旋转周期结构参激振动频率分裂研究  

Frequency splitting of parametric excitation vibration of rotating periodic structures

作　　者：高鹏 魏振航 王世宇[1,2,3] GAO Peng;WEI Zhenhang;WANG Shiyu(School of Mechanical Engineering,Tianjin University,Tianjin 300350,China;Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education,Tianjin University,Tianjin 300350,China;Tianjin Key Laboratory of Nonlinear Dynamics and Control,Tianjin 300350,China)

机构地区：[1]天津大学机械工程学院,天津300350 [2]天津大学机构理论与装备设计教育部重点实验室,天津300350 [3]天津市非线性动力学与控制重点实验室,天津300350

出　　处：《振动与冲击》2024年第21期253-262,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(52175109)。

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。该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。Rotating periodic structures are widely used in field of mechanical engineering,and parametric excitation vibration is their common vibration form.Here,a time-varying elasto-dynamic model in partial differential equation form was proposed using the spatiotemporal symmetry characteristics of periodic structures,and then a multi-DOF parametric excitation vibration model in ordinary differential equation form was obtained using Galerkin method and modal orthogonality.Then,vibration behavior of rotating periodic structure under time-varying stiffness excitation was studied.In order to study frequency splitting law of parametric excitation vibration,the modulation feedback principle was used to analyze vibration responses under different feedback types,and reveal mapping relations between basic parametric combinations,such as,time-varying stiffness and vibration wave number and frequency splitting.Excitation frequencies corresponding to parametric excitation instability under different feedback types were predicted.Finally,parametric instability regions and response frequencies under different feedback types were verified with Floquét theory and Runge-Kutta method,respectively.

关 键 词：旋转周期结构 参激振动 时变刚度 调制反馈 频率分裂 

分 类 号：TH113.1[机械工程—机械设计及理论]