BIFURCATION AND CHAOS OF THE CIRCULAR PLATES ON THE NONLINEAR ELASTIC FOUNDATION

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (8): 880-885.

BIFURCATION AND CHAOS OF THE CIRCULAR PLATES ON THE NONLINEAR ELASTIC FOUNDATION

邱平¹, 王新志¹, 叶开沅²

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

收稿日期:2002-07-11 修回日期:2003-05-02 出版日期:2003-08-18 发布日期:2003-08-18
基金资助:
the Natural Science Foundation of Gansu Province(ZSQ21-A25-007-Z)

BIFURCATION AND CHAOS OF THE CIRCULAR PLATES ON THE NONLINEAR ELASTIC FOUNDATION

QIU Ping¹, WANG Xin-zhi¹, YEH Kai-yuan²

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:2002-07-11 Revised:2003-05-02 Online:2003-08-18 Published:2003-08-18
Supported by:
the Natural Science Foundation of Gansu Province(ZSQ21-A25-007-Z)

摘要/Abstract

摘要： According to the large amplitude equation of the circular plate on nonlinear elastic foundation, elastic resisting force has linear item, cubic nonlinear item and resisting bend elastic item. A nonlinear 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.

Abstract: According to the large amplitude equation of the circular plate on nonlinear elastic foundation, elastic resisting force has linear item, cubic nonlinear item and resisting bend elastic item. A nonlinear 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.

中图分类号:

O343.5
O326

邱平;王新志;叶开沅. BIFURCATION AND CHAOS OF THE CIRCULAR PLATES ON THE NONLINEAR ELASTIC FOUNDATION[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(8): 880-885.

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 (English Edition), 2003, 24(8): 880-885.

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BIFURCATION AND CHAOS OF THE CIRCULAR PLATES ON THE NONLINEAR ELASTIC FOUNDATION

BIFURCATION AND CHAOS OF THE CIRCULAR PLATES ON THE NONLINEAR ELASTIC FOUNDATION

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