Browse > Article
http://dx.doi.org/10.12989/sem.2018.65.3.335

Free vibration analysis of chiral double-walled carbon nanotube embedded in an elastic medium using non-local elasticity theory and Euler Bernoulli beam model  

Dihaj, Ahmed (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes)
Zidour, Mohamed (Universite Ibn Khaldoun)
Meradjah, Mustapha (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes)
Rakrak, Kaddour (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes)
Heireche, Houari (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes)
Chemi, Awda (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes)
Publication Information
Structural Engineering and Mechanics / v.65, no.3, 2018 , pp. 335-342 More about this Journal
Abstract
The transverse free vibration of chiral double-walled carbon nanotube (DWCNTs) embedded in elastic medium is modeled by the non-local elasticity theory and Euler Bernoulli beam model. The governing equations are derived and the solutions of frequency are obtained. According to this study, the vibrational mode number, the small-scale coefficient, the Winkler parameter and chirality of double-walled carbon nanotube on the frequency ratio (xN) of the (DWCNTs) are studied and discussed. The new features of the vibration behavior of (DWCNTs) embedded in an elastic medium and the present solutions can be used for the static and dynamic analyses of double-walled carbon nanotubes.
Keywords
vibration; nanotube; zigzag; armchair; chirality; non-local;
Citations & Related Records
Times Cited By KSCI : 34  (Citation Analysis)
연도 인용수 순위
1 Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Modell., 39, 2489-2508.   DOI
2 Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., 18(3), 793-809.   DOI
3 Moradi-Dastjerdi, R. (2016), "Wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube", Struct. Eng. Mech., 57(3), 441-456.   DOI
4 Murmu, T. and Adhikari, S. (2010), "Thermal effects on the stability of embedded carbon nanotubes", Phys. E, 43, 415-422.   DOI
5 Pradhan, S.C. and Phadikar, J.K. (2009), "Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory", Struct. Eng. Mech., 33(2), 193-213.   DOI
6 Ranjbartoreh, A.R., Ghorbanpour, A. and Soltani, B. (2007), "Double-walled carbon nanotube with surrounding elastic medium under axial pressure", Phys. E, 39, 230-239.   DOI
7 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.   DOI
8 Sudak, L.J. (2003), "Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics", J. Appl. Phys., 94(11), 7281-7288.   DOI
9 Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011.   DOI
10 Adda Bedia, W., Benzair, A., Semmah, A., Tounsi, A. and Mahmoud, S.R. (2015), "On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity", Brazil. J. Phys., 45(2), 225-233.   DOI
11 Ahouel, M., Houari, M.S.A., Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981.   DOI
12 Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct. J., 19(2), 369-384.   DOI
13 Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165.   DOI
14 Akavci, S.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676.   DOI
15 Becheri, T., Amara K., Bouazza, M. and Benseddiq, N. (2016), "Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects", Struct., 21(6), 1347-1368.
16 Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630.   DOI
17 Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212.   DOI
18 Baghdadi, H., Tounsi, A., Zidour, M. and Benzair, A. (2015), "Thermal effect on vibration characteristics of armchair and zigzag single-walled carbon nanotubes using nonlocal Parabolic beam theory", Fulleren. Nanot. Carb. Nanostruct., 23, 266-272.   DOI
19 Bao, W.X., Zhu, C.C. and Cui, W.Z. (2004), "Simulation of Young's modulus of single-walled carbon nanotubes by molecular dynamics", Phys. B, 352, 156-163.   DOI
20 Batra, R.C. and Sears, A. (2007), "Continuum models of multi-walled carbon nanotubes", J. Sol. Stuct., 44, 7577-7596.   DOI
21 Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283.   DOI
22 Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., 18(4), 755-786.   DOI
23 Tu, Z.C. and Ou-Yang, Z.C. (2002), "Single-walled and multiwalled carbon nanotubes viewed as elastic tubes with the effective young's modulus dependent on layer number", Phys. Rev. B, 65, 233407.   DOI
24 Thostenson, E.T. and Chou, T.W. (2003), "On the elastic properties of carbon nanotube-based composites: Modelling and characterization", J. Phys. A-Appl. Phys., 36(5), 573-582.   DOI
25 Tokio, Y. (1995), Synthetic Metals, 70 1511.   DOI
26 Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerospace Sci. Technol., 24, 209-220.   DOI
27 Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four-variable refined plate theory", Aerospace Sci. Technol., 34, 24-34.   DOI
28 Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., 60(4), 547-565.   DOI
29 Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38(1), 265-275.   DOI
30 Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081.   DOI
31 Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higher order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15, 671-703.   DOI
32 Benferhat, R., Hassaine Daouadji, T., Hadji L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., 21(1), 123-136.   DOI
33 Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale rffects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B, 57, 21-24.   DOI
34 Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431.   DOI
35 Bouafia, K., Kaci, A., Houri, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., 19(2), 115-126.   DOI
36 Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249.   DOI
37 Bouazza, M., Becheri, T., Boucheta A. and Benseddiq, N. (2016), "Thermal buckling analysis of nanoplates based on nonlocal elasticity theory with four-unknown shear deformation theory resting on Winkler-Pasternak elastic foundation", J. Comput. Meth. Eng. Sci. Mech., (17) 5-6.
38 Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104.   DOI
39 Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422.   DOI
40 Boukhari, A., Ait Atmane, H., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., 57(5), 837-859.   DOI
41 Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249.   DOI
42 Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423.   DOI
43 Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297.   DOI
44 Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335.   DOI
45 Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", J. Comput. Meth., 11(6), 1350082.   DOI
46 Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A.A. (2015), "Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity", Adv. Nano Res., 3(4), 193-206.   DOI
47 Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: Potential and current challenges", Mater. Des., 28(9), 2394-2401.   DOI
48 Darilmaz, K. (2015) "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., 18(2), 395-408.   DOI
49 Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., 11(5), 671-690.   DOI
50 Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710.   DOI
51 Gupta, A. and Talha, M. (2016), "An assessment of a non-polynomial based higher order shear and normal deformation theory for vibration response of gradient plates with initial geometric imperfections", Compos. Part B Eng., 107.
52 Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccan., 49, 795-810.   DOI
53 Foroutan, M., Moradi-Dastjerdi, R. and Sotoodeh-Bahreini, R. (2012) "Static analysis of FGM cylinders by a mesh-free method", Steel Compos. Struct., 12(1), 1-11.   DOI
54 Griebel, M. and Hamaekers, J. (2004), "Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites", Comput. Method. Appl. Mech. Eng., 193(17-20), 1773-1788.   DOI
55 Gupta, A., Joshi, A.Y., Sharma, S.C. and Harsha, S.P. (2012), "Dynamic analysis of fixed-free single-walled carbon nanotube-based bio-sensors because of various viruses", IET Nanobiotechnol., 6(3), 115-121.   DOI
56 Gupta, A., Sharma, S.C. and Harsha, S.P. (2012), "Vibration analysis of carbon nanotube-based mass sensor using different boundary conditions", J. Mech. Eng., 2(1), 8-12.
57 Hajnayeb, A. and Khadem, S.E. (2015), "An analytical study on the nonlinear vibration of a doublewalled carbon nanotube", Struct. Eng. Mech., 54(5), 987-998.   DOI
58 Gupta, A., Talha, M. and Seemann, W. (2017), "Free vibration and flexural response of functionally graded plates resting on Winkler-Pasternak elastic foundations using non-polynomial higher order shear and normal deformation theory", Mech. Adv. Mater. Struct., 1-16.
59 Hadji, L., Daouadji, T.H., Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519.   DOI
60 Hadji, L., Zouatnia, N. and Amar, K. (2016), "Bending analysis of FGM plates using a sinusoidal shear deformation theory", Wind Struct., 23(6), 543-558.   DOI
61 Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253.   DOI
62 Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comp. Mater. Sci., 39(2), 315-323.   DOI
63 Hasan, R.P., Hossein, V., Mohammad, M.H.GB. and Alireza, A. (2015), "Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method", Struct. Eng. Mech., 54(6), 1061-1073.   DOI
64 Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140, 374-383.   DOI
65 Iijima, S. and Ichihashi, T. (1993), "Single-shell carbon nanotubes of 1 nm diameter", Nat., 363, 603.   DOI
66 Houari, M.S.A., Tounsi, A., Bessaim A. and Mahmoud S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct.", 22(2), 257-276.   DOI
67 Hu, N., Fukunaga, H., Lu, C., Kameyama, M. and Yan, B. (2005), "Prediction of elastic properties of carbon nanotube reinforced composites", P. Roy. Soc. A, 461(2058), 1685-1710.   DOI
68 Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nat., 354, 56-58.   DOI
69 Jahangiri, R., Jahangiri, H. and Khezerloo, H. (2015) "FGM micro-gripper under electrostatic and intermolecular van-der Waals forces using modified couple stress theory", Steel Compos. Struct., 18(6), 1541-1555.   DOI
70 Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442.   DOI
71 Lei, Z.X., Liew, K.M. and Yu, J.L. (2013), "Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment", Compos. Struct., 106, 128-138.   DOI
72 Lei, Z.X., Liew, K.M. and Yu, J.L. (2013b), "Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates by the element-free kp-Ritz method", Comput. Meth. Appl. Mech. Eng., 256, 189-199.   DOI
73 Lu, P., Lee, H.P., Lu, C. and Zhang, P.Q. (2006), "Dynamic properties of flexural beams using a nonlocal elasticity model", J. Appl. Phys., 99, 073510.   DOI