针对非线性隔振系统不容易产生小幅值混沌振动的难题，选择合适的多涡卷混沌系统及其参数，实现了非线性隔振Duffing系统与涡卷混沌系统同步，重构了隔振系统响应信号的频谱，得到小幅值的宽频动力学行为。研究了不同参数条件下涡卷混沌行为以及对应的频谱特征，通过计算系统响应的最大Lyapunov指数，证实该系统处于混沌状态。通过参数驱动同步策略，发现非线性隔振系统在周期状态下，能够被有效地同步到混沌状态。而且从系统的分岔图以及吸引子相图可以看出，同步后系统的混沌响应具有明显的小幅值特性；同时驱动系统的涡卷参数可调，可以满足不同系统的同步需求。
Abstract
The nonlinear vibration isolation system was hard to produce chaotic vibration with small amplitude. In order to solve this problem, the synchronization between a multi-scroll chaotic system and Duffing system is achieved. The frequency and spectrum of the isolation system was reconstructed, and then the dynamics behavior with broadband and small amplitude was realized. Firstly, the chaotic dynamic characteristics with different parameters of the multi-scroll system and its corresponding frequency spectrum characteristics were studied. Secondly, the largest Lyapunov exponent of the system response was calculated to confirm the system was in chaotic state. Finally, the synchronization strategy was simulated, and the results showed that the synchronization between nonlinear isolation system under periodic state and chaotic system could be achieved exactly, and the chaotic response after synchronization had the obvious characteristics of small amplitude which could be presented in the bifurcation and attractor diagram. At the same time, the scroll numbers of drive system are adjustable, so the synchronizations of different system are still applicative.
关键词
多涡卷 /
混沌 /
同步 /
Duffing系统 /
小幅值
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Key words
multi-scroll /
chaos /
synchronization /
Duffing system /
small amplitude;
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