On the Mutual Interaction of Weakly Coupled Self-Excited Oscillators with Dry Friction

弱耦合自激振荡器与干摩擦的相互作用

• 批准号: 61550192
• 负责人: ARAKI Y.
• 金额: $ 1.02万
• 依托单位: Kyushu Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1986
• 资助国家: 日本
• 起止时间: 1986 至 1987
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61550192/
• 关键词: Self-Excited oscillations; Synchronization; Frequency entrainment; Mutual interaction; Mutual synchronization of intercoupled oscillators

The mutual synchronization and the almost entrained or chaotic motions of the weakly intercoupled self-excited oscillators with dry friction are investigated theoretically and numerically. The analyses were developed for the system in which a definite number (e.g. 2,3,4 and 5) of the self-excited oscillators that have small detuning between their natural frequencies, are connected by viscous elements.The dynamic model of the system are analyzed numerically by use of the Willson's-theta-method, for both the synchronous conditions and non-synchronous conditions. And after the out-put data of each oscillator are analyzed by the First Fourier Transformer. When the coupling factors are strong enough, there occurs mutual entrainment. The resulting entrained oscillation can be expressed as a aproximately harmonic oscillation, and the frequency becomes approximately average value of their natural frequencies. When the factors of the coupling elements are rather weak, there occur-non-entranined oscillations, i.e. chaotic motions, In the chaos region, there can be observed, generally, the relative coarrescense of the neighboring frequencies, some stages with different behavior of chaotic oscillations. The theoretical results using the averaging method and harmonic balance method, agreed well with the results of numerical simulations.

从理论和数值上研究了具有干摩擦的弱耦合自激振子的相互同步和几乎缠绕或混沌运动。对自激振子的固有频率之间有小失谐量的有限个自激振子(如2、3、4和5个)通过粘性元件连接，利用Willson-theta方法对系统的动力学模型进行了数值分析，包括同步和非同步两种情况。并通过第一傅里叶变换对各振荡器的输出数据进行分析。当耦合因素足够强时，就会发生相互卷吸。由此产生的缠绕振动可表示为近似简谐振荡，频率近似为其固有频率的平均值。当耦合元件的因素较弱时，在混沌区域内出现非缠绕振荡，即混沌运动，通常可以观察到相邻频率的相对粗化，某些阶段具有不同的混沌振荡行为。采用平均法和谐波平衡法的理论计算结果与数值模拟结果吻合较好。

项目成果

ARAKI Y.;INOUE J.;JINNOUCHI Y.;TAKADA H: Proceedings of the International Conference On Mechanical Dynamic´s,Shenyang,China. (1987)

ARAKI Y.；INOUE J.；JINNOUCHI Y.；TAKADA H：国际机械动力学会议论文集，中国沉阳（1987）。

Araki, Y., Inoue, J., Jinnouchi, Y., and Takada, H.: "On the Mutual Interaction of Weakly Coupled Self-Excited Oscillators with Dry Friction" Proceedings of the International Conference on Mechanical Dynamics, Shenyang, China. 1. 361-366 (1987)

Araki, Y.、Inoue, J.、Jinnouchi, Y. 和 Takada, H.：“弱耦合自激振荡器与干摩擦的相互作用”国际机械动力学会议论文集，中国沉阳。

ARAKI,Y.;INOUE,J.;JINNOUCHI,Y. and TAKADA,H: Proceedings of the International Conference On Mechanical Dynamics, Shenyang, China.

荒木，Y.；井上，J.；阵内，Y.