Browse > Article
http://dx.doi.org/10.12989/sss.2020.25.6.693

Large amplitude free vibrations of FGM shallow curved tubes in thermal environment  

Babaei, Hadi (Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University)
Kiani, Yaser (Faculty of Engineering, Shahrekord University)
Eslami, M. Reza (Mechanical Engineering Department, Amirkabir University of Technology)
Publication Information
Smart Structures and Systems / v.25, no.6, 2020 , pp. 693-705 More about this Journal
Abstract
In the current investigation, large amplitude free vibration behavior of shallow curved pipes (tubes) made of functionally graded materials is investigated. Properties of the tube are distributed across the radius of the tube and are obtained by means of a power law function. It is also assumed that all thermo-mechanical properties are temperature dependent. The governing equations of the tube are obtained using a higher order shear deformation tube theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large displacements and small strains. Uniform temperature elevation of the tube is also included into the formulation. For the case of tubes which are simply supported in flexure and axially immovable, the governing equations are solved using the two-step perturbation technique. Closed form expressions are provided to obtain the small and large amplitude fundamental natural frequencies of the FGM shallow curved tubes in thermal environment. Numerical results are given to explore the effects of thermal environment, radius ratio, and length to thickness ratio of the tube on the fundamental linear and non-linear frequencies.
Keywords
nonlinear free vibration; FGM; shallow curved tube; von $K{\acute{a}}rm{\acute{a}}n$ nonlinearity; two-step perturbation method; thermal environment;
Citations & Related Records
Times Cited By KSCI : 8  (Citation Analysis)
연도 인용수 순위
1 Shafiei, N. and She, G.L. (2018), "On vibration of functionally graded nanotubes in thermal environment", Int. J. Eng. Sci., 133, 84-98. https://doi.org/10.1016/j.ijengsci.2018.08.004   DOI
2 She, G.L., Yuan, F.G. and Ren, Y.R. (2017), "Nonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory", Compos. Struct., 165, 74-82. https://doi.org/10.1016/j.compstruct.2017.01.013   DOI
3 She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018a), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063   DOI
4 She, G.L., Ren, Y.R., Yuan, F.G. and Xiao, W.S. (2018b), "On vibrations of porous nanotubes", Int. J. Eng. Sci., 125, 23-35. https://doi.org/10.1016/j.ijengsci.2017.12.009   DOI
5 She, G.L., Ren, Y.R., Yuan, F.G. (2019), "Hygro-thermal wave propagation in functionally graded double-layered nanotubes systems", Steel Compos. Struct., Int. J., 31(6), 641-653. https://doi.org/10.12989/scs.2019.31.6.641
6 Shen, H.S. (2009), Functionally Graded Materials Nonlinear Analysis of Plates and Shells, CRC Press, Boca Raton, FL, USA. https://doi.org/10.1201/9781420092578
7 Arefi, M. (2015), "The effect of different functionalities of fgm and FGPM layers on free vibration analysis of the FG circular plates integrated with piezoelectric layers", Smart Struct. Syst., Int. J., 15(5), 1345-1362. https://doi.org/10.12989/sss.2015.15.5.1345   DOI
8 Babaei, H., Kiani, Y. and Eslami, M.R. (2018a), "Application of two-steps perturbation technique to geometrically nonlinear analysis of long FGM cylindrical panels on elastic foundation under thermal load", J. Therm. Stress., 41(7), 847-865. https://doi.org/10.1080/01495739.2017.1421054   DOI
9 Shen, H.S. (2013), A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells, Wiley & Sons, Singapore.
10 Shen, H.S. (2011), "A novel technique for nonlinear analysis of beams on two-parameter elastic foundations", Int. J. Struct. Stab. Dyn. 11(6), 999-1014. https://doi.org/10.1142/S0219455411004440   DOI
11 Shen, H.S. and Wang, H. (2014b), "Nonlinear vibration of shear deformable FGM cylindrical panels resting on elastic foundation in thermal environment", Compos. Part B, 60, 167-177. https://doi.org/10.1016/j.compositesb.2013.12.051   DOI
12 Babaei, H., Kiani, Y. and Eslami, M.R. (2019d), "Large amplitude free vibration analysis of shear deformable FGM shallow arches on nonlinear elastic foundation", Thin-wall. Struct., 144, 106237. https://doi.org/10.1016/j.tws.2019.106237   DOI
13 Babaei, H., Kiani, Y. and Eslami, M.R. (2018b), "Geometrically nonlinear analysis of shear deformable FGM shallow pinned arches on nonlinear elastic foundation under mechanical and thermal loads", Acta Mech., 229(7), 3123-3141. https://doi.org/10.1007/s00707-018-2134-2   DOI
14 Babaei, H., Kiani, Y. and Eslami, M.R. (2018c), "Geometrically nonlinear analysis of functionally graded shallow curved tubes in thermal environment", Thin-wall. Struct., 132, 48-57. https://doi.org/10.1016/j.tws.2018.08.008   DOI
15 Babaei, H., Kiani, Y. and Eslami, M.R. (2019a), "Thermal buckling and post-buckling analysis of geometrically imperfect FGM clamped tubes on nonlinear elastic foundation", Appl. Math. Model., 71, 12-30. https://doi.org/10.1016/j.apm.2019.02.009   DOI
16 Babaei, H., Kiani, Y. and Eslami, M.R. (2019b), "Buckling and post-buckling analysis of geometrically imperfect FGM pin-ended tubes surrounded by nonlinear elastic medium under compressive and thermal loads", Int. J. Struct. Stabil. Dyn., 19(7), 1950089. https://doi.org/10.1142/S0219455419500895   DOI
17 Babaei, H., Kiani, Y. and Eslami, M.R. (2019c), "Large amplitude free vibrations of long FGM cylindrical panels on nonlinear elastic foundation based on physical neutral surface", Compos. Struct., 220, 888-898. https://doi.org/10.1016/j.compstruct.2019.03.064   DOI
18 Babaei, H., Kiani, Y. and Eslami, M.R. (2019e), "Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method", ZAMM- J. App. Math. Mech., 99(2), Article No. e201800148. https://doi.org/10.1002/zamm.201800148
19 Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2019), "Refined shear deformation theories for laminated composite arches and beams with variable thickness: Natural frequency analysis", Engin. Anal. Boundary Elem., 100, 24-47. https://doi.org/10.1016/j.enganabound.2017.07.029   DOI
20 Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62(1), 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014   DOI
21 Wu, C.P. and Li, H.Y. (2012), "Exact solutions of free vibration of rotating multilayered fgm cylinders", Smart Struct. Syst., Int. J., 9(2), 105-125. https://doi.org/10.12989/sss.2012.9.2.105   DOI
22 Wu, C.P. and Liu, W.L. (2013), "3D buckling analysis of FGM sandwich plates under bi-axial compressive loads", Smart Struct. Syst., Int. J., 13(1), 111-135. https://doi.org/10.12989/sss.2014.13.1.111
23 Zhang, D.G. (2014), "Thermal post-buckling and nonlinear vibration analysis of FGM beams based on physical neutral surface and high order shear deformation theory", Meccanica, 49(2), 283-293. https://doi.org/10.1007/s11012-013-9793-9   DOI
24 Zhang, P. and Fu, Y. (2013), "A higher-order beam model for tubes", Eur. J. Mech. A/Solids, 38, 12-19. https://doi.org/10.1016/j.euromechsol.2012.09.009   DOI
25 Zhong, J., Fu, Y., Wan, D. and Li, Y. (2016), "Nonlinear bending and vibration of functionally graded tubes resting on elastic foundations in thermal environment based on a refined beam model", Appl. Math. Model., 40(17-18), 7601-7614. https://doi.org/10.1016/j.apm.2016.03.031   DOI
26 Shen, H.S. and Wang, Z.X. (2014a), "Nonlinear Analysis of shear deformable FGM beams resting on elastic foundations in thermal environments", Int. J. Mech. Sci., 81, 195-206. https://doi.org/10.1016/j.ijmecsci.2014.02.020   DOI
27 Duc, N.D. (2013), "Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation", Compos. Struct., 102, 306-314. https://doi.org/10.1016/j.compstruct.2012.11.017   DOI
28 Babaei, H., Kiani, Y. and Eslami, M.R. (2019f), "Thermomechanical nonlinear In-plane analysis of fix-ended FGM shallow arches on nonlinear elastic foundation using twostep perturbation technique", Int. J. Mech. Mater. Des., 15(2), 225-244. https://doi.org/10.1007/s10999-018-9420-y   DOI
29 Chen, Y.Z. (2018), "Transfer matrix method for solution of FGMs thick-walled cylinder with arbitrary inhomogeneous elastic response", Smart Struct. Syst., Int. J., 21(4), 469-477. https://doi.org/10.12989/sss.2018.21.4.469
30 Chen, Y., Fu, Y., Zhong, J. and Li, Y. (2017), "Nonlinear dynamic responses of functionally graded tubes subjected to moving load based on a refined beam model", Nonlinear Dyn., 88(2), 1441-1452. https://doi.org/10.1007/s11071-016-3321-0   DOI
31 Duc, N.D. (2016), "Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory", Eur. J. Mech. A-Solid, 58, 10-30. https://doi.org/10.1016/j.euromechsol.2016.01.004   DOI
32 Duc, N.D. (2018), "Nonlinear thermo-electro-mechanical dynamic response of shear deformable piezoelectric Sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations", J. Sandw. Struct. Mater., 20(3), 351-378. https://doi.org/10.1177/1099636216653266   DOI
33 Duc, N.D. and Cong, P.H. (2018), "Nonlinear dynamic response and vibration of sandwich composite plates with negative Poisson's ratio in auxetic honeycombs", J. Sandw. Struct. Mater., 20(6), 692-717. https://doi.org/10.1177/1099636216674729   DOI
34 Fariborz, J. and Batra, R.C. (2019), "Free vibration of bi-directional functionally graded material circular beam using shear deformation theory employing logarithmic function of radius", Compos. Struct., 210, 217-230. https://doi.org/10.1016/j.compstruct.2018.11.036   DOI
35 Duc, N.D., Bich, D.H. and Cong, P.H. (2016), "Nonlinear thermal dynamic response of shear deformable FGM plates on elastic foundations", J. Therm, Stresses, 39(3), 278-297. https://doi.org/10.1080/01495739.2015.1125194   DOI
36 Duc, N.D., Nguyen, P.D. and Khoa N.D. (2017), "Nonlinear dynamic analysis and vibration of eccentrically stiffened S-FGM elliptical cylindrical shells surrounded on elastic foundations in thermal environments", Thin Wall. Struct., 117, 178-189. https://doi.org/10.1016/j.tws.2017.04.013   DOI
37 Duc, N.D., Quang, V.D., Nguyen, P.D. and Chien T.M. (2018), "Nonlinear dynamic response of FGM porous plates on elastic foundation subjected to thermal and mechanical loads using the first order shear deformation theory", J. Appl. Computat. Mech., 4(4), 245-259. https://doi.org/10.22055/jacm.2018.23219.1151
38 Duc, N.D., Hadavinia, H., Quan, T.Q. and Khoa, N.D. (2019), "Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment", Eur. J. Mech. A-Solid, 75, 355-366. https://doi.org/10.1016/j.euromechsol.2019.01.024   DOI
39 Eslami, M.R. (2018), Buckling and Postbuckling of Beams, Plates, and Shells, Springer, Switzerland.
40 Fu, Y., Zhong, J., Shao, X. and Chen, Y. (2015), "Thermal postbuckling analysis of functionally graded tubes based on a refined beam model", Int. J. Mech. Sci., 96-97, 58-64. https://doi.org/10.1016/j.ijmecsci.2015.03.019   DOI
41 Keibolahi, A., Kiani, Y. and Eslami, M.R. (2018), "Dynamic snap-through of shallow arches under thermal shock", Aerosp. Sci. Tech., 77, 545-554. https://doi.org/10.1016/j.ast.2018.04.003   DOI
42 Hetnarski, R.B. and Eslami, M.R. (2019), Thermal Stresses, Advanced Theory and Applications, (2th Edition), Springer, Switzerland.
43 Hosseini, S.A.H. and Rahmani, O. (2016), "Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model", Appl. Phy. A, 122, 169-178. https://doi.org/10.1007/s00339-016-9696-4   DOI
44 Huang, Y. and Li, X.F. (2010a), "Buckling of functionally graded circular columns including shear deformation", Mater. Des., 31(7), 3159-3166. https://doi.org/10.1016/j.matdes.2010.02.032   DOI
45 Huang, Y. and Li, X.F. (2010b), "Bending and vibration of circular cylindrical beams with arbitrary radial nonhomogeneity", Int. J. Mech. Sci., 52(4), 595-601. https://doi.org/10.1016/j.ijmecsci.2009.12.008   DOI
46 Jun, L., Guangwei, R., Jin, P., Xiaobin, L. and Weiguo, W. (2014), "Free vibration analysis of a laminated shallow curved beam based on Trigonometric shear deformation theory", Mech. Based Des. Struct., 42(1), 111-129. https://doi.org/10.1080/15397734.2013.846224   DOI
47 Malekzadeh, P., Atashi, M.M. and Karami, G. (2009), "In-plane free vibration of functionally graded circular arches with temperature-dependent properties under thermal environment", J. Sound. Vib., 326(3-5), 837-851. https://doi.org/10.1016/j.jsv.2009.05.016   DOI
48 Malekzadeh, P., Golbahar Haghighi, M.R. and Atashi, M.M. (2010), "Out-of-plane free vibration of functionally graded circular curved beams in thermal environment", Compos. Struct., 92(2), 541-552. https://doi.org/10.1016/j.compstruct.2009.08.040   DOI
49 Piovan, M.T., Domini, S. and Ramirez, J.M. (2012), "In-plane and out-of-plane dynamics and buckling of functionally graded circular curved beams", Compos. Struct., 94(11), 3194-3206. https://doi.org/10.1016/j.compstruct.2012.04.032   DOI
50 Rahmani, O., Hosseini, S.A.H., Ghoytasi, I. and Golmohammadi, H. (2018), "Free vibration of deep curved FG nano-beam based on modified couple stress theory", Steel Compos. Struct., Int. J., 26(5), 607-620. https://doi.org/10.12989/scs.2018.26.5.607