Theoretical impact of Kelvin's theory for vibration of double walled carbon nanotubes |
Hussain, Muzamal
(Department of Mathematics, Government College University Faisalabad)
Naeem, Muhammad N. (Department of Mathematics, Government College University Faisalabad) Asghar, Sehar (Department of Mathematics, Government College University Faisalabad) Tounsi, Abdelouahed (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria Faculty of Technology Civil Engineering Department) |
1 | Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45, 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004 DOI |
2 | Rouhi, H., Ansari, R. and Arash, B. (2013), "Vibrational analysis of double-walled carbon nanotubes based on the nonlocal Donnell shell theory via a new numerical approach", Int J. Mech. Sei., 37, 91-105. |
3 | Rouhi, H., BazdidVahdati, M. and Ansari, R. (2015), "Rayleigh-Rits vibrational analysis of multi-walled carbon nanotubes based on the non-local Flugge shell theory", J. Compos., 750392. https://doi.org/10.1155/2015/750392 |
4 | Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory", Earthq. Struct., Int. J., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.3.329 |
5 | Ansari, R. and Rouhi, H. (2013), "Nonlocal analytical Flugge shell model forr the vibrations of double-walled carbon nanotubes with different end conditions", Int. J. Appl. Mech., 80, 021006-1. https://doi.org/10.1142/S179329201250018X DOI |
6 | Ansari, R., Sahmani, S. and Arash, B. (2010), "Nonlocal plate model for free vibrations of single-layered graphene sheets", Phy. Letters A., 375(1), 53-62. https://doi.org/10.1016/j.physleta.2010.10.028 DOI |
7 | Ansari, R., Hemmatnezhad, M. and Rezapour, J. (2011), "The thermal effect on nonlinear oscillations of carbon nanotubes with arbitrary boundary conditions", Current Appl. Phys., 11(3), 692-697. https://doi.org/10.1016/j.cap.2010.11.034 DOI |
8 | 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 |
9 | Mehar, K. and Panda, S.K. (2016b), "Free vibration and bending behaviour of CNT reinforced composite plate using different shear deformation theory", Proceedings of IOP Conference Series: Materials Science and Engineering, 115(1), 012014. https://doi.org/10.1088/1757-899X/115/1/012014 DOI |
10 | Mehar, K. and Panda, S.K. (2018a), "Dynamic response of functionally graded carbon nanotube reinforced sandwich plate", Proceedings of IOP Conference Series: Materials Science and Engineering, 338(1), p. 012017. https://doi.org/10.1088/1757-899X/338/1/012017 DOI |
11 | Mehar, K. and Panda, S.K. (2018b), "Thermal free vibration behavior of FG-CNT reinforced sandwich curved panel using finite element method", Polym. Compos., 39(8), 2751-2764. https://doi.org/10.1002/pc.24266 DOI |
12 | Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., Int. J., 7(3), 181-190. https://doi.org/10.12989/anr.2019.7.3.181 DOI |
13 | Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2016), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", J. Sandw. Struct. Mater., 18(2), 151-173. https://doi.org/10.1177/1099636215613324 DOI |
14 | Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017a), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech.- A/Solids, 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005 DOI |
15 | Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017b), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Thermal Stress., 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689 DOI |
16 | Wang, Q., Varadan, V.K. and Quek, S.T. (2006a), "Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models", Phys. Lett. A, 357(2), 130-135. https://doi.org/10.1016/j.physleta.2006.04.026 DOI |
17 | Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017c), "Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure", Int. J. Mech. Sci., 133, 319-329. https://doi.org/10.1016/j.ijmecsci.2017.08.057 DOI |
18 | Vodenitcharova, T. and Zhang, L.C. (2003), "Effective wall thickness of single walled carbon nanotubes", Phy. Rev. B, 68, 165401. https://doi.org/10.1103/PhysRevB.68.165401 DOI |
19 | Wang, J. and Gao, Y. (2016), "Nonlocal orthotropic shell model applied on wave propagation in microtubules", Appl. Mathe. Model., 40(11-12), 5731-5744. https://doi.org/10.1016/j.apm.2016.01.013 DOI |
20 | Wang, C.Y. and Zhang, L.C. (2007), "Modeling the free vibration of single-walled carbon nanotubes", Proceedings of the 5th Australasian Congress on Applied Mechanics, ACAM, Brisbane, Australia, pp. 252-257. |
21 | Wang, Q., Zhou, G.Y. and Lin, K.C. (2006b), "Scale effect on wave propagation of double-walled carbon nanotubes", Int. J. Solids Struct., 43, 6071-6084. https://doi.org/10.1016/j.ijsolstr.2005.11.005 DOI |
22 | Xiaobin, L., Shuangxi, X., Weiguo, W. and Jun, L. (2014), "An exact dynamic stiffness matrix for axially loaded double-beam systems", Sadhana, 39(3), 607-623. https://doi.org/10.1007/s12046-013-0214-5 DOI |
23 | 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 |
24 | Fatahi-Vajari. A., Azimzadeh, Z. and Hussain. M. (2019), "Nonlinear coupled axial-torsional vibration of single-walled carbon nanotubes using Galerkin and Homotopy perturbation method", Micro Nano Lett., 14(14), 1366-1371. https://doi.org/10.1049/mnl.2019.0203 DOI |
25 | Flugge, W. (1962), Statik und Dynamik der Scahlen, Springer, Berlin, Germany. |
26 | Jassas, M.R., Bidgoli, M.R. and Kolahchi, R. (2019), "Forced vibration analysis of concrete slabs reinforced by agglomerated SiO2 nanoparticles based on numerical methods", Constr. Build. Mater., 211, 796-806. https://doi.org/10.1016/j.conbuildmat.2019.03.263 DOI |
27 | Hussain, M., Naeem, M.N., Sehar, A. and Tounsi, A. (2020e), "Eringen's nonlocal model sandwich with Kelvin's theory for vibration of DWCNT", Comput. Concrete, Int. J., 25(4), 343-354. https://doi.org/10.12989/cac.2020.25.4.343 |
28 | Hussain, M., Naeem, M.N., Khan, M.S. and Tounsi, A. (year), "Computer-aided approach for modelling of FG cylindrical shell sandwich with ring supports", Comput. Concrete, Int. J., 25(5), 411-425. https://doi.org/10.12989/cac.2020.25.5.411 |
29 | Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(7), 56-58. https://doi.org/10.1038/354056a0 DOI |
30 | Karami, B., Janghorban, M. and Tounsi, A. (2018), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025 DOI |
31 | Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2019), "Elastic guided waves in fully-clamped functionally graded carbon nanotube-reinforced composite plates", Mater. Res. Express, 6(9), 0950a9. https://doi.org/10.1088/2053-1591/ab3474 DOI |
32 | 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", Computat. Mater. Sci., 47(2), 409-417. https://doi.org/10.1016/j.commatsci.2009.09.002 DOI |
33 | Khosrazadeh, A. and Hajabasi, M.A. (2012), "Free vibrations of embedded doube-walled carbon nanotubes considering nonlinear interlayer van der Waals forces", Appl. Mathe. Model., 36(3), 997-1007 https://doi.org/10.1016/j.apm.2011.07.063 DOI |
34 | Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018c), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), 04018094. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001519 DOI |
35 | Mehar, K., Panda, S.K. and Patle, B.K. (2017d), "Thermoelastic vibration and flexural behavior of FG-CNT reinforced composite curved panel", Int. J. Appl. Mech., 9(4), 1750046. https://doi.org/10.1142/S1758825117500466 DOI |
36 | Mehar, K., Panda, S.K. and Patle, B.K. (2018a), "Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach", Polym. Compos., 39(10), 3792-3809. https://doi.org/10.1002/pc.24409 DOI |
37 | Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018b), "Nonlinear frequency responses of functionally graded carbon nanotubereinforced sandwich curved panel under uniform temperature field", Int. J. Appl. Mech., 10(3), 1850028. https://doi.org/10.1142/S175882511850028X DOI |
38 | Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002 DOI |
39 | Mercan, K. and Civalek, O. (2016), "DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix", Compos. Struct., 143, 300-309. https://doi.org/10.1016/j.compstruct.2016.02.040 DOI |
40 | Mohsen, M. and Eyvazian, A. (2020), "Post-buckling analysis of Mindlin Cut out-plate reinforced by FG-CNTs", Steel Compos. Struct., Int. J., 34(2), 289-297. https://doi.org/10.12989/scs.2020.34.2.289 |
41 | Moradi-Dastjerdi, R. and Payganeh, G. (2017), "Transient heat transfer analysis of functionally graded CNT reinforced cylinders with various boundary conditions", Steel Compos. Struct., Int. J., 24(3), 359-367. https://doi.org/10.12989/scs.2017.24.3.359 |
42 | Motezaker, M., Jamali, M. and Kolahchi, R. (2020), "Application of differential cubature method for nonlocal vibration, buckling and bending response of annular nanoplates integrated by piezoelectric layers based on surface-higher order nonlocalpiezoelasticity theory", J. Computat. Appl. Mathe., 369, 112625. https://doi.org/10.1016/j.cam.2019.112625 DOI |
43 | Motezaker, M. and Eyvazian, A. (2020), "Buckling load optimization of beam reinforced by nanoparticles", Struct. Eng. Mech., Int. J., 73(5), 481-486. https://doi.org/10.12989/sem.2020.73.5.481 |
44 | Motezaker, M. and Kolahchi, R. (2017a), "Seismic response of concrete columns with nanofiber reinforced polymer layer", Comput. Concrete, Int. J., 20(3), 361-368. https://doi.org/10.12989/cac.2017.20.3.361 |
45 | Motezaker, M. and Kolahchi, R. (2017b), "Seismic response of nanoparticles-reinforced concrete pipes based on DQ and newmark methods", Comput. Concrete, Int. J., 19(6), 745-753. https://doi.org/10.12989/cac.2017.19.6.745 |
46 | Narwariya, M., Choudhury, A. and Sharma, A.K. (2018), "Harmonic analysis of moderately thick symmetric cross-ply laminated composite plate using FEM", Adv. Computat. Des., Int. J., 3(2), 113-132. https://doi.org/10.12989/acd.2018.3.2.113 |
47 | Natsuki, T., Endo, M. and Tsuda, H. (2006), "Vibration analysis of embedded carbon nanotubes using wave propagation approach", J. Appl. Phys., 99(3), 034311. https://doi.org/10.1063/1.2170418 DOI |
48 | Kumar, B.R. (2018), "Investigation on mechanical vibration of double-walled carbon nanotubes with inter-tube Van der waals forces", Adv. Nano Res., Int. J., 6(2), 135. https://doi.org/10.12989/anr.2018.6.2.135 |
49 | Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2020), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-viscopiezoelasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater., 22(1), 3-27. https://doi.org/10.1177/1099636217731071 DOI |
50 | 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 |
51 | Lal, A., Jagtap, K.R. and Singh, B.N. (2017), "Thermomechanically induced finite element based nonlinear static response of elastically supported functionally graded plate with random system properties", Adv. Computat. Des., Int. J., 2(3), 165-194. https://doi.org/10.12989/acd.2017.2.3.165 |
52 | Lei, Z. and Zhang, Y. (2018), "Characterizing buckling behavior of matrix-cracked hybrid plates containing CNTR-FG layers", Steel Compos. Struct., Int. J., 28(4), 495-508. https://doi.org/10.12989/scs.2018.28.4.495 |
53 | Li, C. and Chou, T.W. (2003), "A structural mechanics approach for the analysis of carbon nanotubes", Int. J. Solids Struct., 40(10), 2487-2499. https://doi.org/10.1016/S0020-7683(03)00056-8 DOI |
54 | Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNTreinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., Int. J., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889 DOI |
55 | Mehar, K. and Panda, S.K. (2016a), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038 DOI |
56 | Akgoz, B. and Civalek, O. (2011), "Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified couple stress theories", J. Computat. Theor. Nanosci., 8, 1821-1827. https://doi.org/10.1166/jctn.2011.1888 DOI |
57 | Natsuki, T., Ni, Q.Q. and Endo, M. (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 |
58 | 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 |
59 | Adela, I. (2018), Computational Fluid Dynamics, Romania. |
60 | Akgoz, B. and Civalek, O. (2015), "A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory", Acta Mechanica, 226(7), 2277-2294. https://doi.org/10.1007/s00707-015-1308-4 DOI |
61 | Amara, K., Tounsi, A., Mechab, I. and Adda-Bedia, E.A. (2010), "Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field", Appl. Mathe. Model., 34(12), 3933-3942. https://doi.org/10.1016/j.apm.2010.03.029 DOI |
62 | 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 |
63 | Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by nanoparticles subjected to blast load experimentally and theoretically", Constr. Build. Mater., 174, 633-644. https://doi.org/10.1016/j.conbuildmat.2018.04.140 DOI |
64 | Ansari, R. and Arash, B. (2013), "Nonlocal Flugge shell model for vibrations of double-walled carbon nanotubes with different boundary conditions", J. Appl. Mech., 80(2), 021006. https://doi.org/10.1115/1.4007432 DOI |
65 | Ansari, R. and Rouhi, H. (2012), "Nonlocal analytical Flugge shell model for the axial buckling of double-walled carbon nanotubes with different end conditions", Int. J. Nano, 7, 1250081. https://doi.org/10.1142/S179329201250018X |
66 | Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of Nonlocal Continuum Models to Nanotechnology", Int. J. Eng. Sei., 41, 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0 DOI |
67 | Pradhan, S.C. and Phadikar, J.K. (2009), "Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models", Phy. Lett. A, 373(11), 1062-1069. https://doi.org/10.1016/j.physleta.2009.01.030 DOI |
68 | 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 DOI |
69 | Rakrak, K., Zidour, M., Heireche, H., Bousahla, A.A. and Chemi, A. (2016), "Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory", Adv. Nano Res., Int. J., 4(1), 31-44. https://doi.org/10.12989/anr.2016.4.1.031 DOI |
70 | Arefi, M., Mohammadi, M., Tabatabaeian, A., Dimitri, R. and Tornabene, F. (2018), "Two-dimensional thermo-elastic analysis of FG-CNTRC cylindrical pressure vessels", Steel Compos. Struct., Int. J., 27(4), 525-536. https://doi.org/10.12989/scs.2018.27.4.525 |
71 | Asghar, S., Hussain, M. and Naeem, M. (2019), "Non-local effect on the vibration analysis of double walled carbon nanotubes based on Donnell shell theory", Physica E: Low-dimens. Syst. Nanostruct., 116, 113726. https://doi.org/10.1016/j.physe.2019.113726 DOI |
72 | Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., Int. J., 55(4), 871-884. https://doi.org/10.12989/sem.2015.55.4.871 DOI |
73 | Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603 |
74 | Aydogdu, M.A. (2009), "A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration", Physica E, 41, 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014 DOI |
75 | Sahouane, A., Hadji, L. and Bourada, M. (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., Int. J., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031 |
76 | Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A. and Tounsi, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., Int. J., 33(6), 805-822. https://doi.org/10.12989/scs.2019.33.6.805 |
77 | Sanchez-Portal, D., Artacho, E., Soler, J.M., Rubio, A. and Ordejon, P. (1999), "Ab-initio structural, elastic, and Vibrational Properties of Carbon Nanotubes", Phys. Rev. B, 59, 12678-2688. http://dx.doi.org/10.1103/PhysRevB.59.12678 DOI |
78 | Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., Int. J., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037 DOI |
79 | Flugge, S. (1973), Stresses in Shells, Springer, 2nd Edition, Berlin, Germany. |
80 | Fu, Y.M., Hong, J.W. and Wang, X.Q. (2006), "Analysis of nonlinear vibration for embedded carbon nanotubes", J. Sound Vib., 296(4-5), 746-756. https://doi.org/10.1016/j.jsv.2006.02.024 DOI |
81 | 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.2010.05r.022 DOI |
82 | Ghodrati, B., Yaghootian, A., Ghanbar Zadeh, A. and Mohammad-Sedighi, H. (2018), "Lamb wave extraction of dispersion curves in micro/nano-plates using couple stress theories", Waves Random Complex Media, 28(1), 15-34. https://doi.org/10.1080/17455030.2017.1308582 DOI |
83 | Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., Int. J., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231 |
84 | Hajmohammad, M.H., Farrokhian, A. and Kolahchi, R. (2018a), "Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory", Aerosp. Sci. Technol., 78, 260-270. https://doi.org/10.1016/j.ast.2018.04.030 DOI |
85 | Yakobson, B.I., Brabec, C.J. and Bernholc, J. (1996), "Nanomechanics of carbon tubes: instabilities beyond linear response", Phy. Rev. Lett, 76, 2511-2514. https://doi.org/10.1103/PhysRevLett.76.2511 DOI |
86 | Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlinear Dyn., 90(1), 479-492. https://doi.org/10.1007/s11071-017-3676-x DOI |
87 | Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016 DOI |
88 | Kolahchi, R. and Bidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Mathe. Mech., 37(2), 265-274. https://doi.org/10.1007/s10483-016-2030-8 DOI |
89 | Iijima, S., Brabec, C., Maiti, A. and Bernholc, J. (1996), "Structural flexibility of carbon nanotubes", J. Chem. Phys., 104(5), 2089. https://doi.org/10.1063/1.470966 DOI |
90 | 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 DOI |
91 | 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 DOI |
92 | Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017a), "Wave propagation of embedded viscoelastic FG-CNTreinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039 DOI |
93 | Sharma, P., Singh, R. and Hussain, M. (2019), "On modal analysis of axially functionally graded material beam under hygrothermal effect", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. https://doi.org/10.1177/0954406219888234 |
94 | Sedighi, H.M. and Sheikhanzadeh, A. (2017), "Static and dynamic pull-in instability of nano-beams resting on elastic foundation based on the nonlocal elasticity theory", Chin. J. Mech. Eng., 30, 385-397. https://doi.org/10.1007/s10033-017-0079-3 DOI |
95 | Sehar, A., Hussain, M., Naeem, M.N. and Tounsi, A. (2020), "Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis", Comput. Concrete, Int. J., 25(2), 133-144. https://doi.org/10.12989/cac.2020.25.2.133 |
96 | Shafiei, H. and Setoodeh, A.R. (2017), "Nonlinear free vibration and post-buckling of FG-CNTRC beams on nonlinear foundation", Steel Compos. Struct., Int. J., 24(1), 65-77. https://doi.org/10.12989/scs.2017.24.1.065 DOI |
97 | She, G.L., Ren, Y.R. and Yuan, F.G. (2019), "Hygro-thermal wave propagation in functionally graded double-layered nanotubes systems", Steel Compos. Struct., Int. J., 31(6), 641-653. https://doi.org/10.12989/scs.2019.31.6.641 |
98 | Batou, B., Nebab, M., Bennai, R., Atmane, H.A., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., Int. J., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699 |
99 | Behera, S. and Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Computat. Des., Int. J., 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213 |
100 | Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale effects on mechanical and buckling properties of zigzag double-walled carbon nanotubes", Composites Part B, 57, 21-24. https://doi.org/10.1016/j.compositesb.2013.08.020 DOI |
101 | Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with nano-particles", Wind Struct., Int. J., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043 DOI |
102 | Yakobson, B.I., Campbell, M.P., Brabec, C.J. and Bemholc, J. (1997), "High strain rate fracture and C-chain unravelling in carbon nanotubes", Comput. Mater. Sei., 8(4), 341-348. https://doi.org/10.1016/S0927-0256(97)00047-5 DOI |
103 | Yoon, J., Ru, C.Q. and Mioduchowski, A. (2003), "Vibration of an embedded multiwall carbon nanotube", Compos. Sei. Tech., 63(11), 1533-1542. https://doi.org/10.1016/S0266-3538(03)00058-7 DOI |
104 | Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams surface stress effects", Smart Struct. Syst., Int. J., 21(1), 65-74. https://doi.org/10.12989/sss.2018.21.1.065 |
105 | Zarei, M.S., Kolahchi, R., Hajmohammad, M.H. and Maleki, M. (2017), "Seismic response of underwater fluid-conveying concrete pipes reinforced with nanoparticles and fiber reinforced polymer (FRP) layer", Soil Dyn. Earthq. Eng., 103, 76-85. https://doi.org/10.1016/j.soildyn.2017.09.009 DOI |
106 | Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., Int. J., 54(4), 693-710. http://dx.doi.org/10.12989/sem.2015.54.4.693 DOI |
107 | Zidour, M., Daouadji, T.H., Benrahou, K.H., Tounsi, A., Bedia, E.A.A. and Hadji, L. (2014), "Buckling analysis of chiral singlewalled carbon nanotubes by using the nonlocal Timoshenko beam theory", Mech. Compos. Mater., 50(1), 95-104. https://doi.org/10.1007/s11029-014-9396-0 DOI |
108 | Bensattalah, T., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2018), "Critical buckling loads of carbon nanotube embedded in Kerr's medium", Adv. Nano Res., Int. J., 6(4), 339-356. https://doi.org/10.12989/anr.2018.6.4.339 |
109 | Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017b), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016 DOI |
110 | Kolahchi, R., Hosseini, H., Fakhar, M.H., Taherifar, R. and Mahmoudi, M. (2019), "A numerical method for magneto-hygrothermal postbuckling analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions", Comput. Mathe. Applicat., 78(6), 2018-2034. https://doi.org/10.1016/j.camwa.2019.03.042 DOI |
111 | 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 |
112 | Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147 |
113 | Brischotto, S. (2015), "A continuum shell model including van der Waals interaction for free vibrations of double-walled carbon nanotubes", CMES, 104, 305-327. |
114 | Chemi, A., Zidour, M., Heireche, H., Rakrak, K. and Bousahla, A.A. (2018), "Critical Buckling Load of Chiral Double-Walled Carbon Nanotubes Embedded in an Elastic Medium", Mech. Compos. Mater., 53(6), 827-836. https://doi.org/10.1007/s11029-018-9708-x DOI |
115 | Shen, H.S. and Zhang, C.L. (2010), "Torsional buckling and post buckling of double-walled carbon nanotubes by nonlocal shear deformable shell model", Compos. Struct., 92(5), 1073-1084. https://doi.org/10.1016/j.compstruct.2009.10.002 DOI |
116 | Soldano, C. (2015), "Hybrid metal-based carbon nanotubes", "Novel platform for multifunctional applications", Progress in Mater. Sci., 69, 183-212. https://doi.org/10.1016/j.pmatsci.2014.11.001 DOI |
117 | Sosa, E.D., Darlington, T.K., Hanos, B.A. and O'Rourke, M.J.E. (2014), "Multifunctional thermally remendable nanocomposites", J. Compos., 12 p. http://dx.doi.org/10.1155/2014/705687 |
118 | Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Nouri, A.H. (2019), "Dynamic response of auxetic honeycomb plates integrated with agglomerated CNT-reinforced face sheets subjected to blast load based on visco-sinusoidal theory", Int. J. Mech. Sci., 153, 391-401. https://doi.org/10.1016/j.ijmecsci.2019.02.008 DOI |
119 | Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018b), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27. https://doi.org/10.1016/j.soildyn.2018.04.002 DOI |
120 | Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Maleki, M. (2018c), "Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects", Compos. Struct., 187, 498-508. https://doi.org/10.1016/j.compstruct.2017.12.004 DOI |
121 | Hajnayeb, A. and Khadem, S.E. (2015), "An analytical study on the nonlinear vibration of a double walled carbon nanotube", Struct. Eng. Mech., Int. J., 54(5), 987-998. https://doi.org/10.12989/sem.2015.54.5.987 DOI |
122 | Hao, M.J., Guo, X.M. and Wang, Q. (2010), "Small-scale effect on torsional buckling of multi-walled carbon nanotubes", Eur. J. Mech. A/Solids, 29(1), 49-55. https://doi.org/10.1016/j.euromechsol.2009.05.008 DOI |
123 | Hernandez, E., Goze, C., Bemier, P. and Rubio, A. (1998), "Elastic properties of C and BxCyNz composite nanotubes", Phys. Rev. Lett., 80, 4502-4505. https://doi.org/10.1103/PhysRevLett.80.4502 DOI |
124 | 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 |
125 | Taj, M., Safeer, M., Hussain, M., Naeem, M.N., Majeed, A., Ahmad, M., Khan, H.U. and Tounsi, A. (2020a), "Non-local orthotropic elastic shell model for vibration analysis of protein microtubules", Comput. Concrete, Int. J., 25(3), 245-253. https://doi.org/10.12989/cac.2020.25.3.245 |
126 | Sudak, L.J. (2003), "Column buckling of multi-walled carbon nanotubes using nonlocal continuum mechanics", J. Appl. Phys., 94, 7281-7287. https://doi.org/10.1063/1.1625437 DOI |
127 | Sun, C.T. and Zhang, H. (2002), "Size-dependent elastic moduli of plate like nanomaterials", J. Appl. Phys., 93, 212-1218. https://doi.org/10.1063/1.1530365 |
128 | Tahouneh, V. (2017), "Effects of CNTs waviness and aspect ratio on vibrational response of FG-sector plate", Steel Compos. Struct., Int. J., 25(6), 649-661. https://doi.org/10.12989/scs.2017.25.6.649 |
129 | Taj, M., Safeer, M., Hussain, M., Naeem, M.N., Ahmad, M., Abbas, K., Khan, A.Q. and Tounsi, A. (2020b), "Effect of external force on buckling of cytoskeleton intermediate filaments within viscoelastic media", Comput. Concrete, Int. J., 25(3), 205-214. https://doi.org/10.12989/cac.2020.25.3.205 |
130 | Taj, M., Hussain, M., Naeem, M.N. and Tounsi, A. (2020c), "Effects of elastic medium on buckling of microtubules due to bending and torsion", Adv. Concrete Constr., Int. J., 9(5), 491-501. https://doi.org/10.12989/acc.2020.9.5.491 |
131 | Das, B., Mandal, M., Upadhyay, A., Chattopadhyay, P. and Karak, N. (2013), "Bio-based hyperbranched polyurethane/Fe3O4 nanocomposites: smart antibacterial biomaterials for biomedical devices and implants", Biomed. Mater., 8(3), 035003. https://doi.org/10.1088/1748-6041/8/3/035003 DOI |
132 | Do, Q.C., Pham, D.N., Vu, D.Q., Vu, T.T.A. and Nguyen, D.D. (2019), "Nonlinear buckling and post-buckling of functionally graded CNTs reinforced composite truncated conical shells subjected to axial load", Steel Compos. Struct., Int. J., 31(3), 243-259. https://doi.org/10.12989/scs.2019.31.3.243 |
133 | Hu, Y.G., Liew, K.M. and Wang, Q. (2012), "Modeling of vibrations of carbon nanotubes", Procedia Eng., 31, 343-347. https://doi.org/10.1016/j.proeng.2012.01.1034 DOI |
134 | Hosseini, H. and Kolahchi, R. (2018), "Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment", Physica E: Low-dimens. Syst. Nanostruct., 102, 101-109. https://doi.org/10.1016/j.physe.2018.04.037 DOI |
135 | Zouatnia, N. and Hadji, L. (2019), "Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory", Earthq. Struct., Int. J., 16(2), 177-183. https://doi.org/10.12989/eas.2019.16.2.177 |
136 | 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. Phy. Solids, 56, 3475-3485. https://doi.org/10.1016/j.jmps.2008.08.010 DOI |
137 | Hussain, M. and Naeem, M.N. (2017), "Vibration analysis of single-walled carbon nanotubes using wave propagation approach", Mech. Sci., 8(1), 155-164. https://doi.org/10.5194/ms-8-155-2017 DOI |
138 | Hussain, M. and Naeem, M. (2018a), "Vibration of single-walled carbon nanotubes based on Donnell shell theory using wave propagation approach", Chapter, Intechopen, In: Novel Nanomaterials - Synthesis and Applications. ISBN 978-953-51-5896-7 https://doi.org/10.5772 /intechopen.73503 |
139 | Hussain, M. and Naeem, M.N. (2018b), "Effect of various edge conditions on free vibration characteristics of rectangular plates", Chapter, Intechopen, In: Advance Testing and Engineering. ISBN 978-953-51-6706-8 |
140 | Hussain, M. and Naeem, M.N. (2019a), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes". Appl. Math. Modeling, 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039 DOI |
141 | Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X DOI |
142 | Ebrahimi, F. and Mahmoodi, F. (2018), "Vibration analysis of carbon nanotubes with multiple cracks in thermal environment", Adv. Nano Res., Int. J., 6(1), 57-80. https://doi.org/10.12989/anr.2018.6.1.057 |
143 | Ehyaei, J. and Daman, M. (2017), "Free vibration analysis of double walled carbon nanotubes embedded in an elastic medium with initial imperfection", Adv. Nano Res., Int. J., 5(2), 179-192. https://doi.org/10.12989/anr.2017.5.2.179 |
144 | Eltaher, M., Emam, S.A. and Mahmoud, F. (2013), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030 DOI |
145 | Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.33280 DOI |
146 | Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer Science & Business Media. |
147 | Fakhrabadi, M.M.S., Rastgoo, A. and Ahmadian, M.T. (2015), "Application of electrostatically actuated carbon nanotubes in nanofluidic and bio-nanofluidic sensors and actuators", Measurement, 73, 127-136. https://doi.org/10.1016/j.measurement.2015.05.009 DOI |
148 | Tounsi, A., Benguediab, S., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of doublewalled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001 DOI |
149 | Usuki, T. and Yogo, K. (2009), "Beam equations for multi-walled carbon nanotubes derived from Flugge shell theory", Proceedings of Royal Society A, 465(2104). https://doi.org/10.1098/rspa.2008.0394 |
150 | Hussain, M. and Naeem, M.N. (2019b), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. Part B: Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144 DOI |
151 | Hussain, M. and Naeem, M.N. (2019c), "Vibration characteristics of zigzag and chiral functionally graded material rotating carbon nanotubes sandwich with ring supports", J. Mech. Eng. Sci., Part C, 233(16), 5763-5780. https://doi.org/10.1177/0954406219855095 DOI |
152 | Hussain, M. and Naeem, M. (2019d), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Mathe. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039 DOI |
153 | Hussain, M. and Naeem, M. (2019e), "Vibration characteristics of single-walled carbon nanotubes based on non-local elasticity theory using wave propagation approach (WPA) including chirality", Chapter, Intechopen, In: Perspective of Carbon Nanotubes. https://doi.org/10.5772/intechopen.85948 |
154 | Hussain, M. and Naeem, M.N. (2020a), "Mass density effect on vibration of zigzag and chiral SWCNTs", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636220906257 |
155 | Hussain, M. and Naeem, M.N. (2020b), "Vibration characteristics of zigzag FGM single-walled carbon nanotubes based on Ritz method with ring-stiffeners", Indian J. Phys. [In Press] |
156 | 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 Advances, 7(4), 045114. https://doi.org/10.1063/1.4979112 DOI |
157 | Hussain, M., Naeem, M., Shahzad, A. and He, M. (2018a), "Vibration characteristics of fluid-filled functionally graded cylindrical material with ring supports", Chapter, Intechopen, Computational Fluid Dynamics. ISBN 978-953-51-5706-9 https://doi.org/10.5772 /intechopen.72172 |
158 | Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019a), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., Int. J., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431 DOI |
159 | Hussain, M., Naeem, M.N., Shahzad, A., He, M. and Habib, S. (2018b), "Vibrations of rotating cylindrical shells with functionally graded material using wave propagation approach", IMechE Part C: J. Mech. Eng. Sci., 232(23), 4342-4356. https://doi.org/10.1177/0954406218802320 DOI |
160 | Hussain, M., Naeem, M.N. and Isvandzibaei, M. (2018c), "Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical sheel", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232(24), 4564-4577. https://doi.org/10.1177/0954406217753459 DOI |
161 | Hussain, M., Naeem, M.N. and Taj, M. (2019b), "Effect of length and thickness variations on the vibration of SWCNTs based on Flugge's shell model", Micro Nano Lett., 15(1), 1-6. https://doi.org/10.1049/mnl.2019.0309 DOI |
162 | Hussain, M., Naeem, M.N. and Tounsi, A. (2020a), "Simulating vibration of single-walled carbon nanotube using Rayleigh-Ritz's method", 8(3), 215-228. https://doi.org/10.12989/anr.2020.8.3.215 DOI |
163 | Hussain, M., Naeem, M.N. and Tounsi, A. (2020b), "On mixing the Rayleigh-Ritz formulation with Hankel's function for vibration of fluid-filled Fluid-filled cylindrical shell", Adv. Computat. Des., Int. J. [In Press] |
164 | Hussain, M., Naeem, M.N. and Tounsi, A. (2020c), "Numerical Study for nonlocal vibration of orthotropic SWCNTs based on Kelvin's model", Adv. Concrete Constr., Int. J., 9(3), 301-312. https://doi.org/10.12989/acc.2020.9.3.301 |
165 | Hussain, M., Naeem, M.N. and Tounsi, A. (2020d), "Response of orthotropic Kelvin modeling for single-walled carbon nanotubes: Frequency analysis", Adv. Nano Res., Int. J., 8(3), 229-244. https://doi.org/10.12989/anr.2020.8.3.229 |