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http://dx.doi.org/10.12989/sem.2020.75.1.087

Combination resonances of imperfect SSFG cylindrical shells rested on viscoelastic foundations  

Foroutan, Kamran (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology)
Ahmadi, Habib (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology)
Publication Information
Structural Engineering and Mechanics / v.75, no.1, 2020 , pp. 87-100 More about this Journal
Abstract
The present paper investigates the combination resonance behavior of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal and external functionally graded stiffeners under two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. With regard to classical plate theory of shells, von-Kármán equation and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The combination resonance is obtained by using the multiple scales method. Finally, the influences of the stiffeners angles, foundation type, the nonlinear elastic foundation coefficients, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.
Keywords
nonlinear vibrations; combination resonance behaviors; spiral stiffened FG cylindrical shell; multiple scales method; geometric imperfections; nonlinear viscoelastic foundation; two-term excitation;
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1 Qin, Z. Chu, F. and Zu, J. (2017), "Free vibrations of cylindrical shells with arbitrary boundary conditions: A comparison study", Int. J. Mech. Sci., 133 91-99. https://doi.org/10.1016/j.ijmecsci.2017.08.012.   DOI
2 Rodrigues, L., Gonçalves, P.B. and Silva, F.M.A. (2017), "Internal resonances in a transversally excited imperfect circular cylindrical shell", Pro. Eng., 199, 838-843. https://doi.org/10.1016/j.proeng.2017.09.010.   DOI
3 Sarigul, M. and Boyaci, H. (2010), "Nonlinear vibrations of axially moving beams with multiple concentrated masses Part I: primary resonance", Struct. Eng. Mech., 36(2), 149-163. https://doi.org/10.12989/sem.2010.36.2.149.   DOI
4 Shariyat, M. (2011), "Non-linear dynamic thermo-mechanical buckling analysis of the imperfect laminated and sandwich cylindrical shells based on a global-local theory inherently suitable for non-linear analyses", Int. J. Non-Lin. Mech., 46, 253-271. https://doi.org/10.1016/j.ijnonlinmec.2010.09.006.   DOI
5 Shaterzadeh, A. and Foroutan, K. (2016), "Post-buckling of cylindrical shells with spiral stiffeners under elastic foundation", Struct. Eng. Mech., 60, 615-631. https://doi.org/10.12989/sem.2016.60.4.615.   DOI
6 Shen, H.S. (2017), Postbuckling Behavior of Plates and Shells, World Scientific, Singapore.
7 Sheng, G.G. and Wang, X. (2018a), "Nonlinear vibrations of FG cylindrical shells subjected to parametric and external excitations", Compos. Struct., 191, 78-88. https://doi.org/10.1016/j.compstruct.2018.02.018.   DOI
8 Sheng, G.G. and Wang, X. (2018b), "The dynamic stability and nonlinear vibration analysis of stiffened functionally graded cylindrical shells", Appl. Math. Model., 56, 389-403. https://doi.org/10.1016/j.apm.2017.12.021.   DOI
9 Sofiyev, A.H. (2016), "Large amplitude vibration of FGM orthotropic cylindrical shells interacting with the nonlinear Winkler elastic foundation", Compos. Part B, 98, 141-50. https://doi.org/10.1016/j.compositesb.2016.05.018.   DOI
10 Ahmadi, H. and Foroutan, K. (2019c), "Combination resonance analysis of FG porous cylindrical shell under two-term excitation", Steel Compos. Struct., 32(2), 253-264. https://doi.org/10.12989/scs.2019.32.2.253.   DOI
11 Alijani, F., Amabili, M. and Bakhtiari-Nejad, F. (2011), "On the accuracy of the multiple scales method for non-linear vibrations of doubly curved shallow shells", Int. J. Nonlin. Mech., 46, 170-179. https://doi.org/10.1016/j.ijnonlinmec.2010.08.006.   DOI
12 Bich, D.H., Van Dung, D., Nam, V.H. and Phuong, N.T. (2013), "Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression", Int. J. Mech. Sci., 74, 190-200. https://doi.org/10.1016/j.ijmecsci.2013.06.002.   DOI
13 Dai, H.L., Dai, T. and Zheng, H.Y. (2013), "Creep buckling and post-buckling analyses for a hybrid laminated viscoelastic FGM cylindrical shell under in-plane loading", Int. J. Mech. Mater. Des., 9(4), 309-323. https://doi.org/10.1007/s10999-013-9223-0.   DOI
14 Dat, N.D., Quan, T.Q. and Duc, N.D. (2019), "Nonlinear thermal vibration of carbon nanotube polymer composite elliptical cylindrical shells", Int. J. Mech. Mater. Des., 1-20. https://doi.org/10.1007/s10999-019-09464-y.
15 Du, C. and Li, Y. (2013), "Nonlinear resonance behavior of functionally graded cylindrical shells in thermal environments", Compos. Struct., 102, 164-174. https://doi.org/10.1016/j.compstruct.2013.02.028.   DOI
16 Gao, K., Gao, W., Chen, D. and Yang, J. (2018a), "Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation", Compos. Struct., 204, 831-846. https://doi.org/10.1016/j.compstruct.2018.08.013.   DOI
17 Eslami, M.R. (2018), Buckling and Postbuckling of Beams, Plates, and Shells, Springer International Publishing, Switzerland.
18 Eslami, M.R., Shariyat, M. and Shakeri, M. (1998), "Layerwise theory for dynamic buckling and postbuckling of laminated composite cylindrical shells", AIAA J., 36, 1874-1882. https://doi.org/10.2514/2.281.   DOI
19 Foroutan, K., Shaterzadeh, A. and Ahmadi, H. (2018), "Nonlinear dynamic analysis of spiral stiffened functionally graded cylindrical shells with damping and nonlinear elastic foundation under axial compression", Struct. Eng. Mech., 66(3), 295-303. https://doi.org/10.12989/sem.2018.66.3.295.   DOI
20 Gao, K., Huang, Q., Kitipornchai, S. and Yang, J. (2019), "Nonlinear dynamic buckling of functionally graded porous beams", Mech. Adv. Mat. Struct., 1-12. https://doi.org/10.1080/15376494.2019.1567888.
21 Gao, K., Gao, W., Wu, B., Wu, D. and Song, C. (2018), "Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales", Thin Wall. Struct., 125, 281-293. https://doi.org/10.1016/j.tws.2017.12.039.   DOI
22 Gao, K., Gao, W., Wu, D. and Song, C. (2017), "Nonlinear dynamic characteristics and stability of composite orthotropic plate on elastic foundation under thermal environment", Compos. Struct., 168, 619-632. https://doi.org/10.1016/j.compstruct.2017.02.054.   DOI
23 Gao, K., Gao, W., Wu, D. and Song, C. (2018b), "Nonlinear dynamic stability of the orthotropic functionally graded cylindrical shell surrounded by Winkler-Pasternak elastic foundation subjected to a linearly increasing load", J. Sound Vib., 415, 147-168. https://doi.org/10.1016/j.jsv.2017.11.038.   DOI
24 Van Dung, D. and Hoa, L.K. (2013), "Nonlinear buckling and post-buckling analysis of eccentrically stiffened functionally graded circular cylindrical shells under external pressure", Thin Wall. Struct., 63,117-124. https://doi.org/10.1016/j.tws.2012.09.010.   DOI
25 Gao, K., Li, R. and Yang, J. (2019), "Dynamic characteristics of functionally graded porous beams with interval material properties", Eng. Struct., 197, 109441. https://doi.org/10.1016/j.engstruct.2019.109441.   DOI
26 Huang, B.W., Yu, P.P. and Jou, J.M. (2008), "Parametric resonance of a rotating taper pre-twisted beam with cracks", Struct. Eng. Mech., 28(2), 259-262. https://doi.org/10.12989/sem.2008.28.2.259.   DOI
27 Sofiyev, A.H., Avcar, M., Ozyigit, P. and Adigozel, S. (2009), "The Free Vibration of non-homogeneous truncated conical shells on a winkler foundation", Int. J. Eng. Appl. Sci., 1, 34-41.
28 Sofiyev, A.H., Hui, D., Haciyev, V.C., Erdem, H., Yuan, G.Q., Schnack, E. and Guldal, V. (2017), "The nonlinear vibration of orthotropic functionally graded cylindrical shells surrounded by an elastic foundation within first order shear deformation theory", Compos. Part B, 116, 170-85. https://doi.org/10.1016/j.compositesb.2017.02.006.   DOI
29 Udar, R.S. and Datta, P.K. (2007), "Dynamic combination resonance characteristics of doubly curved panels subjected to non-uniform tensile edge loading with damping", Struct. Eng. Mech., 25(4), 481-500. https://doi.org/10.12989/sem.2007.25.4.481.   DOI
30 Van Dung, D. and Nam, V.H. (2014), "Nonlinear dynamic analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium", Eur. J. Mech. A-Solid, 46, 42-53. https://doi.org/10.1016/j.euromechsol.2014.02.008.   DOI
31 Wang, Y.Q., Liang, L. and Guo, X.H. (2013), "Internal resonance of axially moving laminated circular cylindrical shells", J. Sound Vib., 332, 6434-6450. https://doi.org/10.1016/j.jsv.2013.07.007.   DOI
32 Li, X., Du, C.C. and Li, Y.H. (2018), "Parametric resonance of a FG cylindrical thin shell with periodic rotating angular speeds in thermal environment", Appl. Math. Model., 59, 393-409. https://doi.org/10.1016/j.apm.2018.01.048.   DOI
33 Wang, Y.Q., Ye, Ch. and Zu, J.W. (2019), "Vibration analysis of circular cylindrical shells made of metal foams under various boundary conditions", Int. J. Mech. Mater. Des., 15(2), 333-344. https://doi.org/10.1007/s10999-018-9415-8.   DOI
34 Zhang, W., Liu, T., Xi, A. and Wang, Y.N. (2018), "Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes", J. Sound Vib., 423, 65-99. https://doi.org/10.1016/j.jsv.2018.02.049.   DOI
35 Kumar, R., Kumar, A. and Panda, S.K. (2015), "Parametric resonance of composite skew plate under non-uniform in-plane loading", Struct. Eng. Mech., 55(2), 435-459. https://doi.org/10.12989/sem.2015.55.2.435.   DOI
36 Lezgy-Nazargah, M., Shariyat, M. and Beheshti-Aval, S.B. (2011), "A refined high-order global-local theory for finite element bending and vibration analyses of the laminated composite beams", Acta Mech., 217(3-4), 219-242. https://doi.org/10.1007/s00419-012-0621-9.   DOI
37 Li, F.M. and Yao, G. (2013), "1/3 Subharmonic resonance of a nonlinear composite laminated cylindrical shell in subsonic air flow", Compos. Struct., 100, 249-256. https://doi.org/10.1016/j.compstruct.2012.12.035.   DOI
38 Nayfeh, A.H. and Mook D.T. (1995), Nonlinear Oscilations, John Wiley and Sons, New Jersey, USA.
39 Mahmoudkhani, S., Navazi, H.M. and Haddadpour, H. (2011), "An analytical study of the non-linear vibrations of cylindrical shells", J. Nonlin. Mech., 46, 1361-1372. https://doi.org/10.1016/j.ijnonlinmec.2011.07.012.   DOI
40 Mustafa, B.A.J. and Ali, R. (1989), "An energy method for free vibration analysis of stiffened circular cylindrical shells", Comput. Struct., 32, 355-363. https://doi.org/10.1016/0045-7949(89)90047-3.   DOI
41 Pendhari, S.S., Kant, T., Desai, Y.M. and Subbaiah, C.V. (2012), "Static solutions for functionally graded simply supported plates", J. Mech. Mater. Des., 8(1), 51-69. https://doi.org/10.1007/s10999-011-9175-1.   DOI
42 Pellicano F. (2007), "Vibrations of circular cylindrical shells: theory and experiments", J. Sound Vib., 303(1-2), 154-170. https://doi.org/10.1016/j.jsv.2007.01.022.   DOI
43 Ahmadi, H. and Foroutan, K. (2019b), "Superharmonic and subharmonic resonances of spiral stiffened functionally graded cylindrical shells under harmonic excitation", J. Struct. Stability Dynamics. https://doi.org/10.1142/S0219455419501141.
44 Zarouni, E., Rad, M.J. and Tohidi, H. (2014), "Free vibration analysis of fiber reinforced composite conical shells resting on Pasternak-type elastic foundation using Ritz and Galerkin methods", Int. J. Mech. Mater. Des., 10(4), 421-438. https://doi.org/10.1007/s10999-014-9254-1.   DOI
45 Abe, A., Kobayashi, Y. and Yamada, G. (2007), "Nonlinear dynamic behaviors of clamped laminated shallow shells with one-to-one internal resonance", J. Sound Vib., 304, 957-968. https://doi.org/10.1016/j.jsv.2007.03.009.   DOI
46 Ahmadi, H. (2018), "Nonlinear primary resonance of imperfect spiral stiffened functionally graded cylindrical shells surrounded by damping and nonlinear elastic foundation", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-018-0679-2.
47 Ahmadi, H. and Foroutan, K. (2019a), "Nonlinear primary resonance of spiral stiffened functionally graded cylindrical shells with damping force using the method of multiple scales", Thin Wall. Struct., 135, 33-44. https://doi.org/10.1016/j.tws.2018.10.028.   DOI