Bifurcation and Chaos of the Circular Plates on the Nonlinear Elastic Foundation

QIU Ping; WANG Xin-zhi; YEH Kai-yuan

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(8): 779-784

QIU Ping, WANG Xin-zhi, YEH Kai-yuan. Bifurcation and Chaos of the Circular Plates on the Nonlinear Elastic Foundation[J]. Applied Mathematics and Mechanics, 2003, 24(8): 779-784.

Citation:

QIU Ping, WANG Xin-zhi, YEH Kai-yuan. Bifurcation and Chaos of the Circular Plates on the Nonlinear Elastic Foundation[J]. Applied Mathematics and Mechanics, 2003, 24(8): 779-784.

Citation:

QIU Ping, WANG Xin-zhi, YEH Kai-yuan. Bifurcation and Chaos of the Circular Plates on the Nonlinear Elastic Foundation[J]. Applied Mathematics and Mechanics, 2003, 24(8): 779-784.

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Bifurcation and Chaos of the Circular Plates on the Nonlinear Elastic Foundation

1.
School of Science, Lanzhou University of Science and Technology, Lanzhou 730050, P. R. China;
2.
Physics College, Lanzhou University, Lanzhou 730000, P. R. China

Received Date: 2002-07-11
Rev Recd Date: 2003-05-02
Publish Date: 2003-08-15

Abstract

Abstract

According to the large amplitude equation of the circular plate on nonlinear elastic foundation,elastic resisting force has linearitem,cubic nonlinearitem and resisting bend elasticitem.Anonlinear vibration equation is obtained with the method of Galerkin under the condition of fixed boundary.Floquet exponent at equilibrium point is obtained without external excitation.Its stability and condition of possible bifurcation is analysed.Possible chaotic vibration is analysed and studied with the method of Melnikov with external excitation.The critical curves of the chaotic region and phase figure under some foundation parameters are obtained with the method of digital artificial.
- bifurcation,
- chaos,
- large amplitude,
- nonlinear

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References(7)

References

[1]	Gajiendar N.Large amplitude vibrations of plates on elastic foundations[J].Int J Nonlinear Mech,1967,2(1):163-168.
[2]	Nath Y.Large amplitude response of circular plate on elastic foundation[J].Int J Nonlinear Mech,1982,17(4):285-296.
[3]	Dumir P C.Nonlinear vibration and postbuckling of isotropic thin circular plate on elastic foundation[J].Journal of Sound and Vibration,1986,107(2):253-263.
[4]	赵永刚,王新志,丁雪兴,等.静载荷作用下弹性地基上圆薄板的小阻尼非线性振动[A].见:焦善庆主编.数学、力学、物理、高新技术研究进展[C].成都:西南交通大学出版社,2000,104-109.
[5]	丁雪兴,赵永刚,王新志.弹性地基上圆薄板的变参数迭代解[J].甘肃工业大学学报,1999,25(4):101-105.
[6]	唐建宁,刘文明,刘曾荣.硬弹簧Duffing方程的全局分叉[J].力学与实践,1987,9(1):33-37.
[7]	陈予恕,唐云.非线性动力学的现代分析方法[M].北京:科学出版社,2000,167-168.