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) |
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 |