基于最优时延反馈控制的主-被动非线性隔振方法研究

摘要

The effective frequency of nonlinear vibration isolation is generally greater than the jump-down frequency, I.e. The jumping frequency range due to the multiple solutions of the nonlinear dynamic equations is excluded. However, when the oscillation amplitude is on the non-resonance branch of the response curve,the nonlinear isolator is capable of reducing the transmitted force efficiently. How to make the response amplitude be on the non-resonance branch by control strategy is the key for isolator design in the jumping frequency range. In this paper, an optimal time-delay feedback control method is proposed to shift the amplitude from resonance branch to non-resonance branch, when the amplitude is on the resonance branch due to certain initial conditions or variation of excitation frequency. Although the control makes system chaotic, the oscillation amplitude is reduced significantly. Furthermore, the control is removed, when the transient response of chaotic vibration dies away and the system states (displacement, velocity) are in the basin approaching to the steady focus, corresponding to the non-resonance branch, in the Von der Pol Plane. After the halt of the control, the system will recover harmonic vibration and the amplitude will be on the non-resonance branch. Consequently, the nonlinear isolator will be active in the jumping frequency range under any conditions by means of optimal time-delay feedback control. The efficiency of this method is verified by numerical simulations. Comparisons between the nonlinear isolator and the corresponding linear one and discussions on the effects of damping factor are carried out, which shows that the nonlinear isolator, including quasi-zero stiffness springs and optimal time-delay feedback control, is favorable for low frequency isolation.%非线性隔振系统的有效隔振频率区间要求越过跳跃区间,大于向下跳跃频率.然而,在跳跃区间内,当系统响应振幅位于幅频曲线的非共振支上时,系统具有隔振效果,问题在于如何将振幅保持在非共振支上.当初始条件或激励频率变化使系统响应幅值位于共振支时,提出利用最优时延反馈控制将幅值从共振支切换至非共振支.时延反馈控制虽然使系统处于混沌状态,但振幅得到了充分降低.待混沌状态稳定,且系统状态位于趋向于非共振支的流域中时,撤除反馈控制,系统将恢复简谐振动且振幅最终落在非共振支上,实现了在跳跃区间内的有效隔振,从而拓宽了非线性隔振的频率区间.通过数值仿真计算,验证了本方法的有效性；同时,也证实了基于最优时延反馈控制和准零刚度的非线性隔振系统适用于低频隔振.