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Original Articles

Non-linear parametric vibration of the laminated composite shallow shells including primary and 1:2 internal resonances

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Pages 3444-3475 | Received 09 Nov 2022, Accepted 04 Feb 2023, Published online: 20 Feb 2023

References

  • A. Shaterzadeh, and K. Foroutan, Post-buckling of cylindrical shells with spiral stiffeners under elastic foundation, Struct. Eng. Mech., vol. 60, no. 4, pp. 615–631, 2016. DOI: 10.12989/sem.2016.60.4.615.
  • N.D. Duc, and P.T. Thang, Nonlinear response of imperfect eccentrically stiffened ceramic-metal-ceramic sigmoid functionally graded material (S-FGM) thin circular cylindrical shells surrounded on elastic foundations under uniform radial load, Mech. Adv. Mater. Struct., vol. 22, no. 12, pp. 1031–1038, 2015. DOI: 10.1080/15376494.2014.910320.
  • A.H. Sofiyev, D. Hui, V.C. Haciyev, H. Erdem, G.Q. Yuan, E. Schnack, and V. Guldal, The nonlinear vibration of orthotropic functionally graded cylindrical shells surrounded by an elastic foundation within first order shear deformation theory, Compos. B. Eng., vol. 116, pp. 170–185, 2017. DOI: 10.1016/j.compositesb.2017.02.006.
  • D.H. Bich, N.D. Duc, and T.Q. Quan, Nonlinear vibration of imperfect eccentrically stiffened functionally graded double curved shallow shells resting on elastic foundation using the first order shear deformation theory, Int. J. Mech. Sci., vol. 80, pp. 16–28, 2014. DOI: 10.1016/j.ijmecsci.2013.12.009.
  • A.H. Sofiyev, Application of the first order shear deformation theory to the solution of free vibration problem for laminated conical shells, Compos. Struct., vol. 188, pp. 340–346, 2018. DOI: 10.1016/j.compstruct.2018.01.016.
  • B. Wu, A. Pagani, W.Q. Chen, and E. Carrera, Geometrically nonlinear refined shell theories by Carrera Unified Formulation, Mech. Adv. Mater. Struct., vol. 28, no. 16, pp. 1721–1741, 2021. DOI: 10.1080/15376494.2019.1702237.
  • B. Wu, A. Pagani, M. Filippi, W.Q. Chen, and E. Carrera, Large-deflection and post-buckling analyses of isotropic rectangular plates by Carrera Unified Formulation, Int. J. Non Linear Mech., vol. 116, pp. 18–31, 2019. DOI: 10.1016/j.ijnonlinmec.2019.05.004.
  • A. Mehditabar, and G.H. Rahimi, Multiaxial ratcheting evaluation of functionally graded cylindrical shell by means of Ohno–Wang’s type models, Eng. Comput., vol. 37, no. 1, pp. 609–622, 2021. DOI: 10.1007/s00366-019-00845-7.
  • H. Jrad, J. Mars, M. Wali, and F. Dammak, Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells, Eng. Comput., vol. 35, no. 3, pp. 833–847, 2019. DOI: 10.1007/s00366-018-0633-3.
  • K. Foroutan, E. Carrera, A. Pagani, and H. Ahmadi, Post-buckling and large-deflection analysis of a sandwich FG plate with FG porous core using Carrera’s Unified Formulation, Compos. Struct., vol. 272, p. 114189, 2021.‏ DOI: 10.1016/j.compstruct.2021.114189.
  • R. Zhong, B. Qin, Q. Wang, W. Shao, and C. Shuai, Prediction of the in-plane vibration behavior of porous annular plate with porosity distributions in the thickness and radial directions, Mech. Adv. Mater. Struct., vol. 29, no. 25, pp. 4206–4223, 2022. DOI: 10.1080/15376494.2021.1922960.
  • M.C. Trinh, and H. Jun, Stochastic bending and buckling analysis of laminated composite plates using Latin hypercube sampling, Eng. Comput., pp. 1–39, 2021. DOI: 10.1007/s00366-021-01544-y.
  • A. Pagani, R. Augello, and E. Carrera, Numerical simulation of deployable ultra-thin composite shell structures for space applications and comparison with experiments, Mech. Adv. Mater. Struct., pp. 1–13, 2022. DOI: 10.1080/15376494.2022.2037173.
  • M. Salim, M. Bodaghi, S. Kamarian, and M. Shakeri, Free vibration analysis and design optimization of SMA/Graphite/Epoxy composite shells in thermal environments, Lat. Am. j. solids Struct., vol. 15, no. 1, pp. 1–16, 2018. DOI: 10.1590/1679-78253070.
  • M.D. Awruch, and H.M. Gomes, A fuzzy α-cut optimization analysis for vibration control of laminated composite smart structures under uncertainties, Appl. Math. Model., vol. 54, pp. 551–566, 2018. DOI: 10.1016/j.compstruct.2019.110964.
  • K. Foroutan, S.M. Varedi-Koulaei, N.D. Duc, and H. Ahmadi, Non-linear static and dynamic buckling analysis of laminated composite cylindrical shell embedded in non-linear elastic foundation using the swarm-based metaheuristic algorithms, Eur. J. Mech. A Solids., vol. 91, pp. 104420, 2022. DOI: 10.1016/j.euromechsol.2021.104420.
  • S.S. Rao, Engineering Optimization: Theory and Practice, John Wiley & Sons, Florida, 2019.
  • L. Dai, Non-Linear Dynamics of Piecewise Constant Systems and Implementation of Piecewise Constant Arguments, World Scientific Publishing Co, New Jersey, 2008.
  • Ö. Civalek, Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations, Int. J. Press. Vessel. Pip., vol. 113, pp. 1–9, 2014. DOI: 10.1016/j.ijpvp.2013.10.014.
  • H. Ersoy, K. Mercan, and Ö. Civalek, Frequencies of FGM shells and annular plates by the methods of discrete singular convolution and differential quadrature methods, Compos. Struct., vol. 183, pp. 7–20, 2018. DOI: 10.1016/j.compstruct.2016.11.051.
  • Ö. Civalek, S. Dastjerdi, and B. Akgöz, Buckling and free vibrations of CNT-reinforced cross-ply laminated composite plates, Mech. Based Des. Struct. Mach., vol. 50, no. 6, pp. 1914–1931, 2022. DOI: 10.1080/15397734.2020.1766494.
  • M. Farrokh, and H.S. Mousavi Fard, An extension of Carrera unified formulation in polar coordinates for mechanical and thermal buckling analysis of axisymmetric FG circular plate using FEM, Mech. Adv. Mater. Struct., pp. 1–9, 2022. DOI: 10.1080/15376494.2022.2142885.
  • E. Carrera, A. Pagani, R. Augello, and B. Wu, Popular benchmarks of nonlinear shell analysis solved by 1D and 2D CUF-based finite elements, Mech. Based Des. Struct. Mach., vol. 27, no. 13, pp. 1098–1109, 2020. ‏ DOI: 10.1080/15376494.2020.1728450.
  • A. Pagani, and E. Carrera, Large-deflection and post-buckling analyses of laminated composite beams by Carrera Unified Formulation, Compos. Struct., vol. 170, pp. 40–52, 2017. DOI: 10.1016/j.compstruct.2017.03.008.
  • A. Pagani, and E. Carrera, Unified formulation of geometrically nonlinear refined beam theories, Mech. Based Des. Struct. Mach., vol. 25, no. 1, pp. 15–31, 2018.‏ DOI: 10.1080/15376494.2016.1232458.
  • A. Pagani, E. Carrera, and R. Augello, Evaluation of various geometrical nonlinearities in the response of beams and shells, AIAA J., vol. 57, no. 8, pp. 3524–3533, 2019.‏ DOI: 10.2514/1.J057877.
  • X. Li, C. Du, and Y. Li, Parametric resonance of a FG cylindrical thin shell with periodic rotating angular speeds in thermal environment, Appl. Math. Model., vol. 59, pp. 393–409, 2018. DOI: 10.1016/j.apm.2018.01.048.
  • F. Alijani, M. Amabili, and F. Bakhtiari-Nejad, On the accuracy of the multiple scales method for non-linear vibrations of doubly curved shallow shells, Int. J. Non Linear Mech., vol. 46, no. 1, pp. 170–179, 2011. DOI: 10.1016/j.ijnonlinmec.2010.08.006.
  • G. Sheng, and X. Wang, Nonlinear vibrations of FG cylindrical shells subjected to parametric and external excitations, Compos. Struct., vol. 191, pp. 78–88, 2018. DOI: 10.1016/j.compstruct.2018.02.018.
  • C. Du, and Y. Li, Nonlinear resonance behavior of functionally graded cylindrical shells in thermal environments, Compos. Struct., vol. 102, pp. 164–174, 2013. DOI: 10.1016/j.compstruct.2013.02.028.
  • K. Gao, W. Gao, B. Wu, D. Wu, and C. Song, Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales, Thin Wall. Struct., vol. 125, pp. 281–293, 2018. DOI: 10.1016/j.tws.2017.12.039.
  • G. Sheng, and X. Wang, The dynamic stability and nonlinear vibration analysis of stiffened functionally graded cylindrical shells, Appl. Math. Model., vol. 56, pp. 389–403, 2018. DOI: 10.1016/j.apm.2017.12.021.
  • H. Ahmadi, Nonlinear primary resonance of imperfect spiral stiffened functionally graded cylindrical shells surrounded by damping and nonlinear elastic foundation, Eng. Comput., vol. 35, no. 4, pp. 1491–1505, 2019. DOI: 10.1007/s00366-018-0679-2.
  • H. Ahmadi, and K. Foroutan, Nonlinear primary resonance of spiral stiffened functionally graded cylindrical shells with damping force using the method of multiple scales, Thin Wall. Struct., vol. 135, pp. 33–44, 2019. DOI: 10.1016/j.tws.2018.10.028.
  • H. Ahmadi, and K. Foroutan, Superharmonic and subharmonic resonances of spiral stiffened functionally graded cylindrical shells under harmonic excitation, Int. J. Str. Stab. Dyn., vol. 19, no. 10, p. 1950114, 2019. DOI: 10.1142/S0219455419501141.
  • K. Foroutan, H. Ahmadi, and M. Shariyat, Asymmetric large deformation superharmonic and subharmonic resonances of spiral stiffened imperfect FG cylindrical shells resting on generalized nonlinear viscoelastic foundations, Int. J. Appl. Mech., vol. 12, no. 5, p. 2050052, 2020. DOI: 10.1142/S1758825120500520.
  • H. Ahmadi, and K. Foroutan, Nonlinear vibration of stiffened multilayer FG cylindrical shells with spiral stiffeners rested on damping and elastic foundation in thermal environment, Thin Wall. Struct., vol. 145, p. 106388, 2019. DOI: 10.1016/j.tws.2019.106388.
  • K. Foroutan, and H. Ahmadi, Combination resonances of imperfect SSFG cylindrical shells rested on viscoelastic foundations, Struct. Eng. Mech., vol. 75, no. 1, pp. 87–100, 2020. DOI: 10.12989/sem.2020.75.1.087.
  • H. Ahmadi, and K. Foroutan, Combination resonance analysis of FG porous cylindrical shell under two-term excitation, Steel Compos. Struct., vol. 32, no. 2, pp. 253–264, 2019. DOI: 10.12989/scs.2019.32.2.253.
  • K. Foroutan, and L. Dai, Nonlinear dynamic responses of porous FG sandwich cylindrical shells with a viscoelastic core resting on a nonlinear viscoelastic foundation, Mech. Adv. Mater. Struct., pp. 1–20, 2022. DOI: 10.1080/15376494.2022.2070803.
  • W. Zhang, T. Liu, A. Xi, and Y. Wang, Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes, J. Sound Vib., vol. 423, pp. 65–99, 2018. DOI: 10.1016/j.jsv.2018.02.049.
  • A. Abe, Y. Kobayashi, and G. Yamada, Nonlinear dynamic behaviors of clamped laminated shallow shells with one-to-one internal resonance, J. Sound Vib., vol. 304, no. 3–5, pp. 957–968, 2007. DOI: 10.1016/j.jsv.2007.03.009.
  • L. Rodrigues, P.B. Gonçalves, and F.M. Silva, Internal resonances in a transversally excited imperfect circular cylindrical shell, Pro. Eng., vol. 199, pp. 838–843, 2017. DOI: 10.1016/j.proeng.2017.09.010.
  • S. Mahmoudkhani, H. Navazi, and H. Haddadpour, An analytical study of the non-linear vibrations of cylindrical shells, Int. J. Non Linear Mech., vol. 46, no. 10, pp. 1361–1372, 2011. DOI: 10.1016/j.ijnonlinmec.2011.07.012.
  • T. Liu, W. Zhang, J. Mao, and Y. Zheng, Nonlinear breathing vibrations of eccentric rotating composite laminated circular cylindrical shell subjected to temperature, rotating speed and external excitations, Mech. Syst. Signal Process., vol. 127, pp. 463–498, 2019. DOI: 10.1016/j.ymssp.2019.02.061.
  • F.M. Li, and G. Yao, 1/3 Subharmonic resonance of a nonlinear composite laminated cylindrical shell in subsonic air flow, Compos. Struct., vol. 100, pp. 249–256, 2013. DOI: 10.1016/j.compstruct.2012.12.035.
  • K. Foroutan, and H. Ahmadi, Nonlinear parametric vibration of imperfect SSMFG cylindrical shells in thermal environment including internal and subharmonic resonances, Mech. Adv. Mater. Struct., vol. 29, no. 24, pp. 3499–3522, 2022.‏ DOI: 10.1080/15376494.2021.1904526.
  • C. Li, P. Li, B. Zhong, and X. Miao, Large-amplitude vibrations of thin-walled rotating laminated composite cylindrical shell with arbitrary boundary conditions, Thin Wall. Struct., vol. 156, p. 106966, 2020. DOI: 10.1016/j.tws.2020.106966.
  • V.G. Belardi, P. Fanelli, and F. Vivio, On the radial bending of shear-deformable composite circular plates with rectilinear orthotropy, Eur. J. Mech. A Solids., vol. 86, p. 104157, 2021. DOI: 10.1016/j.euromechsol.2020.104157.
  • D.O. Brush, and B.O. Almroth, Buckling of Bars, Plates, and Shells, McGraw-Hill, New York, 1975.
  • J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, 2003.
  • S.S. Rao, Vibration of Continuous Systems, John Wiley & Sons, New Jersey, 2007.
  • N.D. Duc, H. Hadavinia, T.Q. Quan, and N.D. Khoa, Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment, Eur. J. Mech. A Solids., vol. 75, pp. 355–366, 2019. DOI: 10.1016/j.euromechsol.2019.01.024.
  • J. Kennedy, and R. Eberhart, Particle swarm optimization, Proceedings of the International Joint Conference on Neural Networks, Nov. 1995, pp. 1942–1948.
  • A. Sardashti, H.M. Daniali, and S.M. Varedi, Optimal free-defect synthesis of four-bar linkage with joint clearance using PSO algorithm, Meccanica., vol. 48, no. 7, pp. 1681–1693, ‏2013. DOI: 10.1007/s11012-013-9699-6.
  • X. Zhang, G. Liu, and K. Lam, Vibration analysis of thin cylindrical shells using wave propagation approach, J. Sound Vib., vol. 239, no. 3, pp. 397–403, 2001. DOI: 10.1006/jsvi.2000.3139.
  • Z.G. Song, and F.M. Li, Aerothermoelastic analysis and active flutter control of supersonic composite laminated cylindrical shells, Compos. Struct., vol. 106, pp. 653–660, 2013. DOI: 10.1016/j.compstruct.2013.07.029.
  • S. Yang, W. Zhang, and J. Mao, Nonlinear vibrations of carbon fiber reinforced polymer laminated cylindrical shell under non-normal boundary conditions with 1:2 internal resonance, Eur. J. Mech. A Solids., vol. 74, pp. 317–336, 2019. DOI: 10.1016/j.euromechsol.2018.11.014.
  • M. Malik, and C.W. Bert, Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method, Int. J. Solids Struct., vol. 35, no. 3–4, pp. 299–318, 1998. DOI: 10.1016/S0020-7683(97)00073-5.

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