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http://dx.doi.org/10.12989/cac.2020.25.2.133

Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis  

Asghar, Sehar (Department of Mathematics, Govt. College University Faisalabad)
Naeem, Muhammad N. (Department of Mathematics, Govt. College University Faisalabad)
Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad)
Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir)
Tounsi, Abdelouahed (Materials and Hydrology Laboratory, University of SidiBel Abbes, Algeria Faculty of Technology Civil Engineering Department)
Publication Information
Computers and Concrete / v.25, no.2, 2020 , pp. 133-144 More about this Journal
Abstract
This paper aims to study vibration characteristics of chiral and zigzag double-walled carbon nanotubes entrenched on Donnell shell model. The Eringen's nonlocal elastic equations are being combined with Donnell shell theory to observe small scale response. Wave propagation is proposed technique to establish field equations of model subjected to four distinct end supports. A nonlocal model has been formulated to explore the frequency spectrum of both chiral and zigzag double-walled CNTs along with diversity of indices and nonlocal parameter. The significance of scale effect in relevance of length-to-diameter and thickness- to- radius ratios are discussed and displayed in detail. The numerical solution based on this nonlocal Donnell shell model can be further used to predict other frequency phenomena of double-walled and multi-walled CNTs.
Keywords
CNT; Chiral and zigzag; nonlocal parameter; Donnell shell model;
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1 Lu, Y.J., Wang, X. and Lu, G. (2007), "Buckling of embedded multi-walled carbon nanotubes under combined torsion and axial loading", Int. J. Solid. Struct., 44(1), 336-351. https://doi.org/10.1016/j.ijsolstr.2006.04.031.   DOI
2 Mehar, K. and Kumar Panda, S. (2018), "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
3 Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181. https://doi.org/10.12989/anr.2019.7.3.181.   DOI
4 Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018), "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
5 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/Solid., 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005.   DOI
6 Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017b), "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
7 Mehar, K., Panda, S.K. and Patle, B.K. (2018), "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
8 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
9 Mori, H., Hirai, Y., Ogata, S., Akita, S. and Nakayama, Y. (2005), "Chirality dependence of mechanical properties of single walled cabon nanotubes under axial tensile strain", JPN J. Appl. Phys., 44(2), 42-45. https://doi.org/10.1143/JJAP.44.L1307.
10 Mumrmu, T. and Pradhan, S.C. (2010), "Thermal effects on the stability of embedded carbon nanotubes", Comput. Mater. Sci., 47(3), 721-726. https://doi.org/10.1016/j.commatsci.2009.10.015.   DOI
11 Nejad, M.Z., Hadi, A. and Rastgoo, A. (2016), "Buckling analysis of arbitrary two-directional functionally graded Euler-Bernonllinano-beams based on non-local elasticity theory", Eng. Sci., 103, 1-10. https://doi.org/10.1016/j.ijengsci.2016.03.001.
12 Nogales, E. (2001), "Structural insights into microtubule function", Ann. Rev. Biophys. Biomol. Struct., 30(1), 397-420. https://doi.org/10.1146/annurev.biophys.30.1.397.   DOI
13 Pradhan, S.C. and Reddy, G.K. (2011), "Thermo mechanical buckling analysis of carbon nanotubes on Winkler foundation using non-local elasticity theory and DTM", Sadhana, 36(6), 1009-1019. https://doi.org/10.1007/s12046-011-0052-2.   DOI
14 Rafiee, R. and Moghadam, R.M. (2014), "On the modeling of carbon nanotubes: A critical review", Compos. Part B: Eng., 56, 435-449. https://doi.org/10.1016/j.compositesb.2013.08.037.   DOI
15 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., 4(1), 31-44. http://dx.doi.org/10.12989/anr.2016.4.1.031.   DOI
16 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., 32(5), 595-610. https://doi.org/10.12989/scs.2019.33.6.805.   DOI
17 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
18 Regi, M. (2007), "6-synthesis, characteristics and applications of carbon nanotubes: the case of aerospace engineering", Nanofib. Nanotech. Textil., 113-193. https://doi.org/10.1533/9781845693732.2.113.
19 Reilly, R.M. (2007), "Carbon nanotubes: Potential benefits and risks of nanotechnology in nuclear medicine", J. Nucl. Med., 48(7), 1039-1042. http://doi.org/10.2967/jnumed.107.041723.   DOI
20 Sharma, P., Singh, R. and Hussain, M. (2019), "On modal analysis of axially functionally graded material beam under hygrothermal effect", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 10.1177/0954406219888234, 2019.
21 Soldano, C. (2015), "Hybrid metal-based carbon nanotubes: Novel platform for multifunctional applications", Prog. Mater. Sci., 69, 183-212. https://doi.org/10.1016/j.pmatsci.2014.11.001.   DOI
22 Sosa, E.D., Darlington, T.K., Hanos, B.A. and O'Rourke, M.J.E. (2014), "Multifunctional thermally remendable nanocomposites", J. Compos., Article ID 705687, 12. http://dx.doi.org/10.1155/2014/705687.
23 Wang, C.M., Ma, Y.Q., Zhang, Y.Y. and Ang, K.K. (2006), "Buckling of double-walled carbon nanotubes modeled by solid shell elements", J. Appl. Phys., 99(11), 114317-114312. https://doi.org/10.1063/1.2202108.   DOI
24 Wang, Q. and Liew, K.M. (2007), "Application of nonlocal continuum mechanics to static analysis of micro-and nano-structures", Phys. Lett. A, 363, 236-242. https://doi.org/10.1016/j.physleta.2006.10.093.   DOI
25 Zidour, M., Benrahou, K., Semmah, A.W., Naceri, M., Belhadj, H.A., Bakhti, K. and Tounsi, A. (2012), "The thermal effect on vibration of single walled carbon nanotubes using nonlocal Timoshenko beam theory", J. Comput. Mater. Sci., 51(1), 252-260. https://doi.org/10.1016/j.commatsci.2011.07.021.   DOI
26 Xu, K.Y., 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. https://doi.org/10.1115/1.2793133.   DOI
27 Zhang, Y.Q., Liu, G.R. and Xie, X.Y. (2005), "Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity", Phys. Rev. B, 71(19), 195404. https://doi.org/10.1103/PhysRevB.71.195404.   DOI
28 Zhao, J., Buldum, A., Lu, J.P. and Han, J. (2002), "Gas molecule adsorption in carbon nanotubes and nanotubes bundles", Nanotechnol., 13(2), 195.   DOI
29 Zidour, M., Daouadji, T.H., Benrahou, K.H., Tounsi, A., AddaBedia, E.A. and Hadji, L. (2014), "Buckling analysis of chiral single-walled 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
30 Zidour, M., Daouadji, T.H., Benrahou, K.H., Tounsi, A., Bedia, E.A.A. and Hadji, L. (2014), "Buckling analysis of chiral single-walled carbon nanotubes by using nonlocal Timoshenko beam theory", Mech. Compos. Mater., 50(1), 95-104. https://doi.org/10.1007/s11029-014-9396-0.   DOI
31 Chang, W.J. and Lee, H.L. (2009), "Free vibration of single-walled carbon nanotubes containing a fluid flow using a Timoshenko beam model", Phys. Lett. A, 373(10), 982-985. https://doi.org/10.1016/j.physleta.2009.01.011.   DOI
32 Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale effects on mechanical 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
33 Bisen, H.B., Hirwani, C.K., Satankar, R.K., Panda, S.K., Mehar, K. and Patel, B. (2018), "Numerical study of frequency and deflection responses of natural fiber (Luffa) reinforced polymer composite and experimental validation", J. Nat. Fib., 1-15. https://doi.org/10.1080/15440478.2018.1503129.
34 Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and El Abbas, A.B. (2014), "Thermal effect on buckling of multiwalled carbon nanotubes using different gradient elasticity theories", Nanosci. Nanotechnol., 4(2) 27-33. https://doi.org/10.5923/j.nn.20140402.02.
35 Brischetto, S. (2014), "A continuum elastic three-dimensional model for natural frequencies of single walled carbon nanotubes", Compos. Part B: Eng., 61, 222-228. https://doi.org/10.1016/j.compositesb.2014.01.046.   DOI
36 Chang, T., Li, G. and Gua, X. (2005), "Elastic axial buckling of carbon nanotubes via molecular mechanics model", Carbon, 43, 287-294. https://doi.org/10.1016/j.carbon.2004.09.012.   DOI
37 Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A.A. (2015), "Critical buckling load chiral double-walled carbon nanotubes using non-local elasticity theory", Adv. Neno Res., 3(4), 193-206. https://doi.org/10.12989/anr.2015.3.4.193.   DOI
38 Cornwell, C.F and Wille, L.T. (1997), "Elastic properties of single-walled carbon nanotubes in compression", Solid State Commun., 101(8), 555-558. https://doi.org/10.1016/S0038-1098(96)00742-9.   DOI
39 Ebrahimi, F., Barati, M.R. and Mahesh, V. (2019), "Dynamic modeling of smart magneto-electro-elastic curved nanobeams", Adv. Nano Res., 7(3), 145-155. https://doi.org/10.12989/anr.2019.7.3.145.   DOI
40 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
41 Eltaher, M.A., Eman, S.A. and Mahmoud, F.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
42 Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.   DOI
43 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/10.1063/1.332803.   DOI
44 Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer Science and Business Media, New York.
45 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
46 Ghavanloo, E. and Fazelzadeh, S.A. (2009), "Vibrations characteristics of single walled carbon nanotubes based on the nonlocal Flugge shell theory". ASME J. Eng. Mater. Technol., 134, 011008. https://doi.org/10.1016/j.apm.2011.12.036.
47 Gohardani, O., Elola, M.C. and Elizetxea, C. (2014), "Potential and prospective implementation of carbon nanotubes on next generation aircraft and space vehicle: A review of current and expected applications in aerospace sciences", Prog. Aerosp. Sci., 70, 42-68. https://doi.org/10.1016/j.paerosci.2014.05.002.   DOI
48 Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and AddaBedia, E.A. (2008), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Physica E: Low Dimens. Syst. Nanostr., 40(8), 2791-2799. https://doi.org/10.1016/j.physe.2007.12.021.   DOI
49 Hao, X., Qiang, H. and Xiaouh, Y. (2008), "Buckling of defective single-walled and double-walled carbon nanotubes under axial compression by molecular dynamic simulation", Compos. Sci. Technol., 68(7-8), 1809-1814. https://doi.org/10.1016/j.compscitech.2008.01.013.   DOI
50 Hashemi, S.H., Ilkhani, M.R. and Fadaee, M. (2012), "Identification of the validity of the Donnell and Sanders shell theories using an exact vibration analysis of the functionally graded thick cylindrical shell panel", Acta Mechanica, 223(5), 1101-1118. https://doi.org/10.1007/s00707-011-0601-0.   DOI
51 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
52 Hu, Y.G., Liew, K.M. and Wang, Q. (2012), "Modeling of vibrations of carbon nanotube"s, Procedia Eng., 31, 343-347. https://doi.org/10.1016/j.proeng.2012.01.1034.   DOI
53 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. Solid., 56(12), 3475-3485. https://doi.org/10.1016/j.jmps.2008.08.010.   DOI
54 Hussain, M. and Naeem, M. (2018b), "Vibration of single-walled carbon nanotubes based on Donnell shell theory using wave propagation approach", Novel Nanomater. Synth. Appl., 18, 77. https://doi.org/10.5772/intechopen.73503.
55 Hussain, M. and Naeem, M. (2019c), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Math. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039.   DOI
56 Hussain, M. and Naeem, M.N. (2019), "Vibration characteristics of single-walled carbon nanotubes based on nonlocal elasticity theory using Wave Propagation Approach (WPA) Including Chirality", Perspective of Carbon Nanotubes. http://dx.doi.org/10.5772/intechopen.85948.
57 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 Dimens., 7(3), 1250081. https://doi.org/10.1142/S179329201250018X.
58 Ansari, R., Rouhi, H. and Arash, B. (2013), "Vibration analysis of double-walled carbon nanotubes based on the nonlocal donnell shell via a new numerical approach", Int. J. Sci. Technol. Tran. B: Eng., 37, 91-105.
59 Asghar, S., Hussain, M. and Naeem, M. (2019a), "Non-local effect on the vibration analysis of double walled carbon nanotubes based on Donnell shell theory", Physica E: Low Dimens. Syst. Nanostr., 116, 113726. https://doi.org/10.1016/j.physe.2019.113726.   DOI
60 Hussain, M. and Naeem, M.N. (2018a), "Effect of various edge conditions on free vibration characteristics of rectangular plates", Advance Testing and Engineering.
61 Hussain, M. and Naeem, M.N. (2019a), "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
62 Hussain, M. and Naeem, M.N. (2019b), "Vibration characteristics of zigzag and chiral FGM rotating carbon nanotubes sandwich with ring supports", J. Mech. Eng. Sci., Part C, 233(16), 5763-5780. https://doi.org/10.1177/0954406219855095.   DOI
63 Hussain, M., Naeem, M., Shahzad, A. and He, M, (2018a), "Vibration characteristics of fluid-filled functionally graded cylindrical material with ring supports", Comput Fluid Dyn Basic Instrum Appl Sci., 333. https://doi.org/10.5772/intechopen.72172.
64 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 shell", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 232(24), 4564-4577. https://doi.org/10.1177/0954406217753459.   DOI
65 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, 2019.   DOI
66 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
67 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., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.   DOI
68 Asghar, S., Hussain, M. and Naeem, M.N. (2019b), "Non-local effect on the vibration analysis of double walled carbon nanotubes based on Donnell shell theory", Physica E: Low Dimens. Syst. Nanostr., 116, 11326. https://doi.org/10.1016/j.physe.2019.113726.
69 Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.   DOI
70 Aydogdu, M. (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
71 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
72 Hussain, M., Naeem, M.N., Shahzad, A, He, M. and Habib, S. (2018b), "Vibrations of rotating cylindrical shells with FGM using wave propagation approach", IMechE Part C: J. Mech. Eng. Sci., 232(23), 4342-4356.   DOI
73 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., 7(6), 431. https://doi.org/10.12989/anr.2019.7.6.431.   DOI
74 Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2020), "Simulating vibration of single-walled carbon nanotube using Rayleigh-Ritz's method", Adv. Nano Res., 8(3).
75 Jamali, M., Shojaee, T., Mohammadi, B. and Kolahchi, R. (2019), "Cut out effect on nonlinear post-buckling behavior of FG-CNTRC micro plate subjected to magnetic field via FSDT", Adv. Nano Res., 7(6), 405-417. https://doi.org/10.12989/anr.2019.7.6.405.   DOI
76 Jorio, A., Saito, R., Hafner, J.H., Lieber, C.M., Hunter, M., McClure, T., Dresselhaus, G. and Dresselhaus, M.S. (2001), "Structural (n,m) determination of isolated single-wall carbon nanotubes by resonant raman scattering", Phys. Rev. Lett., 86(6) 1118-1121. https://doi.org/10.1103/PhysRevLett.86.1118.   DOI
77 Jung, N.Y. and Han, S.C. (2013), "Analysis of sigmoid functionally materials (S-FGM) nanoscale plates using nonlocal elasticity theory", Math. Prob. Eng., 476131. http://dx.doi.org/10.1155/2013/476131
78 Karami, B., Janghorban, M., Shahsavari, D., Dimitri, R., & Tornabene, F. (2019), "Nonlocal buckling analysis of composite curved beams reinforced with functionally graded carbon nanotubes", Molecul., 24, 2750, https://doi.org/10.3390/molecules24152750.   DOI
79 Ke, L.L., Xiang, Y., Yang, J. and Kitipornchai, S. (2009), "Non linear 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
80 Kasas, S., Cibert, C., Kis, A., De Rios, P.L., Riederer, B.M., Forro, L., Dietler, G. and Catsicas, S. (2004), "Oscillation modes of microtubules", Biology Cell, 96(9), 697-700. https://doi.org/10.1016/j.biolcel.2004.09.002.   DOI
81 Kolohchi, R., Bidholi, M.M. and Heydari, M.M. (2015), "Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., 55, 1001-1014. http://dx.doi.org/10.12989/sem.2015.55.5.1001.   DOI
82 Kostarelos, K., Bianco, A. and Prato, M. (2009), "Promises, facts and challenges for carbon nanotubes in imaging and therapeutics", Nat. Nanotechnol., 4(10), 627-633. https://doi.org/10.1038/nnano.2009.241.   DOI
83 Lau, K.T. and Hui, D. (2002), "The revolutionary creation of new advanced materials-carbon nanotube composites", Compos. Part B: Eng., 33(4), 263-277. https://doi.org/10.1016/S1359-8368(02)00012-4.   DOI
84 Li, R. and Kardomateas, G.A. (2007) "Vibration characteristics of multiwalled carbon nanotubes embedded in elastic media by a nonlocal elastic shell model", J. Appl. Mech., 74(6), 1087-1094. https://doi.org/10.1115/1.2722305.   DOI
85 Lieber, C.M. (2003), "Nanoscale science and technology building", MRS Bulletin. https://doi.org/10.1557/mrs2003.144.
86 Liew, K.M., Wong, C.H., He, X.Q. and Tan, M.J. (2005), "Thermal stability of single and multi-walled carbon nanotubes", Phys. Rev B, 71, 075424. https://doi.org/10.1103/PhysRevB.71.075424.   DOI
87 Liu, L. and Zang, Y. (2004), "Multi-wall carbon nanotubes as a new infrared detected material", Sens. Actu. A: Phys., 116(3), 394-339. https://doi.org/10.1016/j.sna.2004.05.016.   DOI