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首页> 外文期刊>International journal of non-linear mechanics >Dynamics of a time delayed Duffing oscillator
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Dynamics of a time delayed Duffing oscillator

机译：延时Duffing振荡器的动力学

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This paper focuses on the primary resonance of the time delayed Duffing oscillator solved by means of the multiple scales method. The second order approximation is used because the first approximation applied in the literature does not exhibit specific phenomena of the studied system. The Duffing system is investigated in two aspects. First of all, how delay displacement feedback influences the primary resonance of the classical Duffing oscillator in order to control the system and, on the other hand, how the external harmonic force influences vibrations of the system with time delay which is essential in applications, e.g. in machining. Stability of solutions and their bifurcations caused by the system parameters are shown. Especially, coexistence of possible stable and unstable solutions is investigated versus time delay and external excitation parameters. The selected analytical results are compared with numerical simulations. The model presented in the paper is considered as a general problem of nonlinear oscillator with time delay but specific attention is paid to cutting process control.
机译：本文重点研究了通过多尺度方法解决的延时Duffing振荡器的初级共振。之所以使用二阶近似，是因为文献中应用的一阶近似没有表现出所研究系统的特定现象。在两个方面研究了Duffing系统。首先，延迟位移反馈如何影响经典Duffing振荡器的初级共振以控制系统，另一方面，外部谐波力如何随时间延迟影响系统的振动，这在应用中至关重要，例如在加工中。显示了系统参数引起的解及其分支的稳定性。特别是，研究了可能的稳定和不稳定解的共存与时延和外部激励参数的关系。将所选的分析结果与数值模拟进行比较。本文提出的模型被认为是具有时滞的非线性振荡器的一个普遍问题，但要特别注意切削过程的控制。

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