Browse > Article
http://dx.doi.org/10.12989/sem.2019.70.6.683

Free vibration analysis of thick cylindrical MEE composite shells reinforced CNTs with temperature-dependent properties resting on viscoelastic foundation  

Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Arshid, Ehsan (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Alhosseini, Seyed Mohammad Amin Rasti (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Amir, Saeed (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Arani, Mohammad Reza Ghorbanpour (Electrical Engineering Department, Amirkabir University of Technology)
Publication Information
Structural Engineering and Mechanics / v.70, no.6, 2019 , pp. 683-702 More about this Journal
Abstract
The present study aims to analyze the magneto-electro-elastic (MEE) vibration of a functionally graded carbon nanotubes reinforced composites (FG-CNTRC) cylindrical shell. Electro-magnetic loads are applied to the structure and it is located on an elastic foundation which is simulated by visco-Pasternak type. The properties of the nano-composite shell are assumed to be varied by temperature changes. The third-order shear deformation shells theory is used to describe the displacement components and Hamilton's principle is employed to derive the motion differential equations. To obtain the results, Navier's method is used as an analytical solution for simply supported boundary condition and the effect of different parameters such as temperature variations, orientation angle, volume fraction of CNTs, different types of elastic foundation and other prominent parameters on the natural frequencies of the structure are considered and discussed in details. Design more functional structures subjected to multi-physical fields is of applications of this study results.
Keywords
vibration analysis; third-order shear deformation theory; cylindrical shell; carbon nanotubes; electromagnetic loads; Visco-Pasternak foundation;
Citations & Related Records
Times Cited By KSCI : 13  (Citation Analysis)
연도 인용수 순위
1 Mohammadimehr, M., Akhavan Alavi, S. M., Okhravi, S. V and Edjtahed, S. H. (2018a), "Free vibration analysis of micromagneto-electro-elastic cylindrical sandwich panel considering functionally graded carbon nanotube-reinforced nanocomposite face sheets, various circuit boundary conditions, and temperature-dependent material properties using high-order sandwich panel theory and modified strain gradient theory", J. Intelligent Mater. Syst. Struct., 29(5), 863-882. https://doi.org/10.1177/1045389X17721048.   DOI
2 Mohammadimehr, M., Emdadi, M. and Rousta Navi, B. (2018c), "Dynamic stability analysis of microcomposite annular sandwich plate with carbon nanotube reinforced composite facesheets based on modified strain gradient theory", J. Sandwich Struct. Mater., https://doi.org/10.1177/1099636218782770.
3 Mohammadimehr, M., Mohandes, M. and Moradi, M. (2016a), "Size dependent effect on the buckling and vibration analysis of double-bonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory", J. Vib. Control, 22(7), 1790-1807. https://doi.org/10.1177/1077546314544513.   DOI
4 Mohammadimehr, M., Moradi, M. and Loghman, A. (2014), "Influence of the elastic foundation on the free vibration and buckling of thin-walled piezoelectric-based FGM cylindrical shells under combined loadings", J. Solid Mech, 6(4), 347-365.
5 Mohammadimehr, M., Zarei, H. B., Parakandeh, A. and Arani, A. G. (2017b), "Vibration analysis of double-bonded sandwich microplates with nanocomposite facesheets reinforced by symmetric and un-symmetric distributions of nanotubes under multi physical fields", Struct. Eng. Mech., 64(3), 361-379. https://doi.org/10.12989/sem.2017.64.3.361.   DOI
6 Mohammadimehr, M., Rostami, R. and Arefi, M. (2016d), "Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., 20(3), 513-544. https://doi.org/10.12989/scs.2016.20.3.513.   DOI
7 Bhardwaj, G., Singh, I.V., Mishra, B.K. and Bui, T.Q. (2015), "Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions", Compos. Struct., 126, 347-359. https://doi.org/10.1016/j.compstruct.2015.02.066.   DOI
8 Bui, T.Q., Do, T.V., Ton, L.H.T., Doan, D.H., Tanaka, S., Pham, D.T. and Hirose, S. (2016), "On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Compos. Part B, 92, 218-241. https://doi.org/10.1016/j.compositesb.2016.02.048.   DOI
9 Soedel, W. (1983), "Simplified equations and solutions for the vibration of orthotropic cylindrical shells", J. Sound Vib., 87(4), 555-566.   DOI
10 Yu, T., Bui, T. Q., Liu, P. and Hirose, S. (2016), "A stabilized discrete shear gap extended finite element for the analysis of cracked Reissner-Mindlin plate vibration problems involving distorted meshes", J. Mech. Mater. Design, 12(1), 85-107. https://doi.org/10.1007/s10999-014-9282-x.   DOI
11 Soedel, W. (2004), Vibrations of Shells and Plates. CRC Press, Florida, USA.
12 Qatu, M.S., Sullivan, R.W. and Wang, W. (2010), "Recent research advances on the dynamic analysis of composite shells: 2000-2009", Compos. Struct., 93(1), 14-31. https://doi.org/10.1016/j.compstruct.2010.05.014.   DOI
13 Razavi, S. and Shooshtari, A. (2015), "Nonlinear free vibration of magneto-electro-elastic rectangular plates", Compos. Struct., 119, 377-384. https://doi.org/10.1016/j.compstruct.2014.08.034.   DOI
14 Reddy, J. N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press, Florida, U.S.A.
15 Shen, H.S. (2011a), "Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells", Compos. Struct., 93(8), 2096-2108. https://doi.org/10.1016/j.compstruct.2011.02.011.   DOI
16 Mohammadimehr, M., Saidi, A.R., Ghorbanpour Arani, A., Arefmanesh, A. and Han Q. (2010), "Torsional Buckling of a DWCNT Embedded on Winkler and Pasternak Foundations Using Nonlocal Theory", J. Mech. Sci. Tech., 24(6), 1289-1299. https://doi.org/10.1007/s12206-010-0331-6.   DOI
17 Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2017a), "Dynamic stability of MSGT sinusoidal viscoelastic piezoelectric polymeric FG-SWNT reinforced nanocomposite plate considering surface stress and agglomeration effects under hydro-thermo-electro-magneto-mechanical loadings", Mech. Adv. Mater. Struct., 24, 1325-1342. http://dx.doi.org/10.1080/15376494.2016.1227507.   DOI
18 Mohammadimehr, M., Salemi, M. and Navi, B.R. (2016c), "Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermomechanical loadings using DQM", Compos. Struct., 138, 361-380. https://doi.org/10.1016/j.compstruct.2015.11.055.   DOI
19 Shen, H.S. (2011b), "Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part II: Pressure-loaded shells", Compos. Struct., 93(10), 2496-2503. https://doi.org/10.1016/j.compstruct.2011.04.005.   DOI
20 Shen, H.S. (2012), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells", Compos. Part B, 43(3), 1030-1038. https://doi.org/10.1016/j.compositesb.2011.10.004.   DOI
21 Shen, H.S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Method. Appl. Mech. Eng., 213, 196-205. https://doi.org/10.1016/j.cma.2011.11.025.   DOI
22 Qatu, M.S. (2004), Vibration of Laminated Shells and Plates, Elsevier, The Netherlands.
23 Shen, H.S. and Xiang, Y. (2013), "Postbuckling of nanotubereinforced composite cylindrical shells under combined axial and radial mechanical loads in thermal environment", Compos. Part B, 52, 311-322. https://doi.org/10.1016/j.compositesb.2013.04.034.   DOI
24 Shen, H.S. and Xiang, Y. (2014), "Nonlinear vibration of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments", Compos. Struct., 111, 291-300. https://doi.org/10.1016/j.compstruct.2014.01.010.   DOI
25 Qatu, M.S. (2002), "Recent research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells", Appl. Mech. Rev., 55(4), 325-350. https://doi.org/10.1115/1.1483079.   DOI
26 Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotubereinforced composite plates", Mater. Design, 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048.   DOI
27 Liu, P., Bui, T.Q., Zhu, D., Yu, T.T., Wang, J.W., Yin, S.H. and Hirose, S. (2015), "Buckling failure analysis of cracked functionally graded plates by a stabilized discrete shear gap extended 3-node triangular plate element", Compos. Part B, 77, 179-193. https://doi.org/10.1016/j.compositesb.2015.03.036.   DOI
28 Zaoui, F. Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.   DOI
29 Van Do, T., Nguyen, D. K., Duc, N. D., Doan, D. H. and Bui, T. Q. (2017), "Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory", Thin Wall. Struct., 119, 687-699. https://doi.org/10.1016/j.tws.2017.07.022.   DOI
30 Vu, T. Van, Khosravifard, A., Hematiyan, M. R. and Bui, T. Q. (2018), "A new refined simple TSDT-based effective meshfree method for analysis of through-thickness FG plates", Appl. Math. Model., 57, 514-534. https://doi.org/10.1016/j.apm.2018.01.004.   DOI
31 Liu, S., Yu, T. and Bui, T.Q. (2017), "Size effects of functionally graded moderately thick microplates: A novel non-classical simple-FSDT isogeometric analysis", Europ. J. Mech. A, 66, 446-458. https://doi.org/10.1016/j.euromechsol.2017.08.008.   DOI
32 Mohammadimehr, M. and Rahmati, A.H. (2013), "Small scale effect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric excitation", Turkish J. Eng. Environ. Sci., 37(1), 1-15.
33 Malekzadeh, P. and Shojaee, M. (2013), "Buckling analysis of quadrilateral laminated plates with carbon nanotubes reinforced composite layers", Thin Wall. Struct., 71, 108-118. https://doi.org/10.1016/j.tws.2013.05.008.   DOI
34 Mohammadimehr M. and Shahedi S. (2017) "High-order buckling and free vibration analysis of two types sandwich beam including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using GDQM", Compos. Part B Eng., 108, 91-107. https://doi.org/10.1016/j.compositesb.2016.09.040.   DOI
35 Nasihatgozar, M., Daghigh, V., Eskandari, M., Nikbin, K. and Simoneau, A. (2016), "Buckling analysis of piezoelectric cylindrical composite panels reinforced with carbon nanotubes", J. Mech. Sci., 107, 69-79. https://doi.org/10.1016/j.ijmecsci.2016.01.010.   DOI
36 Ozdemir, Y.I. (2018), "Using fourth order element for free vibration parametric analysis of thick plates resting on elastic foundation", Struct. Eng. Mech., 65(3), 213-222. https://doi.org/10.12989/sem.2018.65.3.213.   DOI
37 Shooshtari, A. and Razavi, S. (2016), "Vibration analysis of a magnetoelectroelastic rectangular plate based on a higher-order shear deformation theory", Latin American J. Solids Struct., 13(3), 554-572. http://dx.doi.org/10.1590/1679-78251831.   DOI
38 Smith, B.L. and Vronay, D.F. (1970), "Free vibration of circular cylindrical shells of finite length", AIAA J., 8(3), 601-603. https://doi.org/10.2514/3.5726.   DOI
39 Mohammadimehr, M., Okhravi, S.V and Akhavan Alavi, S.M. (2018b), "Free vibration analysis of magneto-electro-elastic cylindrical composite panel reinforced by various distributions of CNTs with considering open and closed circuits boundary conditions based on FSDT", J. Vib. Control, 24(8), 1551-1569. https://doi.org/10.1177/1077546316664022.   DOI
40 Liu, S., Yu, T., Lich, L. Van, Yin, S. and Bui, T.Q. (2019), "Size and surface effects on mechanical behavior of thin nanoplates incorporating microstructures using isogeometric analysis", Comput. Struct., 212, 173-187. https://doi.org/10.1016/j.compstruc.2018.10.009.   DOI
41 Liu, S., Yu, T., Van Lich, L., Yin, S. and Bui, T. Q. (2018), "Size effect on cracked functional composite micro-plates by an XIGA-based effective approach", Meccanica, 53(10), 2637-2658. https://doi.org/10.1007/s11012-018-0848-9.   DOI
42 Loja, M.A.R., Soares, C.M.M. and Barbosa, J.I. (2014), "Optimization of magneto-electro-elastic composite structures using differential evolution", Compos. Struct., 107, 276-287. https://doi.org/10.1016/j.compstruct.2013.08.005.   DOI
43 Greenberg, J.B. and Stavsky, Y. (1980), "Buckling and vibration of orthotropic composite cylindrical shellsBeul-und Schwingverhalten kompositer, orthotroper, zylindrischer Schalen", Acta Mechanica, 36(1-2), 15-29. https://doi.org/10.1007/BF01178233.   DOI
44 Hu, W.C.L. (1964), "A survey of the literature on the vibrations of thin shells", NASA-CR-58048; Southwest Research InsL, San Antonio, USA.
45 Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56. https://doi.org/10.1038/354056a0.   DOI
46 Jam, J.E., Pourasghar, A. and Kamarian, S. (2012), "Effect of the aspect ratio and waviness of carbon nanotubes on the vibrational behavior of functionally graded nanocomposite cylindrical panels", Polym. Compos., 33(11), 2036-2044.   DOI
47 Jooybar, N., Malekzadeh, P. and Fiouz, A. (2016), "Vibration of functionally graded carbon nanotubes reinforced composite truncated conical panels with elastically restrained against rotation edges in thermal environment", Compos. Part B, 106, 242-261. https://doi.org/10.1016/j.compositesb.2016.09.030.   DOI
48 Wattanasakulpong, N. and Bui, T. Q. (2018), "Vibration analysis of third-order shear deformable FGM beams with elastic support by Chebyshev collocation method", J. Struct. Stability Dynam., 18(05), https://doi.org/10.1142/S0219455418500712.
49 Wang, Z.-X. and Shen, H.-S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Comput. Mater. Sci., 50(8), 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005.   DOI
50 Wang, Z.-X. and Shen, H.-S. (2012), "Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments", Nonlinear Dynam., 70(1), 735-754. https://doi.org/10.1007/s11071-012-0491-2.   DOI
51 Xuebin, L. (2006), "A new approach for free vibration analysis of thin circular cylindrical shell", J. Sound Vib., 296(1-2), 91-98. https://doi.org/10.1016/j.jsv.2006.01.065.   DOI
52 Yahiaoui, M., Tounsi, A., Fahsi, B., Bouiadjra, R.B. and Benyoucef, S. (2018), "The role of micromechanical models in the mechanical response of elastic foundation FG sandwich thick beams", Struct. Eng. Mech., 68(1), 53-66.   DOI
53 Yas, M. H., Pourasghar, A., Kamarian, S. and Heshmati, M. (2013), "Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube", Mater. Design, 49, 583-590. https://doi.org/10.1016/j.matdes.2013.01.001.   DOI
54 Yin, S., Yu, T., Bui, T. Q., Liu, P. and Hirose, S. (2016a), "Buckling and vibration extended isogeometric analysis of imperfect graded Reissner-Mindlin plates with internal defects using NURBS and level sets", Comput. Struct., 177, 23-38. https://doi.org/10.1016/j.compstruc.2016.08.005.   DOI
55 Leissa, A. W. (1973), Vibration of Shells (Vol. 288), Scientific and Technical Information Office, National Aeronautics and Space Administration Washington. USA.
56 Yin, S., Yu, T., Bui, T. Q., Zheng, X. and Tanaka, S. (2016b), "Inplane material inhomogeneity of functionally graded plates: A higher-order shear deformation plate isogeometric analysis", Compos. Part B, 106, 273-284. https://doi.org/10.1016/j.compositesb.2016.09.008.   DOI
57 Laiarinandrasana, L., Besson, J., Lafarge, M. and Hochstetter, G. (2009), "Temperature dependent mechanical behaviour of PVDF: experiments and numerical modelling", J. Plasticity, 25(7), 1301-1324. https://doi.org/10.1016/j.ijplas.2008.09.008.   DOI
58 Lang, Z. and Xuewu, L. (2013), "Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic circular cylindrical shells", Appl. Math. Model., 37(4), 2279-2292. https://doi.org/10.1016/j.apm.2012.05.023.   DOI
59 Liu, B., Xing, Y.F., Qatu, M.S. and Ferreira, A.J.M. (2012), "Exact characteristic equations for free vibrations of thin orthotropic circular cylindrical shells", Compos. Struct., 94(2), 484-493. https://doi.org/10.1016/j.compstruct.2011.08.012.   DOI
60 Ghorbanpour Arani A., Hashemian M., Loghman A. and Mohammadimehr M. (2011b), "Study of dynamic stability of the double-walled carbon nanotubes under axial loading embedded in an elastic medium by the energy method", J. Appl. Mech. Technical Physics, 52(5), 815-824. https://doi.org/10.1134/S0021894411050178.   DOI
61 Ghorbanpour Arani, A., Mobarakeh, M.R., Shams, S. and Mohammadimehr, M. (2012), "The effect of CNT volume fraction on the magneto-thermo-electro-mechanical behavior of smart nanocomposite cylinder", J. Mech. Sci. Technol., 26(8), 2565-2572. https://doi.org/10.1007/s12206-012-0639-5.   DOI
62 Duc, N.D. and Quan, T.Q. (2015), "Nonlinear dynamic analysis of imperfect functionally graded material double curved thin shallow shells with temperature-dependent properties on elastic foundation", J. Vib. Control, 21(7), 1340-1362. https://doi.org/10.1177/1077546313494114.   DOI
63 Cong, P. H., Chien, T. M., Khoa, N. D. and Duc, N. D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aerosp. Sci. Technol., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020.   DOI
64 Das, Y. C. (1964), "Vibrations of orthotropic cylindrical shells", Applied Scientific Research, Section A, 12(4-5), 317-326. https://doi.org/10.1007/BF03185004.   DOI
65 Dong, S.B. (1968), "Free vibration of laminated orthotropic cylindrical shells", J. Acoustic. Soc. America, 44(6), 1628-1635. https://doi.org/10.1121/1.1911306.   DOI
66 Arshid, E. and Khorshidvand, A.R. (2017), "Flexural vibrations analysis of saturated porous circular plates using differential quadrature method", Iran J. Mech. Eng. Transac. ISME, 19(1), 78-100.
67 Arshid, E. and Khorshidvand, A.R. (2018), "Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method", Thin Wall. Struct., 125(January), 220-233. https://doi.org/10.1016/j.tws.2018.01.007.   DOI
68 Arshid, E., Kiani, A. and Amir, S. (2019), "Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications. https://doi.org/10.1177/1464420719832626.
69 Abdel-Rahman, E.M., Younis, M.I. and Nayfeh, A.H. (2002), "Characterization of the mechanical behavior of an electrically actuated microbeam", J. Micromech. Microeng., 12(6), 759.   DOI
70 Ghorbanpour Arani, A., BabaAkbar-Zarei, H., Pourmousa, P. and Eskandari, M. (2018a), "Investigation of free vibration response of smart sandwich micro-beam on Winkler-Pasternak substrate exposed to multi physical fields", Microsyst. Technol., 24(7), 3045-3060. https://doi.org/10.1007/s00542-017-3681-5.   DOI
71 Alibeigloo, A. (2014), "Three-dimensional thermoelasticity solution of functionally graded carbon nanotube reinforced composite plate embedded in piezoelectric sensor and actuator layers", Compos. Struct., 118, 482-495. https://doi.org/10.1016/j.compstruct.2014.08.004.   DOI
72 Ashrafi, B., Hubert, P. and Vengallatore, S. (2006), "Carbon nanotube-reinforced composites as structural materials for microactuators in microelectromechanical systems", Nanotechnol., 17(19), 4895.   DOI
73 Aragh, B. S., Barati, A. H. N. and Hedayati, H. (2012), "Eshelby-Mori-Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels", Compos. Part B, 43(4), 1943-1954. https://doi.org/10.1016/j.compositesb.2012.01.004.   DOI
74 Arefi, M., Bidgoli, E.M.R. and Zenkour, A.M. (2018), "Sizedependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory", Smart Struct. Syst., 22(1), 27-40.   DOI
75 Mohammadimehr, M. and Mostafavifar, M. (2016), "Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT", Compos. Part B, 94, 253-270. https://doi.org/10.1016/j.compositesb.2016.03.030.   DOI
76 Mohammadimehr, M., Rousta Navi, B. and Arani, A.G. (2015), "Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671.   DOI
77 Ghorbanpour Arani, A., Pourjamshidian, M. and Arefi, M. (2018c), "Non-linear free and forced vibration analysis of sandwich nano-beam with FG-CNTRC face-sheets based on nonlocal strain gradient theory", Smart Struct. Syst., 22(1), 105-120.   DOI
78 Ghorbanpour Arani, A., Haghparast, E. and BabaAkbar-Zarei, H. (2016b), "Vibration of axially moving 3-phase CNTFPC plate resting on orthotropic foundation", Struct. Eng. Mech, 57(1), 105-126. http://dx.doi.org/10.12989/sem.2016.57.1.105.   DOI
79 Ghorbanpour Arani, A. and Kiani, F. (2018b), "Nonlinear free and forced vibration analysis of microbeams resting on the nonlinear orthotropic visco-Pasternak foundation with different boundary conditions", Steel Compos. Struct., 28(2), 149-165. https://doi.org/10.12989/scs.2018.28.2.149.   DOI
80 Ghorbanpour Arani, A., Kiani, F. and Afshari, H. (2019), "Free and forced vibration analysis of laminated functionally graded CNT-reinforced composite cylindrical panels", J. Sandwich Struct. Mater., 1099636219830787. https://doi.org/10.1177/1099636219830787.
81 El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585.   DOI
82 Forsberg, K. (1964), "Influence of boundary conditions on the modal characteristics of thin cylindrical shells", AIAA J., 2(12), 2150-2157. https://doi.org/10.2514/3.55115.   DOI
83 Amir, S., Khani, M., Shajari, A.R. and Dashti, P. (2017), "Instability analysis of viscoelastic CNTs surrounded by a thermo-elastic foundation", Strcut. Eng. Mech., 63(2), 171-180. https://doi.org/10.12989/sem.2017.63.2.171.   DOI
84 Mohammadimehr, M., Rousta Navi, B. and Arani, A.G. (2016b), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FGSWNT", Compos. Part B, 87, 132-148. https://doi.org/10.1016/j.compstruct.2015.05.077.   DOI
85 Amir, S. (2016), "Orthotropic patterns of visco-Pasternak foundation in nonlocal vibration of orthotropic graphene sheet under thermo-magnetic fields based on new first-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, https://doi.org/10.1177/2F1464420716670929.
86 Amir, S., Bidgoli, E.M.R. and Arshid, E. (2018), "Size-dependent vibration analysis of a three-layered porous rectangular nano plate with piezo-electromagnetic face sheets subjected to pre loads based on SSDT", Mech. Adv. Mater. Struct., 1-15. https://doi.org/10.1080/15376494.2018.1487612.
87 Ansari, R. and Gholami, R. (2016), "Nonlocal free vibration in the pre-and post-buckled states of magneto-electro-thermo elastic rectangular nanoplates with various edge conditions", Smart Mater. Struct., 25(9), 95033.   DOI
88 Mehar, K., Panda, S. K., Bui, T. Q. and Mahapatra, T. R. (2017), "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
89 Meksi, A., Benyoucef, S., Houari, M. S. A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., 53(6), 1215-1240.   DOI
90 Ganesan, N. and Sivadas, K.R. (1990), "Vibration analysis of orthotropic shells with variable thickness", Comput. Struct., 35(3), 239-248. https://doi.org/10.1016/0045-7949(90)90343-Z.   DOI
91 Ghorbanpour Arani, A., Haghparast, E. and BabaAkbar-Zarei, H. (2017a), "Vibration analysis of functionally graded nanocomposite plate moving in two directions", Steel Compos. Struct., 23(5), 529-541. https://doi.org/10.12989/scs.2017.23.5.529.   DOI
92 Ghorbanpour Arani, A., Roudbari, M.A. and Amir, S. (2016a), "Longitudinal magnetic field effect on wave propagation of fluid-conveyed SWCNT using Knudsen number and surface considerations", Appl. Math. Model., 40(3), 2025-2038. https://doi.org/10.1016/j.apm.2015.09.055.   DOI
93 Ghorbanpour Arani, A., Maraghi, Z.K. and Ferasatmanesh, M. (2017b), "Theoretical investigation on vibration frequency of sandwich plate with PFRC core and piezomagnetic face sheets under variable in-plane load", Struct. Eng. Mech., 63(1), 65-76. https://doi.org/10.12989/sem.2017.63.1.065.   DOI
94 Ghorbanpour Arani A., Mohammadimehr M., Saidi A. R., Shogaei S. and Arefmanesh A. (2011a), "Thermal buckling analysis of double-walled carbon nanotubes considering the small-scale length effect", Proc. IMechE, Part C, J. Mech. Eng. Sci., 225(1), 248-256. https://doi.org/10.1177/09544062JMES1975.   DOI
95 Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T. and Dihaj, A. (2018), "Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix", Struct. Eng. Mech., 67(5), 517-525. https://doi.org/10.12989/sem.2018.67.5.517.   DOI
96 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. https://doi.org/10.1080/15376494.2014.984088.   DOI