旋转周期结构参激振动频率分裂研究

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (21) : 253-262.

论文

旋转周期结构参激振动频率分裂研究

高鹏1，魏振航1，王世宇1,2,3

作者信息 +

Frequency splitting of parametric excitation vibration of rotating periodic structures

GAO Peng1, WEI Zhenhang1, WANG Shiyu1,2,3

Author information +

文章历史 +

摘要

旋转周期结构广泛应用于机械工程领域，参激振动是其常见的振动形式。本文利用周期结构的时空对称特征提出了一种偏微分形式的时变弹性动力学模型，然后利用Galerkin方法及模态正交性得到了常微分形式的多自由度参激振动模型。研究了时变刚度激励作用下旋转周期结构的振动行为。为了研究参激振动的固频率分裂规律，采用调制反馈原理分析了不同反馈类型下的振动响应，揭示了时变刚度个数及振动波数等基本参数组合与频率分裂之间的映射关系，还预测了不同反馈类型下参激不稳定对应的激励频率，最后利用Floquét理论和Runge-Kutta方法分别验证了参数不稳定域及不同反馈类型下响应频率的正确性。

Abstract

Rotationally periodic structures are widely used in mechanical engineering fields, where parametric vibration is a common form of vibration. A time-varying partial differential elastic dynamic model is proposed by using the time-spatial symmetry of the periodic structures. The mathematical model of ordinary differential multi-freedom parametric vibration is obtained by using Galerkin method and modal orthogonality, based on which the vibration behaviors of the rotationally periodic structures induced by the time-varying stiffness excitation are examined. In order to study the frequency splitting of the parametric vibration, the modulation feedback principle is employed to analyze the dynamic response for different feedback types, and the relationships between parameter combinations, including the time-varying stiffness number and wavenumber, and frequency splitting are revealed. In addition, the excitation frequencies for corresponding to the parametric instability for different feedback types are predicted. Finally, the parametric instability regions and the response frequencies for different feedback types are verified by the Floquét theory and the Runge-Kutta method, respectively.

导出引用

高鹏1, 魏振航1, 王世宇1, 2, 3. 旋转周期结构参激振动频率分裂研究[J]. 振动与冲击, 2024, 43(21): 253-262

GAO Peng1, WEI Zhenhang1, WANG Shiyu1, 2, 3. Frequency splitting of parametric excitation vibration of rotating periodic structures[J]. Journal of Vibration and Shock, 2024, 43(21): 253-262

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