RETRACTED ARTICLE: Investigation of Thermal Impacts and Different Gradient Elasticity Theories on Wave Propagation through the Polymer Matrix Incorporated Carbon Nanotube Walls
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Abstract
Abstract This paper explores the vibrational properties of double-walled carbon nanotubes embedded in a polymer matrix within different gradient elasticity theories. The study considers how the mechanical behavior of double-walled carbon nanotubes and the polymer matrix changes with temperature. The research highlights the significance of scale effects on wave propagation in double-walled carbon nanotubes and shows that certain characteristics of transverse vibrations in double-walled carbon nanotubes are affected by temperature variations. In addition, the paper derives consistent governing equations for modeling free transverse vibrations of double-walled carbon nanotubes using the nonlocal Euler–Bernoulli beam model, considering the effects of temperature and Van der Waals forces between the inner and outer nanotubes.
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OpenAlex topics: Carbon Nanotubes in Composites · Mechanical and Optical Resonators · Smart Materials for Construction
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References (63)
Show source-provided references
1. Iijima, S., Helical Microtubules of Graphitic Carbon, Nature, 1991, vol. 354(6348), pp. 56–58. https://doi.org/10.1038/354056a010.1038/354056a0 ↗
2. Poncharal, P., Wang, Z.L., Ugarte, D., and de Heer, W.A., Electrostatic Deflections and Electromechanical Resonances of Carbon Nanotubes, Science, 1999, vol. 283, pp. 1513–1516. https://doi.org/10.1126/science.283.5407.151310.1126/science.283.5407.1513 ↗
3. Yu, M.-F., Lourie, O., Dyer, M.J., Moloni, K., Kelly, T.F., and Ruoff, R.S., Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes under Tensile Load, Science, 2000, vol. 287, pp. 637–640. https://doi.org/10.1126/science.287.5453.63710.1126/science.287.5453.637 ↗
4. Kahn, D., Kim, K.W., and M.A. Stroscio, Quantized Vibrational Modes of Nanospheres and Nanotubes in the Elastic Continuum Model, J. Appl. Phys., 2001, vol. 89, pp. 5107–5111. https://doi.org/10.1063/1.135642910.1063/1.1356429 ↗
5. Harik, V.M., Ranges of Applicability for the Continuum-Beam Model in the Mechanics of Carbon Nanotubes and Nanorods, Solid State Commun., 2001, vol. 120, pp. 331–335.10.1016/S0038-1098(01)00383-0 ↗
6. Wang, Q., Effective In-Plane Stiffness and Bending Rigidity of Armchair and Zigzag Carbon, Int. J. Solids Struct., 2004, vol. 41, pp. 5451–5461.10.1016/j.ijsolstr.2004.05.002 ↗
7. Zhang, Y.Q., Liu, G.R., and Han, X., Transverse Vibrations of Double-Walled Carbon Nanotubes under Compressive Axial Load, Phys. Lett. A, 2005, vol. 340, pp. 258–266. https://doi.org/10.1016/j.physleta.2005.03.06410.1016/j.physleta.2005.03.064 ↗
8. Zhang, Y.Q., Liu, G.R., and Xie, X.Y., Free Transverse Vibrations of Double-Walled Carbon Nanotubes Using a Theory of Nonlocal Elasticity, Phys. Rev. B, 2005, vol. 71, p. 195404.10.1103/PhysRevB.71.195404 ↗
9. Wang, Q., Hu, T., Chen, G., and Jiang, Q., Bending Instability Characteristics of Double-Walled Carbon Nanotubes, Phys. Rev. B, 2005, vol. 71, p. 045403. https://doi.org/10.1103/PhysRevB.71.04540310.1103/PhysRevB.71.045403 ↗
10. Sun, C. and Liu, K., Vibration of Multi-Walled Carbon Nanotubes with Initial Axial Loading, Solid State Commun., 2007, vol. 143, pp. 202–207.10.1016/j.ssc.2007.05.027 ↗
11. Heireche, H., Tounsi, A., Benzair, A., Maachou, M., and Adda Bedia, E.A., Sound Wave Propagation in Single-Walled Carbon Nanotubes Using Nonlocal Elasticity, Physica E. Low-Dimens. Syst. Nanostruct., 2008, vol. 40, pp. 2791–2799. https://doi.org/10.1016/j.physe.2007.12.02110.1016/j.physe.2007.12.021 ↗
12. Amara, K., Tounsi, A., Mechaba, I., and Adda Bedia, E.A., Nonlocal Elasticity Effect on Column Buckling of Multiwalled Carbon Nanotubes under Temperature Field, Appl. Math. Modell., 2010, vol. 34, pp. 3933–3942. https://doi.org/10.1016/j.apm.2010.03.02910.1016/j.apm.2010.03.029 ↗
13. Iijima, S., Brabec, C., Maiti, A., and Bernholc, J., Structural Flexibility of Carbon Nanotubes, J. Chem. Phys., 1996, vol. 104, pp. 2089–2092. http://dx.doi.org/10.1063/1.470966
14. Yakobson, B.I., Campbell, M.P., Brabec, C.J., and Bernholc, J., High Strain Rate Fracture, and C-Chain Unraveling in Carbon Nanotubes, Comput. Mater. Sci., 1997, vol. 8, pp. 341–348.10.1016/S0927-0256(97)00047-5 ↗
15. Hernandez, E., Goze, C., Bernier, P., and Rubio, A., Elastic Properties of C and BxCyNz Composite Nanotubes, Phys. Rev. Lett., 1998, vol. 80, pp. 4502–4505. https://doi.org/10.1103/Phys-RevLett.80.450210.1103/Phys-RevLett.80.4502 ↗
16. Sanchez-Portal, D., Artacho, E., Soler, J.M., Rubio, A., and Ordejo, P., Ab Initio Structural, Elastic, and Vibrational Properties of Carbon Nanotubes, Phys. Rev. B, 1999, vol. 59, no. 19, pp. 12678–12688. https://doi.org/10.1103/PhysRevB.59.1267810.1103/PhysRevB.59.12678 ↗
17. Yakobson, B.I., Brabec, C.J., and Bernholc, J., Nanomechanics of Carbon Tubes: Instabilities beyond Linear Response, Phys. Rev. Lett., 1996, vol. 76, No. 14, pp. 2511–2514. https://doi.org/10.1103/PhysRevLett.76.251110.1103/PhysRevLett.76.2511 ↗
18. Peddieson, J., Buchanan, G.R., and McNitt, R.P., Application of Nonlocal Continuum Models to Nanotechnology, Int. J. Eng. Sci., 2003, vol. 41, no. 3, pp. 305–312. https://doi.org/10.1016/S0020-7225(02)00210-0810.1016/S0020-7225(02)00210-08 ↗
19. Eringen, A.C., On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves, J. Appl. Phys., 1983, vol. 54(9), pp. 4703–4710.10.1063/1.332803 ↗
20. Sudak, L.J., Column Buckling of Multiwalled Carbon Nanotubes Using Nonlocal Continuum Mechanics, J. Appl. Phys., 2003, vol. 94(11), pp. 7281–7287. https://doi.org/10.1063/1.162543710.1063/1.1625437 ↗
21. Zhang, Y.Q., Liu, G.R., and Wang, J.S., Small-Scale Effects on Buckling of Multiwalled Carbon Nanotubes under Axial Compression, Phys. Rev. B, 2004, vol. 70(20), p. 205430. https://doi.org/10.1103/physrevb.70.20543010.1103/physrevb.70.205430 ↗
22. Wang, L.F. and Hu, H.Y., Flexural Wave Propagation in Single-Walled Carbon Nanotubes, Phys. Rev. B, 2005, vol. 71, p. 195412.10.1103/PhysRevB.71.195412 ↗
23. Wang, Q. and Varadan, V.K., Stability Analysis of Carbon Nanotubes Via Continuum Models, Smart Mater. Struct., 2005, vol. 14, pp. 281–286. https://doi.org/10.1088/0964-1726/14/1/02910.1088/0964-1726/14/1/029 ↗
24. Wang, Q., Wave Propagation in Carbon Nanotubes Via Nonlocal Continuum Mechanics, J. Appl. Phys., 2005, vol. 98(12), p. 124301. https://doi.org/10.1063/1.214164810.1063/1.2141648 ↗
25. Wang, Q., Zhou, G.Y., and Lin, K.C., Scale Effect on Wave Propagation of Double-Walled Carbon Nanotubes, Int. J. Solids Struct., 2006, vol. 43, pp. 6071–6084.10.1016/j.ijsolstr.2005.11.005 ↗
26. Lu, P., Lee, H.P., Lu, C., and Zhang, P.Q., Dynamic Properties of Flexural Beams Using a Nonlocal Elasticity Model, J. Appl. Phys., 2006, vol. 99, p. 073510. https://doi.org/10.1063/1.218921310.1063/1.2189213 ↗
27. Lu, P., Lee, H.P., Lu, C., and Zhang, P.Q., Application of Nonlocal Beam Models for Carbon Nanotubes, Int. J. Solids Struct., 2007, vol. 44, pp. 5289–5300. https://doi.org/10.1016/j.ijsolstr.2006.12.03410.1016/j.ijsolstr.2006.12.034 ↗
28. Wang, X. and Cai, H., Effects of Initial Stress on Non-Coaxial Resonance of Multi-Wall Carbon Nanotubes, Nanotechnology, 2006, vol. 17, pp. 45–53.10.1088/0957-4484/17/1/009 ↗
29. Wang, X. and Cai, H., Crystallographic Features of Lath Martensite in Low-Carbon Steel, Acta Mater., 2006, vol. 54, p. 2067.10.1016/j.actamat.2005.12.039 ↗
30. Lu, P., J. Appl. Phys., 2006, vol. 101, p. 07350410.1063/1.2717140 ↗
31. Wang, H. and Li, Z., Diffusive Shrinkage of a Void within a Grain of a Stressed Polycrystal, J. Mech. Phys. Solids, 2003, vol. 51, pp. 961–976.10.1016/S0022-5096(02)00039-X ↗
32. Wang, H. and Li, Z., Phys. Metall. Mater. Sci., 2003, vol. 34, p. 1493.10.1007/s11661-003-0261-3 ↗
33. Wang, H. and Li, Z., J. Mater. Sci., 2004, vol. 39, p. 3425.10.1023/B:JMSC.0000026945.89767.25 ↗
34. Treacy, M.M., Ebbesen, T.W., and Gibson, J.M., Exceptionally High Young’s Modulus Observed for Individual Carbon Nanotubes, Nature, 1996, vol. 381, pp. 678–680. https://doi.org/10.1038/381678a010.1038/381678a0 ↗
35. Yu, J., Kalia, R.K., and Vashishta, P., Phonons in Graphitic Tubules: A Tight-Binding Molecular Dynamics Study, J. Chem. Phys., 1995, vol. 103, pp. 6697–6705.10.1063/1.470400 ↗
36. Popov, V.N., van Doren, V.E.V., and M. Balkanski, Elastic Properties of Single-Walled Carbon Nanotubes, Phys. Rev. B, 2000, vol. 61, p. 3078.10.1103/PhysRevB.61.3078 ↗
37. Reulet, B., Kasumov, A.Yu., Kociak, M., Deblock, R., Khodos, I.I., Gorbatov, Yu.B., Volkov, V.T., Journet, C., and Bouchiat, H., Acoustoelectric Effects in Carbon Nanotubes, Phys. Rev. Lett., 2000, vol. 85, p. 2829. https://doi.org/10.1103/PhysRevLett.85.282910.1103/PhysRevLett.85.2829 ↗
38. Wang, X.Y. and Wang, X., Composites B, 2004, vol. 35, p. 79.10.1016/S1359-8368(03)00084-2 ↗
39. Wang, X., Zhang, Y.C., Xia, X.H., and Huang, C.H., Effective Bending Modulus of Carbon Nanotubes with Rippling Deformation, Int. J. Solids Struct., 2004, vol. 41, pp. 6429–6439. https://doi.org/10.1016/j.ijsolstr.200410.1016/j.ijsolstr.2004 ↗
40. Govindjee, S. and Sackman, J.L., On the Use of Continuum Mechanics to Estimate the Properties of Nanotubes, Solid State Commun., 1999, vol. 110, pp. 227–230. https://doi.org/10.1016/S0038-1098(98)00626-710.1016/S0038-1098(98)00626-7 ↗
41. Harik, V.M., Mechanics of Carbon Nanotubes: Applicability of the Continuum-Beam Models, Comput. Mater. Sci., 2002, vol. 24, pp. 328–342.10.1016/S0927-0256(01)00255-5 ↗
42. Yoon, J., Ru, C.Q., and Mioduchowski, A., Noncoaxial Resonance of an Isolated Multiwall Carbon Nanotube, Phys. Rev. B, 2002, vol. 66, p. 233402. https://doi.org/10.1103/PhysRevB.66.23340210.1103/PhysRevB.66.233402 ↗
43. Yoon, J., Ru, C.Q., and Mioduchowski, A., Vibration of an Embedded Multiwall Carbon Nanotube, Compos. Sci. Technol., 2003, vol. 63, pp. 1533–1542. https://doi.org/10.1016/S0266-3538(03)00058-710.1016/S0266-3538(03)00058-7 ↗
44. Yoon, J., Ru, C.Q., and Mioduchowski, A., Sound Wave Propagation in Multiwall Carbon Nanotubes, J. Appl. Phys., 2003, vol. 93(8), pp. 4801–4806. https://doi.org/10.1063/1.155993210.1063/1.1559932 ↗
45. Ru, C.Q., Column Buckling of Multiwalled Carbon Nanotubes with Interlayer Radial Displacements, Phys. Rev. B, 2000, vol. 62, p. 16962. https://doi.org/10.1103/PhysRevB.62.1696210.1103/PhysRevB.62.16962 ↗
46. Tien, D.M., Thom, D.V., Van, N.T.H., Tounsi, A., Minh, P.V., and Mai, D.N., Buckling and Forced Oscillation of Organic Nanoplates Taking the Structural Drag Coefficient into Account, Comp. Conc., 2023, vol. 32(6), p. 553.
47. Abouelregal, A.E., Sofiyev, A.H., Sedighi, H.M., and Fahmy, M.A., Generalized Heat Equation with the Caputo–Fabrizio Fractional Derivative for a Nonsimple Thermoelastic Cylinder with Temperature-Dependent Properties, Phys. Mesomech., 2023, vol. 26, no. 2, pp. 224–240. https://doi.org/10.1134/S102995992302010810.1134/S1029959923020108 ↗
48. Abouelregal, A.E., Alanazi, R., Sofiyev, A.H., and Sedighi, H.M., Thermal Analysis of a Rotating Micropolar Medium Using a Two-Temperature Micropolar Thermoelastic Model with Higher-Order Time Derivatives, Phys. Mesomech., 2023, vol. 26, no. 3, pp. 251–266. https://doi.org/10.1134/S102995992303002510.1134/S1029959923030025 ↗
49. Nasri, W., Djebali, R., Chamkha, A.J., and Bezazi, A., Thermal Behavior of Mesoporous Aramid Fiber Reinforced Silica Aerogel Composite for Thermal Insulation Applications: Microscale Modeling, J. Appl. Comput. Mech., 2024, vol. 10(1), p. 1.
50. Kumar, Y., Gupta, A., and Tounsi, A., Size-Dependent Vibration Response of Porous Graded Nanostructure with FEM and Nonlocal Continuum Model, Adv. Nano Res., 2021, vol. 11(1), p. 1.
51. Vinh, P.V. and Tounsi, A., The Role of Spatial Variation of the Nonlocal Parameter on the Free Vibration of Functionally Graded Sandwich Nanoplates, Eng. Comp., 2022, vol. 38, p. 4301.10.1007/s00366-021-01475-8 ↗
52. Vinh, P.V. and Tounsi, A., Dynamics of Imperfect Inhomogeneous Nanoplate with Exponentially-Varying Properties Resting on Viscoelastic Foundation, Eur. J. Mech. A. Solids, 2022, vol. 95, p. 104649.10.1016/j.euromechsol.2022.104649 ↗
53. Garg, A., Belarbi, M.O., Tounsi, A., Li, L., Singh, A., and Mukhopadhyay, T., Predicting Elemental Stiffness Matrix of FG Nanoplates Using Gaussian Process Regression Based Surrogate Model in Framework of Layerwise Model, Eng. Anal. Boun. Elem., 2022, vol. 143, p. 779.10.1016/j.enganabound.2022.08.001 ↗
54. Cuong-Le, T., Nguyen, K.D., Le-Minh, H., Phan-Vu, P., Nguyen-Trong, P., and Tounsi, A., Nonlinear Bending Analysis of Porous Sigmoid FGM Nanoplate via IGA and Nonlocal Strain Gradient Theory, Adv. Nano Res., 2022, vol. 12(5), p. 441.
55. Vinh, P.V. and Tounsi, A., Free Vibration Analysis of Functionally Graded Doubly Curved Nanoshells Using Nonlocal First-Order Shear Deformation Theory with Variable Nonlocal Parameters, Thin-Wall. Struct., 2022, vol. 174, p. 109084.10.1016/j.tws.2022.109084 ↗
56. Timoshenko, S.P., On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars, Philos. Mag., 1921, vol. 41(245), pp. 744–746. https://doi.org/10.1080/1478644210863626410.1080/14786442108636264 ↗
57. Weaver, W., Timoshenko, S.P., and Young, D.H., Vibration Problems in Engineering, New York: Wiley, 1990.
58. Bouazza, M., Amara, Kh., Zidour, M., Tounsi, A., and Adda Bedia, E., Thermal Effect on Buckling of Multiwalled Carbon Nanotubes Using Different Gradient Elasticity Theories, Nanosci. Nanotechnol., 2014, vol. 4(2), pp. 27–33.
59. Amara, Kh., Youbb, O., Bouazza, M., Tounsi, A., and Adda Bedia, E., Influence of Temperature Change on Column Buckling of Double walled Carbon Nanotubes Using Different Theories, Energy Proc., 2014, vol. 50, pp. 634–641.10.1016/j.egypro.2014.06.078 ↗
60. Wang, B.L., Hoffman, M., and Yu, A.B., Buckling Analysis of Embedded Nanotubes Using Gradient Continuum Theory, Mech. Mater., 2012, vol. 45, pp. 52–60.10.1016/j.mechmat.2011.10.003 ↗
61. Zhang, Y.C. and Wang, X., Thermal Effects on Interfacial Stress Transfer Characteristics of Carbon Nanotubes/Polymer Composites, Int. J. Solids Struct., 2005, vol. 42, pp. 5399–5412. https://doi.org/10.1016/j.ijsolstr.2005.02.03810.1016/j.ijsolstr.2005.02.038 ↗
62. Mallick, P.K., Composites Engineering: Handbook, USA: Marcel Dekker, 1997.10.1201/9781482277739 ↗
63. Shen, H.S., Hygrothermal Effects on the Post Buckling of Shear Deformable Laminated Plates, Int. J. Mech. Sci., 2001, vol. 43, pp. 1259–1281.10.1016/S0020-7403(00)00058-8 ↗