Abstract
In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitudé is obtained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.
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Li Dong, Nonlinear vibrations of orthotropic shallow shells of revolutions,Appl. Math. and Mech. (English Ed.),13, 4 (1992), 331–334.
G. C. Sinharay and B. Banerjee, Large amplitude free vibration of shallow spherical shell and cylindrical shell—A new approach,Int. J. Non-linear Mech.,20, 2 (1985), 69–75.
Wang Linxian and Wang Xinzhi, Axisymmetrical nonlinear free vibration of shallow conic shells subjected to the static loads,Proceedings of the 6th National Conference on Nonlinear Vibration, Tianjin University Press, Tianjin, China (1992), 101–106. (in Chinese).
Wu Xingqiang and Xu Cida, Postbucking of axially compressed circular cylindrical thin shells analysed by MWR,Chin, J. Appl. Mech.,8, 2 (1991), 9–17. (in Chinese).
A. H. Nayfeh and D. T. Mook,Nonlinear Oscillations John Wiley & Sons, New York (1979).
T. K. Varadan and K. A. V. Pandalai, Nonlinear flexural oscillation of orthotropic shallow spherical shells,Computer and Structure,9 (1978), 417–425.
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Yonggang, W., Xinzhi, W. & Huifang, S. Nonlinear free vibration of orthotropic shallow shells of revolution under the static loads. Appl Math Mech 18, 585–591 (1997). https://doi.org/10.1007/BF02454118
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DOI: https://doi.org/10.1007/BF02454118