基于HB-AFT算法的阵发性混沌振动研究新方法

阵发性振动最早用来阐述流体中的层流被湍流无规则扰动的现象.在非线性动力学领域,阵发性指的是系统时域响应随着参数的变化出现规则与不规则运动之间伪随机交替的运动特征.响应的阵发性是非线性动力学系统随分岔参数变化进入混沌运动的一种典型途径.不过,对于非线性系统阵发性混沌现象,由于其参数敏感性和动力学行为演化的复杂性,研究手段还有待丰富.半解析半数值的谐波平衡 频时转换(Harmonic balance and alternating frequency/time domain,简称HB AFT)方法可以避开传统方法对于复杂非线性项的积分或者级数展开等处理过程,能够快速而精确地求得系统的谐波解.本文基于HB AFT方法,结合Floquet稳定性理论,给出一套非线性动力系统阵发性混沌演化的研究的半解析方法.并以经典的单频激励Duffing系统为例,对其全局周期解分支及其失稳特性进行分析,阐明了该系统一种阵发I型混沌行为的动力学演化机制.

A new method based on HB-AFT algorithm for intermittent chaotic vibration study

Intermittent vibration refers to the state in which the laminar flow in fluid is interrupted by turbulent outbreaks at irregular intervals. In the field of nonlinear dynamics, the intermittent motions is termed the pseudo random alternating motion between regular motion and irregular motion. Intermittency is a typical route to chaotic motions for nonlinear dynamical systems. However, for the behaviors of intermittency chaos, the research methods have yet to be enriched due to the parametric sensitivity and evolution complexity of the nonlinear dynamic responses. The semi-analytical and semi numerical harmonic balance and alternating frequency/time domain (HB-AFT) method can avoid the traditional integral or series expansion of complicated nonlinear terms, which make it obtain a harmonic solution of the system quickly and accurately. Based on the HB-AFT method and Floquet stability theory, this paper presented a new semi-analytical method for the evolution of intermittency chaos in nonlinear dynamical systems. Taking the classical single frequency excitation Duffing system as an example, the global periodic solution branches and their instabilities are analyzed, and the dynamic evolution mechanism of a type I intermittency chaos is illustrated.