Appl. Sci., 1(2), 47-56.
4 Demir, C. and Civalek, O. (2013), "Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models", Appl. Math. Model., 37(22), 9355-9367.   DOI
5 Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710.   DOI
6 Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer Science & Business Media.
7 Ke, L.L., Xiang, Y., Yang, J. and Kitipornchai, S. (2009), "Nonlinear free vibration of embedded doublewalled carbon nanotubes based on nonlocal Timoshenko beam theory", Computat. Mater. Sci., 47(2), 409-417.   DOI
8 He, X.Q., Wang, C.M., Yan, Y., Zhang, L.X. and Nie, G.H. (2008), "Pressure dependence of the instability of multiwalled carbon nanotubes conveying fluids", Arch. Appl. Mech., 78(8), 637-648.   DOI
9 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(12), 3475-3485.   DOI
10 Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58.   DOI
11 Cigeroglu, E. and Samandari, H. (2014), "Nonlinear free Vibrations of curved double walled carbon Nanotubes using differential quadrature method", Physica E: Low-dimensional Systems and Nanostructures, 64, 95-105.   DOI
12 Li, R. and Kardomateas, G.A. (2007), "Thermal buckling of multi-walled carbon nanotubes by nonlocal elasticity", J. Appl. Mech., 74(3), 399-405.   DOI
13 Murmu, T. and Pradhan, S.C. (2009), "Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM", Physica E: Low-dimensional Systems and Nanostructures, 41(7), 1232-1239.   DOI
14 Lu, P., Lee, H.P., Lu, C. and Zhang, P.Q. (2007), "Application of nonlocal beam models for carbon nanotubes", Int. J. Solid. Struct., 44(16), 5289-5300.   DOI
15 Mayoof, F.N. and Hawwa, M.A. (2009), "Chaotic behavior of a curved carbon nanotube under harmonic excitation", Chaos, Solitons & Fractals, 42(3), 1860-1867.   DOI
16 Mehdipour, I., Barari, A., Kimiaeifar, A. and Domairry, G. (2012), "Vibrational analysis of curved singlewalled carbon nanotube on a Pasternak elastic foundation", Adv. Eng. Software, 48, 1-5.   DOI
17 Mir, M., Hosseini, A. and Majzoobi, G.H., (2008), "A numerical study of vibrational properties of singlewalled carbon nanotubes", Computat. Mater. Sci., 43(3), 540-548.   DOI
18 Mitra, M. and Gopalakrishnan, S. (2009), "Wave propagation in multi-walled carbon nanotube", Computat. Mater. Sci., 45(2), 411-418.   DOI
19 Pantano, A., Parks, D.M. and Boyce, M.C. (2004), "Mechanics of deformation of single-and multi-wall carbon nanotubes", J. Mech. Phys. Solids, 52(4), 789-821.   DOI
20 Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2), 288-307.   DOI
21 Reddy, J.N. and Pang, S.D. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103(2), 023511.   DOI
22 Shen, H.S. and Zhang, C.L. (2007), "Postbuckling of double-walled carbon nanotubes with temperature dependent properties and initial defects under combined axial and radial mechanical loads", Int. J. Solid. Struct., 44(5), 1461-1487.   DOI
23 Wang, Q. and Varadan, V.K. (2007), "Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes", Smart Mater. Struct., 16(1), 178.   DOI
24 Wang, Q, (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98(12), 124301.   DOI
25 Wang, L. (2009), "Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small length scale", Computat. Mater. Sci., 45(2), 584-588.   DOI
26 Wang, L. and Hu, H. (2005), "Flexural wave propagation in single-walled carbon nanotubes", Phys. Rev. B, 71(19), 195412.   DOI
27 Wang, L., Hu, H. and Guo, W. (2006), "Validation of the non-local elastic shell model for studying longitudinal waves in single-walled carbon nanotubes", Nanotechnology, 17(5), 1408.   DOI
28 Wang, X., Lu, G. and Lu, Y.J. (2007a), "Buckling of embedded multi-walled carbon nanotubes under combined torsion and axial loading", Int. J. Solid. Struct., 44(1), 336-351.   DOI
29 Wang, C.M., Zhang, Y.Y. and He, X.Q. (2007b), "Vibration of nonlocal Timoshenko beams", Nanotechnology, 18(10), 105401.   DOI
30 Wang, C.M., Kitipornchai, S., Lim, C.W. and Eisenberger, M. (2008), "Beam bending solutions based on nonlocal Timoshenko beam theory", J. Eng. Mech., 134(6), 475-481.   DOI
31 Zhang, Y.Y., Tan, V.B.C. and Wang, C.M. (2006b), "Effect of chirality on buckling behavior of singlewalled carbon nanotubes", J. Appl. Phys., 100(7), 074304.   DOI
32 Yang, H.K. and Wang, X. (2006), "Bending stability of multi-wall carbon nanotubes embedded in an elastic medium", Model. Simul. Mater. Sci. Eng., 14(1), p. 99.   DOI
33 Yang, J., Jia, X.L. and Kitipornchai, S. (2008), "Pull-in instability of nano-switches using nonlocal elasticity theory", J. Phys. D: Appl. Phys., 41(3), 035103.   DOI
34 Zhang, C.L. and Shen, H.S. (2007), "Buckling and postbuckling of single-walled carbon nanotubes under combined axial compression and torsion in thermal environments", Phys. Rev. B, 75(4), 045408.   DOI
35 Zhang, Y.Y., Wang, C.M. and Tan, V.B.C. (2006a), "Buckling of multiwalled carbon nanotubes using Timoshenko beam theory", J. Eng. Mech., 132(9), 952-958.   DOI