This paper proposes a nonfeedback control to suppress the chaotic response of nonlinear oscillators. A linear vibration absorber is used as nonfeedback method, whose key idea is to find conditions under which the nonlinear oscillator response converges to an equilibrium point or stay oscillating around it. Theoretical results show that if the ratio between the natural frequencies of the primary system $$(\omega _1)$$ ( ω 1 ) and the undamped absorber $$(\omega _2)$$ ( ω 2 ) , that is, $$\omega _r=\frac{\omega _2}{\omega _1}$$ ω r = ω 2 ω 1 is tuned to be equal to the excitation frequency $$(\Omega )$$ ( Ω ) , then the chaotic behavior of a nonlinear oscillator is driven to a stable hyperbolic equilibrium point. Numerical results are presented for the Duffing oscillator shown that if $$\omega _r$$ ω r is tuned close to excitation frequency, then the chaotic response of the Duffing oscillator is driven to periodic orbits. In the case of damped absorber, $$\omega _r$$ ω r to be tuned close to the excitation frequency does not guarantee that the response of the primary system is periodic, it is also necessary to take into account the amplitude of the excitation.

中文翻译：

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使用线性减振器抑制非线性振荡器中的混沌

本文提出了一种无反馈控制来抑制非线性振荡器的混沌响应。线性减振器用作非反馈方法，其关键思想是找到非线性振荡器响应收敛到平衡点或围绕平衡点振荡的条件。理论结果表明，如果主系统的固有频率$$(\omega _1)$$ ( ω 1 ) 与无阻尼吸波器的固有频率$$(\omega _2)$$ ( ω 2 ) 之比，即$ $\omega _r=\frac{\omega _2}{\omega _1}$$ ω r = ω 2 ω 1 被调谐到等于激励频率 $$(\Omega )$$ ( Ω ) ，那么混沌非线性振荡器的行为被驱动到稳定的双曲平衡点。Duffing 振荡器的数值结果表明，如果 $$\omega _r$$ ω r 调谐到接近激励频率，然后将杜芬振荡器的混沌响应驱动到周期性轨道。在阻尼吸收器的情况下，$$\omega _r$$ ω r 被调谐到接近激励频率并不能保证一次系统的响应是周期性的，还需要考虑激励的幅度.