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王德莉, 李晨莹, 吴炳增, 焦一宇, 裴海清, 徐伟. 联合噪声驱动下耦合记忆阻尼Rayleigh振子族的节律模式过渡分析. 力学学报, 待出版. DOI: 10.6052/0459-1879-24-078
引用本文: 王德莉, 李晨莹, 吴炳增, 焦一宇, 裴海清, 徐伟. 联合噪声驱动下耦合记忆阻尼Rayleigh振子族的节律模式过渡分析. 力学学报, 待出版. DOI: 10.6052/0459-1879-24-078
Wang Deli, Li Chenying, Wu Bingzeng, Jiao Yiyu, Pei Haiqing, Xu Wei. Transition analysis on rhythm modes of rayleigh oscillators family coupled with memory damping driven by joint noises. Chinese Journal of Theoretical and Applied Mechanics, in press. DOI: 10.6052/0459-1879-24-078
Citation: Wang Deli, Li Chenying, Wu Bingzeng, Jiao Yiyu, Pei Haiqing, Xu Wei. Transition analysis on rhythm modes of rayleigh oscillators family coupled with memory damping driven by joint noises. Chinese Journal of Theoretical and Applied Mechanics, in press. DOI: 10.6052/0459-1879-24-078

联合噪声驱动下耦合记忆阻尼Rayleigh振子族的节律模式过渡分析

TRANSITION ANALYSIS ON RHYTHM MODES OF RAYLEIGH OSCILLATORS FAMILY COUPLED WITH MEMORY DAMPING DRIVEN BY JOINT NOISES

  • 摘要: 提出引致联合噪声驱动下耦合记忆阻尼Rayleigh振子族的单节律性(monorhythmicity)、双节律性(birhythmicity)及三节律性(trirhythmicity)振态模式过渡的参数设计方案. 应用多尺度扩展、随机平均等方法分析耦合记忆阻尼的随机Rayleigh振子族 (8阶、6阶及4阶变体)的振荡响应, 利用振幅、联合相态及其投影与截面概率密度以及最可能振幅及其反解的参数关系等多元化方式定性评价并定量测算振子族的过渡行为, 初步辨识Rayleigh阻尼变体系数、记忆阻尼重要参数引致节律模式过渡行为的数量关系. 注意到8阶 Rayleigh阻尼振子振态出现三节律性模式, 获得优化的记忆阻尼模型的振态反馈因子、广义弹性模量与Rayleigh阻尼变体系数及随机载荷参数联合有效控制不稳定振态的样本方案. 同步采用Runge-Kutta数值技术展示该随机Rayleigh振子族的相态时空演化序列, 可观察到间歇现象, 进一步揭示吸引子变化规律. 模拟振态概率密度以说明解析方法的可靠性, 并得到联合噪声对振子的影响机制. 基于振态概率密度集成Shannon熵, 分别关于Rayleigh变体系数、记忆阻尼重要参数、随机载荷参数测算Shannon熵、熵变化率及熵-熵变化率联合指标, 发现这些熵指标(尤其熵变化率及关联指标)值发生显著变化时可以指示振子族过渡行为的临界态, 同时不再局限于单点估测而提供引致节律模式过渡的参数的参考设计范围. 文章的探索方法及路径为相关工程交叉应用场景的振动控制及所需的振态模式设计发展了新的改进思路.

     

    Abstract: In this work, a design scheme on the parameters inducing transitions of the monorhythmicity, birhythmicity and trirhythmicity mode for Rayleigh oscillators family coupled with memory damping under joint noises is proposed. The stochastic averaging procedure and multi-scale expansion are used to analyze the oscillatory responses on the stochastic Rayleigh oscillators family (8-power, 6-power, and 4-power variants) with memory damping. The transition behavior of oscillators family is qualitatively and quantitatively evaluated from the most probable amplitude and the parameter relation determined by its inverse solution, and multiple probability densities of such as amplitude, joint phase state and its projection and section. The quantitative relationship of transitions on rhythmic modes caused by the coefficients of Rayleigh damping variant and the important parameters of memory damping is preliminarily identified. We notice that the trirhythmicity mode appears in response of 8-power Rayleigh damping oscillator, and a sample scheme for controlling the unstable vibration by combining the generalized elastic modulus and the feedback gains of improved memory damping model, the Rayleigh damping variant coefficients and the random loads parameters is obtained. Numerical techniques of Runge-Kutta are adopted synchronously to demonstrate evolutionary sequences for the phase state of the oscillators family, and intermittent phenomenon is observed, further revealing variation laws of the attractor. The distribution probabilities of vibrational states are simulated to describe reliability of the analytical method, and influence mechanism of joint noise on the oscillator is gained. Shannon entropy integrated based on the response probability, the entropy derivative and the combined indicator on entropy-entropy derivative varying with Rayleigh damping variant coefficients, important parameters of memory damping and random loads parameters are calculated separately. It is found that these indicators (especially the entropy derivative and its related indicator) changing significantly can indicate tipping points on transitions of the oscillators family. Instead of being limited to single-point estimation, these indicators can provide a reference range for the parameter design causing transitions on rhythm modes. The approaches and paths proposed in this paper develop a new improvement idea for the vibration control and the desired vibrational mode in potential engineering applications.

     

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