一类带有外激的非线性动力系统的混沌运动

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。

Chaos in a nonlinear dynamical system under external excitation

With the aid of the method of multiple scales perturbation technique, the averaged equations of a two-degree-of-freedom elastic and dynamic system with nonlinearities and external excitation are derived. For the unperturbed averaged system, the criteria for the existence and the expressions of heteroclinic orbits are obtained. Using the Melnikov function, for some certain parameters the heteroclinic orbits break with transversal intersections. In this case, Smale horseshoes may existence. Finally, this analysis method is applied to a functionally graded materials plate model. And for some certain parameters the heteroclinic orbits break and Smale horseshoes existence.#$NLKeywords: the method of multiple scales perturbation; heteroclinic orbit; Melnikov function; Smale horseshoes