非线性弹性地基上的圆薄板的分岔与混沌问题  

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

作　　者：邱平[1] 王新志[1] 叶开沅[2] 

机构地区：[1]兰州理工大学理学院,兰州730050 [2]兰州大学物理学院,兰州730000

出　　处：《应用数学和力学》2003年第8期779-784,共6页Applied Mathematics and Mechanics

基　　金：甘肃省自然科学基金资助项目(ZS021_A25_007_Z)

摘　　要：　根据非线性弹性地基上圆薄板大幅度方程,弹性抗力有线性项,三次非线性项和抗弯曲弹性项·　在周边固定的条件下,利用Galerkin法得到了一个非线性振动方程·　在无外激励情况下,求出在平衡点处的Floquet指数·　分析了其稳定性与可能发生的分岔条件·　在外激励条件下,用MelAccording 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.

关 键 词：分岔 混沌 大幅度 非线性 

分 类 号：O343.5[理学—固体力学] O326[理学—力学]