非线性弹性地基上的圆薄板的分岔与混沌问题

基金项目: 甘肃省自然科学基金资助项目(ZS021-A25-007-Z)

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

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Melnikov方法分析研究了可能发生的混沌振动。通过数字仿真给出了各种地基参数下混沌区域的临界曲线和相平面图。
- 分岔 /
- 混沌 /
- 大幅度 /
- 非线性
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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