Browse > Article
http://dx.doi.org/10.12989/acc.2022.13.6.471

Elastic shell model: Effect of Young's Modulus on the vibration of double-walled CNTs  

Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad)
Asghar, Sehar (Department of Mathematics, Govt. College University Faisalabad)
Khadimallah, Mohamed Amine (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department)
Ayed, Hamdi (Department of Civil Engineering, College of Engineering, King Khalid University)
Banoqitah, Essam Mohammed (Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University)
Loukil, Hassen (Department of Electrical Engineering, College of Engineering, King Khalid University)
Ali, Imam (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department)
Mahmoud, S.R. (GRC Department, Faculty of Applied studies, King Abdulaziz University)
Tounsi, Abdelouahed (YFL (Yonsei Frontier Lab), Yonsei University)
Publication Information
Advances in concrete construction / v.13, no.6, 2022 , pp. 471-479 More about this Journal
Abstract
In this paper, vibrational attributes of double-walled carbon nanotubes (CNTs) has been studied based upon nonlocal elastic shell theory. The implication of small scale is being perceived by establishing nonlocal Love shell model. The wave propagation approach has been operated to frame the governing equations as eigen value system. The comparison of local and nonlocal model has been overtly explored by means of scaling parameter. An appropriate selection of material properties and nonlocal parameter has been considered. The influence of changing mechanical parameter Young's modulus has been studied in detail. The dominance of end condition via nonlocal parameter is explained graphically. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.
Keywords
double-walled CNTs; Love shell theory; nonlocal parameter; Poisson's ratio; vibration;
Citations & Related Records
Times Cited By KSCI : 11  (Citation Analysis)
연도 인용수 순위
1 Mehar, K. and Panda, S.K. (2018c), "Elastic bending and stress analysis of carbon nanotube-reinforced composite plate: Experimental, numerical, and simulation", Adv. Polym. Technol., 37(6), 1643-1657. https://doi.org/10.1002/adv.21821.   DOI
2 Mehar, K. and Panda, S.K. (2018d), "Thermoelastic flexural analysis of FG-CNT doubly curved shell panel", Aircraft Eng. Aerosp. Technol., 90(1), 11-23. https://doi.org/10.1108/AEAT11-2015-0237.   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.2019.9.3.181.   DOI
4 Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018a), "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. (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
6 Mehar, K., Panda, S.K. andMahapatra, T.R. (2018d), "Nonlinear frequency responses of functionally graded carbon nanotube-reinforced sandwich curved panel under uniform temperature field", Int. J. Appl Mech., 10(03), 1850028. https://doi.org/10.1142/S175882511850028X.   DOI
7 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
8 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
9 Mehar, K., Panda, S.K. and Patle, B.K. (2018c), "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
10 Basirjafari, S., Esmaeilzadeh Khadem, S. and Malekfar, R. (2013), "Validation of shell theory for modeling the radial breathing mode of a single-walled carbon nanotube", Int. J. Eng. Trans. A, 26(4), 447-454.
11 Budiansky, B. (1963), "On the'best'first-order linear shell theory", The Prager Anniversary Volume-Progress in Applied Mechanics.
12 Cirak, F., Ortiz, M. and Pandolfi, A. (2005), "A cohesive approach to thin-shell fracture and fragmentation", Comput. Meth. Appl. Mech. Eng., 194(21-24), 2604-2618. https://doi.org/10.1016/j.cma.2004.07.048.   DOI
13 Hernandez, E., Goze, C., Bemier, P. and Rubio, A. (1998), "Elastic properties of C and BxCyNz composite nanotubes", Phys. Rev. Lett., 80, 4502-505. https://doi.org/10.1103/PhysRevLett.80.4502.   DOI
14 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
15 Liew, K.M. and Wang, Q. (2007), "Analysis of wave propagation in carbon nanotubes via elastic shell theories", Int. J. Eng. Sci., 45(2-8), 227-241. https://doi.org/10.1016/j.ijengsci.2007.04.001.   DOI
16 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
17 Rabczuk, T., Areias, P.M.A. and Belytschko, T. (2007), "A meshfree thin shell method for non-linear dynamic fracture", Int. J. Numer. Meth. Eng., 72(5), 524-548. https://doi.org/10.1002/nme.2013.   DOI
18 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://doi.org/10.1103/PhysRevB.59.12678.   DOI
19 Simsek M. (2011), "Forced vibration of an embedded single-walled carbon nanotube traversed by a moving load using nonlocal Timoshenko beam theory", Steel Compos. Struct., 11(1), 59-76. https://doi.org/10.12989/scs.2011.11.1.059.   DOI
20 Sosa, E.D., Darlington, TK., Hanos, B.A. and O'Rourke, M.J.E. (2014), "Multifunctional thermally remendable nanocomposites", J. Compos., 2014, Article ID 705687. http://doi.org/10.1155/2014/705687.   DOI
21 Torkaman-Asadi, M.A., Rahmanian, M. and Firouz-Abadi, R.D. (2015), "Free vibrations and stability of high-speed rotating carbon nanotubes partially resting on Winkler foundations", Compos. Struct., 126, 52-61. https://doi.org/10.1016/j.compstruct.2015.02.037.   DOI
22 Wang, Q. Varadan, V.K. and Quek, S.T. (2006), "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
23 Mehar, K. and Panda, S.K. (2018e), "Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure", Struct. Eng. Mech., 67(6), 565-578. https://doi.org/10.12989/sem.2018.67.6.565.   DOI
24 Karami B, Janghorban, M. and Tounsi, A. (2018), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.   DOI
25 Li, C. and Chou, T.W. (2003), "A structural mechanics approach for the analysis of carbon nanotubes", Int. J. Solid. Struct., 40(10), 2487-249992. https://doi.org/10.1016/S0020-7683(03)00056-8.   DOI
26 Love, A.E.H. (2013), A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press.
27 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.   DOI
28 Yakobson, B.I., Brabec, C.J. and Bernholc, J. (1996), "Nano-mechanics of carbon tubes: instabilities beyond linear response", Phy. Rev. Lett., 76, 2511-2514. https://doi.org/10.1103/PhysRevLett.76.2511.   DOI
29 Iijima, S., Brabec, C., Maiti, A., Bemholc, J. (1996), "Structural flexibility of carbon nanotubes", J. Chem. Phys., 104(5), 2089-2092. https://doi.org/10.1063/1.470966.   DOI
30 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
31 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", Measure., 73, 127-136. https://doi.org/10.1016/j.measurement.2015.05.009.   DOI
32 Alibeigloo, A. and Shaban, M. (2013). "Free vibration analysis of carbon nanotubes by using three-dimensional theory of elasticity", Acta Mechanica, 224(7), 1415-1427. https://doi.org/10.1007/s00707-013-0817-2.   DOI
33 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., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147.   DOI
34 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
35 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
36 Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(1), 56-58. https://doi.org/10.1038/354056a0.   DOI
37 Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/scs.2017.25.3.361.   DOI
38 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
39 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(04), 1750046. https://doi.org/10.1142/S1758825117500466.   DOI
40 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. Therm. Stress., 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689.   DOI
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., 24(3), 359-367. https://doi.org/10.12989/scs.2017.24.3.359.   DOI
42 Rayleigh, L. (1882), "On the equilibrium of liquid conducting masses charged with electricity", London, Edinburgh, Dublin Philos. Mag. J. Sci., 14(87), 184-186.   DOI
43 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
44 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. Sci., 8(4), 341-348. https://doi.org/10.1016/S0927-0256(97)00047-5.   DOI
45 Ansari, R., Hemmatnezhad, M. and Rezapour, J. (2011), "The thermal effect on nonlinear oscillations of carbon nanotubes with arbitrary boundary conditions", Curr. Appl. Phys., 11(3), 692-697. https://doi.org/10.1016/j.cap.2010.11.034.   DOI
46 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
47 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., 54(4), 693-710. http://doi.org/10.12989/sem.2015.54.4.693.   DOI
48 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
49 Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Science and Business Media, New York.
50 Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., 21(1), 65-74. https://doi.org/10.12989/sss.2018.21.1.065.   DOI
51 Zhang, X.M., Liu, G.R. and Lam, K.Y. (2001), "Vibration analysis of thin cylindrical shells using wave propagation approach", J. Sound Vib., 239(3), 397-403. https://doi.org/10.1006/jsvi.2000.3139.   DOI
52 Love, A.E.H. (1888), "The small free vibrations and deformation of a thin elastic shell", Proc. Roy. Soc. London Ser. I, 43, 352-353.   DOI
53 Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889.   DOI
54 Markus, S. (1988), Mechanics of Vibrations of Cylindrical Shells, Amsterdam.
55 Mehar, K. and Panda, S.K. (2016b), "Free vibration and bending behaviour of CNT reinforced composite plate using different shear deformation theory", IOP Conf. Ser.: Mater. Sci. Eng., 115(1), 012014.   DOI
56 Mehar, K. and Panda, S.K. (2018a), "Dynamic response of functionally graded carbon nanotube reinforced sandwich plate", IOP Conf. Ser.: Mater. Sci. Eng., 338(1), 012017.   DOI
57 Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018b), "Thermoelastic deflection responses of CNT reinforced sandwich shell structure using finite element method", Scientia Iranica, 25(5), 2722-2737.
58 Yoon, J., Ru, C.Q. and Mioduchowski. A. (2003), "Vibration of an embedded multiwall carbon nanotube", Compos. Sci. Technol., 63(11), 1533-1542. https://doi.org/10.1016/S0266-3538(03)00058-7.   DOI