强制duffing振荡器(FDO)稳定性分析

2016 19th International Conference on Computer and Information Technology (ICCIT) Pub Date : 2016-12-01 DOI:10.1109/ICCITECHN.2016.7860185

Syed Hassaan Ahmed, Sajjad Hussain, S. Rehman, Syed Kashif Abbas, S. A. Sheikh

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引用次数: 1

摘要

Duffing振子是非线性动力学的原型之一。改变激励的幅度或频率都可以引起跳变现象。本文对duffing振荡器的跳变现象在两个参数(激励幅度和频率)下进行了全面的研究。该分析基于多时间尺度(MMS)方法。本文确定了频率响应曲线的稳定条件和不稳定状态。对FDO的动态运动稳定性进行了研究。duffing振荡器的幅值响应在频域内表现出滞后性，在主共振时出现跳变现象。本文还讨论了振幅呈正弦变化的范德波尔振荡器在非线性共振中的响应。这里设计了一种控制振荡幅度的方法。因此，通过调整强制duffing振荡器的三次项，可以得到多次谐波，并控制弹簧的行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Stability analysis of forced duffing oscillator (FDO)

The Duffing oscillator is one of the prototypes of nonlinear dynamics. Jump phenomenon can be induced by either varying the amplitude or the frequency of excitation. A comprehensive study of jump phenomenon of the duffing oscillator in two parameters (amplitude and frequency of excitation) is performed here. The analysis is based on a method of multiple time scale(MMS). In this research the stability conditions as well as unstable regimes on the frequency response curve are determined. The research also focuses on the stability of the dynamic motion of FDO. The amplitude response displays hysteresis in the frequency domain and jump phenomenon is observed in the case of primary resonance of duffing oscillator. The response of a vander Pol oscillator with sinusoidally varying amplitude is also discussed for non linear resonance. Here a method is devised to control the amplitude of oscillations. Hence Multiple harmonics are obtained as well as spring behaviour is also controlled by tweaking the cubic term of forced duffing oscillator.

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2016 19th International Conference on Computer and Information Technology (ICCIT)

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