Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

doi:10.1007/s10483-022-2892-7

Abstract

Abstract: The aim of the present study is to investigate the nonlinear free vibration of spinning cylindrical shells under spinning and arbitrary boundary conditions. Artificial springs are used to simulate arbitrary boundary conditions. Sanders' shell theory is employed, and von Kármán nonlinear terms are considered in the theoretical modeling. By using Chebyshev polynomials as admissible functions, motion equations are derived with the Ritz method. Then, a direct iteration method is used to obtain the nonlinear vibration frequencies. The effects of the circumferential wave number, the boundary spring stiffness, and the spinning speed on the nonlinear vibration characteristics of the shells are highlighted. It is found that there exist sensitive intervals for the boundary spring stiffness, which makes the variation of the nonlinear frequency ratio more evident. The decline of the frequency ratio caused by the spinning speed is more significant for the higher vibration amplitude and the smaller boundary spring stiffness.

Key words: spinning cylindrical shell, nonlinear free vibration, arbitrary boundary condition, Chebyshev polynomial, Sanders' shell theory

2010 MSC Number:

70J30

Qingdong CHAI, Yanqing WANG, Meiwen TENG. Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions. Applied Mathematics and Mechanics (English Edition), 2022, 43(8): 1203-1218.

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References

[1] GANAPATHI, M. and VARADAN, T. Large amplitude vibrations of circular cylindrical shells. Journal of Sound and Vibration, 192, 1-14(1996)
[2] AMABILI, M. A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells:Lagrangian approach. Journal of Sound and Vibration, 264, 1091-1125(2003)
[3] JANSEN, E. A comparison of analytical-numerical models for nonlinear vibrations of cylindrical shells. Computers & structures, 82(31-32), 2647-2658(2004)
[4] GONÇALVES, P., SILVA, F., and PRADO, Z. Low-dimensional models for the nonlinear vibration analysis of cylindrical shells based on a perturbation procedure and proper orthogonal decomposition. Journal of Sound and Vibration, 315, 641-663(2008)
[5] ZHANG, W., HAO, Y., and YANG, J. Nonlinear dynamics of FGM circular cylindrical shell with clamped-clamped edges. Composite Structures, 94(3), 1075-1086(2012)
[6] HASRATI, E., ANSARI, R., and TORABI, J. A novel numerical solution strategy for solving nonlinear free and forced vibration problems of cylindrical shells. Applied Mathematical Modelling, 53, 653-672(2018)
[7] DU, C., LI, Y., and JIN, X. Nonlinear forced vibration of functionally graded cylindrical thin shells. Thin-Walled Structures, 78, 26-36(2014)
[8] JAFARI, A., KHALILI, S., and TAVAKOLIAN, M. Nonlinear vibration of functionally graded cylindrical shells embedded with a piezoelectric layer. Thin-Walled Structures, 79, 8-15(2014)
[9] STROZZI, M. and PELLICANO, F. Nonlinear vibrations of functionally graded cylindrical shells. Thin-Walled Structures, 67, 63-77(2013)
[10] MOHAMADI, A., SHAHGHOLI, M., and GHASEMI, F. A. Nonlinear vibration of axially moving simply-supported circular cylindrical shell. Thin-Walled Structures, 156, 107026(2020)
[11] WANG, Y. Q., YE, C., and ZU, J. W. Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets. Aerospace Science and Technology, 85, 359-370(2019)
[12] YE, C. and WANG, Y. Q. Nonlinear forced vibration of functionally graded graphene plateletreinforced metal foam cylindrical shells:internal resonances. Nonlinear Dynamics, 104, 2051-2069(2021)
[13] LIU, Y., HAO, Y., ZHANG, W., CHEN, J., and LI, S. Nonlinear dynamics of initially imperfect functionally graded circular cylindrical shell under complex loads. Journal of Sound and Vibration, 348, 294-328(2015)
[14] KAMALOO, A., JABBARI, M., YARMOHAMMAD, T. M., and JAVADI, M. Nonlinear free vibration analysis of delaminated composite circular cylindrical shells. Journal of Vibration and Control, 26(19-20), 1697-1707(2020)
[15] PARVEZ, M. T., KHAN A. H., and YASIN, M. Y. On the softening and hardening nonlinear behavior of laminated cylindrical shells. Engineering Structures, 226, 111339(2021)
[16] LEE, Y. S. and KIM, Y. W. Nonlinear free vibration analysis of rotating hybrid cylindrical shells. Computers & structures, 70(2), 161-168(1999)
[17] LIU, T., ZHANG, W., MAO, J., and ZHENG, Y. Nonlinear breathing vibrations of eccentric rotating composite laminated circular cylindrical shell subjected to temperature, rotating speed and external excitations. Mechanical Systems and Signal Processing, 127, 463-498(2019)
[18] LIU, Y. and CHU, F. Nonlinear vibrations of rotating thin circular cylindrical shell. Nonlinear Dynamics, 67, 1467-1479(2012)
[19] WANG, Y. Q. Nonlinear vibration of a rotating laminated composite circular cylindrical shell:traveling wave vibration. Nonlinear Dynamics, 77, 1693-1707(2014)
[20] SHENG, G. and WANG, X. The non-linear vibrations of rotating functionally graded cylindrical shells. Nonlinear Dynamics, 87, 1095-1109(2017)
[21] SUN, S., LIU, L., and CAO, D. Nonlinear travelling wave vibrations of a rotating thin cylindrical shell. Journal of Sound and Vibration, 431, 122-136(2018)
[22] LI, C., LI, P., ZHONG, B., and WEN, B. Geometrically nonlinear vibration of laminated composite cylindrical thin shells with non-continuous elastic boundary conditions. Nonlinear Dynamics, 95, 1903-1921(2019)
[23] QIN, Z., PANG, X., SAFAEI, B., and CHU, F. Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions. Composite Structures, 220, 847-860(2019)
[24] LIU, T., WANG, A., WANG, Q., and QIN, B. Wave based method for free vibration characteristics of functionally graded cylindrical shells with arbitrary boundary conditions. Thin-Walled Structures, 148, 106580(2020)
[25] AMABILI, M. Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, Cambridge University (2008)
[26] CHAI, Q. and WANG, Y. Q. Traveling wave vibration of graphene platelet reinforced porous joined conical-cylindrical shells in a spinning motion. Engineering Structures, 252, 113718(2022)
[27] WANG, Y. Q. and TENG, M. W. Vibration analysis of circular and annular plates made of 3D graphene foams via Chebyshev-Ritz method. Aerospace Science and Technology, 95, 105440(2019)
[28] QIN, Z., CHU, F., and ZU, J. Free vibrations of cylindrical shells with arbitrary boundary conditions:a comparison study. International Journal of Mechanical Sciences, 133, 91-99(2017)
[29] CHAI, Q. and WANG, Y. Q. A general approach for free vibration analysis of spinning joined conical-cylindrical shells with arbitrary boundary conditions. Thin-Walled Structures, 168, 108243(2021)
[30] PELLICANO, F. Vibrations of circular cylindrical shells:theory and experiments. Journal of Sound and Vibration, 303, 154-170(2007)
[31] SAITO, T. and ENDO, M. Vibration of finite length, rotating cylindrical shells. Journal of Sound and Vibration, 107, 17-28(1986)
[32] SUN, S., CAO, D., and HAN, Q. Vibration studies of rotating cylindrical shells with arbitrary edges using characteristic orthogonal polynomials in the Rayleigh-Ritz method. International Journal of Mechanical Sciences, 68, 180-189(2013)
[33] LAKIS, A., SELMANE, A., and TOLEDANO, A. Non-linear free vibration analysis of laminated orthotropic cylindrical shells. International Journal of Mechanical Sciences, 40(1), 27-49(1998)
[34] DONG, Y., ZHU, B., WANG, Y., LI, Y., and YANG, J. Nonlinear free vibration of graded graphene reinforced cylindrical shells:effects of spinning motion and axial load. Journal of Sound and Vibration, 437, 79-96(2018)