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http://dx.doi.org/10.12989/sem.2022.81.6.769

Natural vibrations and hydroelastic stability of laminated composite circular cylindrical shells  

Bochkareva, Sergey A. (Institute of Continuous Media Mechanics, Ural Branch Russian Academy of Sciences)
Lekomtsev, Sergey V. (Institute of Continuous Media Mechanics, Ural Branch Russian Academy of Sciences)
Publication Information
Structural Engineering and Mechanics / v.81, no.6, 2022 , pp. 769-780 More about this Journal
Abstract
This paper studies the dynamic behavior of laminated composite circular cylindrical shells interacting with a fluid. The mathematical formulation of the dynamic problem for an elastic body is developed based on the variational principle of virtual displacements and the relations of linear elasticity theory. The behavior of an ideal compressible fluid is described by the potential theory, the equations of which together with boundary conditions are transformed to a weak form. The hydrodynamic pressure exerted by the fluid on the internal surface of the shell is calculated according to the linearized Bernoulli equation. The numerical implementation of the mathematical formulation has been done using the semi-analytical finite element method. The influence of the ply angle and lay-up configurations of laminated composites on the natural vibration frequencies and the hydroelastic stability boundary have been analyzed for shells with different geometrical dimensions and under different kinematic boundary conditions set at their edges. It has been found that the optimal value of the ply angle depends on the level of filling of the shell with a fluid. The obtained results support the view that by choosing the optimal configuration of the layered composite material it is possible to change upwards or downwards the frequency and mode shape, as well as the critical velocity for stability loss over a wide range.
Keywords
cylindrical shell; elasticity theory; FEM; layered composite material; natural vibrations; potential fluid; stability;
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1 Thinh, T.I. and Cuong, N.M. (2016), "Dynamic Stiffness Method for free vibration of composite cylindrical shells containing fluid", Appl. Math. Model., 40(21), 9286-9301. https://doi.org/10.1016/j.apm.2016.06.015.   DOI
2 Nurul Izyan, M.D. and Viswanathan, K.K. (2019), "Vibration of symmetrically layered angle-ply cylindrical shells filled with fluid", Plos one, 4(7), e0219089. https://doi.org/10.1371/journal.pone.0219089.   DOI
3 Sahebnasagh, M., Nikkhah-Bahrami, M. and Firouz-Abadi, R. (2017), "Stability analysis of whirling composite shells partially filled with two liquid phases", J. Mech. Sci. Technol., 31(5), 2117-2127. https://doi.org/10.1007/s12206-017-0408-6.   DOI
4 Sharma, C.B., Darvizeh, M. and Darvizeh, A. (1998), "Natural frequency response of vertical cantilever composite shells containing fluid", Eng. Struct., 20(8), 732-737. https://doi.org/10.1016/S0141-0296(97)00102-8.   DOI
5 Sheinman, I. and Greif, S. (1984), "Dynamic analysis of laminated shells of revolution", J. Compos. Mater., 18(3), 200-215. https://doi.org/10.1177/002199838401800301.   DOI
6 Sundarasivarao, B.S.K. and Ganesan, N. (1991), "Deformation of varying thickness composite cylindrical shell subjected to fluid loading with various end conditions", Comput. Struct., 41(1), 67-74. https://doi.org/10.1016/0045-7949(91)90156-G.   DOI
7 Ramasamy, R. and Ganesan, N. (1999), "Vibration and damping analysis of fluid filled orthotropic cylindrical shells with constrained viscoelastic damping", Comput. Struct., 70(3), 363-376. https://doi.org/10.1016/S0045-7949(98)00192-8.   DOI
8 Ilgamov, M.A. (1969), Oscillations of Elastic Shells Containing Liqiud and Gas, Nauka, Moscow.
9 Dai, Q., Qin, Z. and Chu, F. (2021), "Parametric study of damping characteristics of rotating laminated composite cylindrical shells using Haar wavelets", Thin Wall. Struct., 161, 107500. https://doi.org/10.1016/j.tws.2021.107500.   DOI
10 Hien, V.Q., Thinh, T.I. and Cuong, N.M. (2016), "Free vibration analysis of joined composite conical-cylindrical-conical shells containing fluid", Vietnam J. Mech., 38(4), 249-265. https://doi.org/10.15625/0866-7136/6954.   DOI
11 Kadoli, R. and Ganesan, N. (2003), "Free vibration and buckling analysis of composite cylindrical shells conveying hot fluid", Compos. Struct., 60(1), 19-32. https://doi.org/10.1016/S0263-8223(02)00313-6.   DOI
12 Chehreghani, M., Pazhooh, M.D. and Shakeri M. (2019), "Vibration analysis of a fluid conveying sandwich cylindrical shell with a soft core", Compos. Struct., 230, 111470. https://doi.org/10.1016/j.compstruct.2019.111470.   DOI
13 Nurul Izyan, M.D., Aziz, Z.A., Ghostine, R., Lee, J.H. and Viswanathan, K.K. (2019), "Free vibration of cross-ply layered circular cylindrical shells filled with quiescent fluid under first order shear deformation theory", Int. J. Press. Ves. Pip., 170, 73-81. https://doi.org/10.1016/j.ijpvp.2019.01.019.   DOI
14 Paidoussis, M.P. and Denise, J.P. (1972), "Flutter of thin cylindrical shells conveying fluid", J. Sound Vib., 20(1), 9-26. https://doi.org/10.1016/0022-460X(72)90758-4.   DOI
15 Zhu, H.Z. and Wu, J.H. (2020), "Free vibration of partially fluid-filled or fluid-surrounded composite shells using the dynamic stiffness method", Acta Mechanica, 231(9), 3961-3978. https://doi.org/10.1007/s00707-020-02734-3.   DOI
16 Kumar, A., Chakrabarti, A. and Bhargava, P. (2013b), "Vibration of laminated composites and sandwich shells based on higher order zigzag theory", Eng. Struct., 56, 880-888. https://doi.org/10.1016/j.engstruct.2013.06.014.   DOI
17 Miramini, S.M. and Ohadi, A. (2019), "Three-dimensional vibration of fluid-conveying laminated composite cylindrical shells with piezoelectric layers", Int. J. Struct. Stab. Dyn., 19(3), 1950026. https://doi.org/10.1142/S0219455419500263.   DOI
18 Muggeridge, D.B. and Buckley, T.J. (1979a), "Flexural vibration of orthotropic cylindrical shells in a fluid medium", AIAA J., 17(9), 1019-1022. https://doi.org/10.2514/3.61270.   DOI
19 Okazaki, K., Tani, J., Qiu, J. and Kosugo, K. (2007), "Vibration test of a cross-ply laminated composite circular cylindrical shell partially filled with liquid", Tran. JPN Soc. Mech. Eng. Ser. C, 73(727), 724-731. https://doi.org/10.1299/kikaic.73.724.   DOI
20 Paidoussis, M.P. (2016), Fluid-Structure Interactions: Slender Structures and Axial Flow, Vol. 2, 2nd Edition, Elsevier Academic Press, London. https://doi.org/10.1016/C2011-0-08058-4.   DOI
21 Xi, Z.C., Yam, L.H. and Leung, T.P. (1997a), "Free vibration of a laminated composite circular cylindrical shell partially filled with fluid", Compos. Part B: Eng., 28(4), 359-374. https://doi.org/10.1016/S1359-8368(96)00047-9.   DOI
22 Pal, N.C., Bhattacharyya, S.K. and Sinha, P.K. (2003), "Non-linear coupled slosh dynamics of liquid-filled laminated composite containers: a two dimensional finite element approach", J. Sound Vib., 261(4), 729-749. https://doi.org/10.1016/S0022-460X(02)01011-8.   DOI
23 Pal, N.C., Bhattacharyya, S.K. and Sinha, P.K. (1999), "Coupled slosh dynamics of liquid-filled, composite cylindrical tanks", J. Eng. Mech., 125(4), 491-495. https://doi.org/10.1061/(asce)0733-9399(1999)125:4(491).   DOI
24 Okazaki, K., Tani, J. and Sugano, M. (2002), "Free vibrations of a laminated composite coaxial circular cylindrical shell partially filled with liquid", Tran. JPN Soc. Mech. Eng. Ser. C, 68(671), 1942-1949. https://doi.org/10.1299/kikaic.68.1942.   DOI
25 Bochkarev, S.A. and Lekomtsev, S.V. (2021), "Stability analysis of composite cylindrical shell containing rotating fluid", J. Phys.: Conf. Ser., 1945, 012034. https://doi.org/10.1088/1742-6596/1945/1/012034.   DOI
26 Alfutov, N.A., Zinov'ev, P.A. and Popov, B.G. (1984), Analysis of Multilayer Plates and Shells of Composite Materials, Mashinosiroenie, Moscow.
27 Kumar, A., Chakrabarti, A. and Bhargava, P. (2014), "Accurate dynamic response of laminated composites and sandwich shells using higher order zigzag theory", Thin Wall. Struct., 77, 174-186. https://doi.org/10.1016/j.tws.2013.09.026   DOI
28 Li, D. (2021), "Layerwise theories of laminated composite structures and their applications: A review", Arch. Comput. Meth. Eng., 28(2), 577-600. https://doi.org/10.1007/s11831-019-09392-2.   DOI
29 Lia, H., Lv, H., Sun, H., Qin, Z., Xiong, J., Han, Q., Liu, J. and Wang, X. (2021), "Nonlinear vibrations of fiber-reinforced composite cylindrical shells with bolt loosening boundary conditions", J. Sound Vib., 496, 115935. https://doi.org/10.1016/j.jsv.2021.115935.   DOI
30 Okazaki, K., Tani, J. and Sugano, M. (1999), "Free vibrations of a laminated composite circular cylindrical shell partially filled with liquid", Tran. JPN Soc. Mech. Eng. Ser. C, 65(640), 4597-4604. https://doi.org/10.1299/kikaic.65.4597.   DOI
31 Xi, Z.C., Yam, L.H. and Leung, T.P. (1997b), "Free vibration of a partially fluid-filled cross-ply laminated composite circular cylindrical shell", J. Acoust. Soc. Am., 101(2), 909-917. https://doi.org/10.1121/1.418049.   DOI
32 Zhang, Y.L., Reese, J.M. and Gorman, D.G. (2002), "A comparative study of axisymmetric finite elements for the vibration of thin cylindrical shells conveying fluid", Int. J. Numer. Meth. Eng., 54(1), 89-110. https://doi.org/10.1002/nme.418.   DOI
33 Mikhasev, G.I. and Altenbach, H. (2019), Thin-Walled Laminated Structures: Buckling, Vibrations and Their Suppression, Springer, Cham.
34 Carrera, E. (2003), "Historical review of ZIG-ZAG theories for multilayered plates and shells", Appl. Mech. Rev., 56(3), 287-308. https://doi.org/10.1115/1.1557614.   DOI
35 Kochupillai, J., Ganesan, N. and Padmanabhan, C. (2002), "A semi-analytical coupled finite element formulation for composite shells conveying fluids", J. Sound Vib., 258(2), 287-307. https://doi.org/10.1006/jsvi.2002.5176.   DOI
36 Bochkarev, S.A. and Matveenko, V.P. (2008), "Numerical study of the influence of boundary conditions on the dynamic behavior of a cylindrical shell conveying a fluid", Mech. Solid., 43(3), 477-486. https://doi.org/10.3103/S0025654408030187.   DOI
37 Firouz-Abadi, R.D., Haddadpour, H. and Kouchakzadeh, M.A. (2009), "Free vibrations of composite tanks partially filled with fluid", Thin Wall. Struct., 47(12), 1567-1574. https://doi.org/10.1016/j.tws.2009.05.007.   DOI
38 Jones, R.M. (1998), Mechanics of Composite Materials, 2nd Edition, Hemisphere Publishing Corporation, New York.
39 Kumar, A., Chakrabarti, A. and Bhargava, P. (2013a), "Finite element analysis of laminated composite and sandwich shells using higher order zigzag theory", Compos. Struct., 106, 270-281. https://doi.org/10.1016/j.compstruct.2013.06.021.   DOI
40 Lehoucq, R.B. and Sorensen, D.C. (1996), "Deflation techniques for an implicitly restarted Arnoldi iteration", SIAM J. Matrix Anal. Appl., 17(4), 789-821. https://doi.org/10.1137/S0895479895281484.   DOI
41 Muggeridge, D.B. and Buckley, T.J. (1979b), "Dynamics of a fluid conveying fiber-reinforced shell", AIAA J., 17(6), 663-666. https://doi.org/10.2514/3.61197.   DOI
42 Ray, M.C. and Reddy, J.N. (2013), "Active damping of laminated cylindrical shells conveying fluid using 1-3 piezoelectric composites", Compos. Struct., 98, 261-271. https://doi.org/10.1016/j.compstruct.2012.09.051.   DOI
43 Petrolo, M. and Carrera, E. (2020), "Methods and guidelines for the choice of shell theories", Acta Mechanica, 231(2), 395-434. https://doi.org/10.1007/s00707-019-02601-w.   DOI
44 Alijani, F. and Amabili, M. (2014), "Nonlinear vibrations and multiple resonances of fluid filled arbitrary laminated circular cylindrical shells", Compos. Struct., 108, 951-962. https://doi.org/10.1016/j.compstruct.2013.10.029.   DOI
45 Amabili, M. (1996), "Free vibration of partially filled, horizontal cylindrical shells", J. Sound Vib., 191(5), 757-780. https://doi.org/10.1006/jsvi.1996.0154.   DOI
46 Qatu, M.S., Asadi, E. and Wang, W. (2012), "Review of recent literature on static analyses of composite shells: 2000-2010", Open J. Compos. Mater., 2(3), 61-86. https://doi.org/10.4236/ojcm.2012.23009.   DOI
47 Qu, Y., Long, X., Wu, S. and Meng, G. (2013), "A unified formulation for vibration analysis of composite laminated shells of revolution including shear deformation and rotary inertia", Compos. Struct., 98, 169-191. https://doi.org/10.1016/j.compstruct.2012.11.001.   DOI
48 Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2 Edition, CRC Press, Florida.
49 Reddy, J.N. and Liu, C.F. (1985), "A higher-order shear deformation theory of laminated elastic shells", Int. J. Eng. Sci., 23(3), 319-330. https://doi.org/10.1016/0020-7225(85)90051-5.   DOI
50 Toorani, M.H. and Lakis, A.A. (2001a), "Shear deformation in dynamic analysis of anisotropic laminated open cylindrical shells filled with or subjected to a flowing fluid", Comput. Meth. Appl. Mech. Eng., 190(37), 4929-4966. https://doi.org/10.1016/S0045-7825(00)00357-1.   DOI
51 Tooth, A.S., Banks, W.M. and Rahman, D.H.A. (1988), "The specially orthotropic GRP multi-layered cylindrical shell-The fluid loading of the partially filled horizontal vessel or pipe", Compos. Struct., 9(2), 101-111. https://doi.org/10.1016/0263-8223(88)90002-5.   DOI
52 Nurul Izyan, M.D., Aziz, Z.A. and Viswanathan, K.K. (2018), "Free vibration of anti-symmetric angle-ply layered circular cylindrical shells filled with quiescent fluid under first order shear deformation theory", Compos. Struct., 193, 189-197. https://doi.org/10.1016/j.compstruct.2018.03.034.   DOI
53 Toorani, M.H. and Lakis, A.A. (2001b), "Dynamic analysis of anisotropic cylindrical shells containing flowing fluid", J. Press. Ves. Technol., 123(4), 454-460. https://doi.org/10.1115/1.1401023.   DOI
54 Toorani, M.H. and Lakis, A.A. (2003), "Dynamics behavior of axisymmetric and beam-like anisotropic cylindrical shells conveying fluid", J. Sound Vib., 259(2), 265-298. https://doi.org/10.1006/jsvi.2002.5161.   DOI