一类带有外激的非线性动力系统的混沌运动
发布时间：2018-07-21 17:58
【摘要】：利用多尺度摄动法推导出一类带有非线性和外部激励的两自由度气弹性动力系统的平均方程,对于非摄动情况下的平均方程,得出其异宿轨存在的条件,并计算出异宿轨的显示表达式,然后利用Melnikov方法得到当某些参数值取特定值时,平均方程的异宿轨破裂,这可能引起Smale马蹄混沌。最后,将该理论分析结果应用到一个功能梯度板模型,得出在一定参数取值下,该模型存在异宿轨破裂引起的Smale马蹄混沌。
[Abstract]:By using the multi-scale perturbation method, the average equations of a class of two-degree-of-freedom aero-elastic dynamic systems with nonlinear and external excitations are derived. For the non-perturbed average equations, the conditions for the existence of heteroclinic orbits are obtained. The display expression of the heteroclinic orbit is calculated, and the Melnikov method is used to obtain the rupture of the average equation when some parameter values are given, which may cause Smale horseshoe chaos. Finally, the theoretical analysis results are applied to a functional gradient plate model, and the Smale horseshoe chaos caused by the rupture of the heteroclinic orbit is obtained under certain parameters.
【作者单位】： 南京航空航天大学航空宇航学院;南京航空航天大学理学院;
【基金】：国家自然科学基金(11202095) 高等学校博士学科点专项科研基金(20133218110025)资助
【分类号】：O322
，
本文编号：2136327
[Abstract]:By using the multi-scale perturbation method, the average equations of a class of two-degree-of-freedom aero-elastic dynamic systems with nonlinear and external excitations are derived. For the non-perturbed average equations, the conditions for the existence of heteroclinic orbits are obtained. The display expression of the heteroclinic orbit is calculated, and the Melnikov method is used to obtain the rupture of the average equation when some parameter values are given, which may cause Smale horseshoe chaos. Finally, the theoretical analysis results are applied to a functional gradient plate model, and the Smale horseshoe chaos caused by the rupture of the heteroclinic orbit is obtained under certain parameters.
【作者单位】： 南京航空航天大学航空宇航学院;南京航空航天大学理学院;
【基金】：国家自然科学基金(11202095) 高等学校博士学科点专项科研基金(20133218110025)资助
【分类号】：O322
，
本文编号：2136327
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