辐射噪声线谱多涡卷混沌同步化方法研究

摘要

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。%The nonlinear vibration isolation system is hard to produce chaotic vibration with small amplitude.In order to solve the problem,an appropriate multi-scroll chaotic system and its parameters were selected and the synchronization between the multi-scroll chaotic system and Duffing system were achieved.The frequency and spectrum of the isolation system was reconstructed,and then the dynamics behavior with broadband spectrum and small amplitude was realized.The chaotic dynamic characteristics under different parameters of the multi-scroll system and the corresponding frequency spectrum characteristics were studied.The largest Lyapunov exponent of the system response was calculated to confirm the chaotic state of system.By using the parametric driven synchronization strategy,it is found that the synchronization between the periodic state and chaotic state of the nonlinear isolation system can be achieved exactly,and the chaotic response after synchronization has obvious characteristics of small amplitude which can be presented in the bifurcation and attractor diagram.In addition,the scroll number of drive system is adjustable,so the synchronizations of different systems can be implemented.