참고문헌
- Akgoz, B. and Civalek, O. (2013), "Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity", Struct. Eng. Mech., 48(2), 195-205. https://doi.org/10.12989/sem.2013.48.2.195
- Alibeigloo, A. (2014), "Free vibration analysis of functionally graded carbon nanotube reinforced composite cylindrical panel embedded in piezoelectric layers by using theory of elasticity", Eur. J. Mech. A/Solids, 44, 104-115. https://doi.org/10.1016/j.euromechsol.2013.10.002
- Ansari, R., Gholami, R. and Norouzzadeh, A. (2016), "Sizedependent thermo-mechanical vibration and instability of conveying fluid functionally graded nanoshells based on Mindlin's strain gradient theory", Thin-Wall. Struct., 105, 172-184. https://doi.org/10.1016/j.tws.2016.04.009
- Ayatollahi, M.R., Naeemi A.R. and Alishahi, E. (2015), "Effects of mixed contents of carbon nanoreinforcements on the impact resistance of epoxy-based nanocomposites", Struct. Eng. Mech., 56(2), 157-167. https://doi.org/10.12989/sem.2015.56.2.157
- Changcheng, D. and Yinghui, L. (2013), "Nonlinear resonance behavior of functionally graded cylindrical shells in thermal environments", Compos. Struct., 102, 164-174. https://doi.org/10.1016/j.compstruct.2013.02.028
- Civalek, E. (2016), "Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method", Compos. Part B, 111, 45-59.
- Gharib, A., Karimi, M.S. and Ghorbanpour Arani, A. (2016), "Vibration analysis of the embedded piezoelectric polymeric nano-composite panels in the elastic substrate", Compos. Part B, 101, 64-76. https://doi.org/10.1016/j.compositesb.2016.06.077
- Gholami, R., Darvizeh, A., Ansari, R. and Sadeghi, F. (2016), "Vibration and buckling of first-order shear deformable circular cylindrical micro-/nano-shells based on Mindlin's strain gradient elasticity theory", Eur. J. Mech. A/Solids, 58, 76-88. https://doi.org/10.1016/j.euromechsol.2016.01.014
- Ghorbanpour Arani, A., Kolahchi, R. and Vossough, H. (2012), "Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory", Physica B, 407(21), 4281-4286. https://doi.org/10.1016/j.physb.2012.07.018
- Guo, S., He, Y., Liu, D., Lei, J., Shen, L. and Li, Zh. (2016), "Torsional vibration of carbon nanotube with axial velocity and velocity gradient effect", Int. J. Mech. Sci., 119, 88-96. https://doi.org/10.1016/j.ijmecsci.2016.09.036
- Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58. https://doi.org/10.1038/354056a0
- Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032
- Kolahchi, R., Safari, M. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
- Lei, J., He, Y., Guo, S., Li, Zh. and Liu, D. (2016), "Sizedependent vibration of nickel cantilever microbeams: Experiment and gradient elasticity", AIP Adv., 6(10), 105202. https://doi.org/10.1063/1.4964660
- Li, S. and Wang, G. (2008), Introduction to Micromechanics and Nanomechanics, World Scientific Publication, Singapore.
- Li, C. (2013), "Size-dependent thermal behaviors of axially traveling nanobeams based on a strain gradient theory", Struct. Eng. Mech., 48(3), 415-434. https://doi.org/10.12989/sem.2013.48.3.415
- Li, L. and Hu, Y. (2016), "Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory", Comput. Mat. Sci., 112, 282-288. https://doi.org/10.1016/j.commatsci.2015.10.044
- Mirzaei, M. and Kiani, Y. (2016), "Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels", Compos. Struct., 142, 45-56. https://doi.org/10.1016/j.compstruct.2015.12.071
- Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall. et Mater., 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
- Paliwal, D., Pandey, R.K. and Nath, T. (1996), "Free vibrations of circular cylindrical shell on Winkler and Pasternak foundations", Int. J. Press. Vessel. Pip., 69(1), 79-89. https://doi.org/10.1016/0308-0161(95)00010-0
- Qian, D., Dickey, E.C., Andrews, R. and Rantell, T. (2000), "Load transfer and deformation mechanisms in carbon nanotubepolystyrene composites", Appl. Phy. Lett., 76(20), 2868-2870. https://doi.org/10.1063/1.126500
- Qian, D., Wagner, G.J., Liu, W.K., Yu, M.F. and Ruoff, R.S. (2002), "Mechanics of carbon nanotubes", Appl. Mech. Rev., 55(6), 495-533. https://doi.org/10.1115/1.1490129
- Razavi, H., Faramarzi Babadi, A. and Tadi Beni, Y. (2016), "Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory", Compos. Struct., 160, 1299-1309.
- Reddy, J.N. (2002), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition, CRC Press.
- Rogacheva, N. (1988), "Forced vibrations of a piezoceramic cylindrical shell with longitudinal polarization", J. Appl. Math. Mech., 52(5), 641-646. https://doi.org/10.1016/0021-8928(88)90114-1
- Saito, R., Dresselhaus, G. and Dresselhaus, M.S. (1998), Physical Properties of Carbon Nanotubes, Imperial College Press, London.
- Shen, H.S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Methods Appl. Mech. Eng., 213-216, 196-205. https://doi.org/10.1016/j.cma.2011.11.025
- Shen, H.S. and Xiang, Y. (2014), "Nonlinear vibration of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments", Compos. Struct., 111, 291-300. https://doi.org/10.1016/j.compstruct.2014.01.010
- Shi, D.L. and Feng, X.Q. (2004), "The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composties", J. Eng. Mat. Tech., ASME, 126, 250-270. https://doi.org/10.1115/1.1751182
- Song, Z.G., Zhang, L.W. and Liew, K.M. (2016), "Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments", Int. J. Mech. Sci., 115, 339-347.
- Tadi Beni, Y., Mehralian, F. and Razavi, H. (2014), "Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of the modified couple stress theory", Compos. Struct., 120, 65-78.
- Yas, M.H., Pourasghar, A., Kamarian, S. and Heshmati, M. (2013), "Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube", Mat. Des., 49, 583-590. https://doi.org/10.1016/j.matdes.2013.01.001
- Zeighampour, H. and Tadi Beni, Y. (2014), "Cylindrical thin-shell model based on modified strain gradient theory", Int. J. Eng. Sci., 78, 27-47. https://doi.org/10.1016/j.ijengsci.2014.01.004
- Zhang, L.W., Cui W.C. and Liew, K.M. (2015a), "Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges", Int. J. Mech. Sci., 103, 9-21. https://doi.org/10.1016/j.ijmecsci.2015.08.021
- Zhang, B., He, Y., Liu, D., Shen, L. and Lei, J. (2015b), "Free vibration analysis of four-unknown shear deformable functionally graded cylindrical microshells based on the strain gradient elasticity theory", Compos. Struct., 119, 578-597. https://doi.org/10.1016/j.compstruct.2014.09.032
- Zhang, B., He, Y., Liu, D., Shen, L. and Lei, J. (2015c), "An efficient size-dependent plate theory for bending, buckling and free vibration analyses of functionally graded microplates resting on elastic foundation", Appl. Math. Model., 39(13), 3814-3845. https://doi.org/10.1016/j.apm.2014.12.001