索末菲效应对自同步系统的影响分析  

Research on the Influence of Sommerfeld Effect on Self-Synchronous Systems

作　　者：甘子川 丁川 王笑 宋汉文[1] Gan Zichuan;Ding Chuan;Wang Xiao;Song Hanwen(School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《动力学与控制学报》2025年第1期69-77,共9页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12272266)。

摘　　要：单自由度二转子系统作为最经典的自同步系统,广泛应用于工程领域.本文利用Lagrange方程建立了单自由度二转子系统动力学模型,并基于动力学模型建立了MATLAB/Simulink仿真模型.首先对参数完全对称的系统进行了数值仿真,并分析了对称情况下的索末菲效应.然后,通过在仿真模型中选取不同参数对系统施加扰动,研究了不同参数下的自同步现象,考察了系统受到扰动后的稳定性和恢复自同步的能力.最后,对仿真中出现的自同步现象进行了分类,同时给出了系统恢复自同步的能力与给定的参数之间的关系.结果表明,选取不同参数的情况下,系统的自同步现象可分为三类:转子工作在系统近谐振区时的同相位同步、转子工作在系统远谐振区时的反相位同步两种稳定自同步,和转子工作在系统剧烈谐振区受到扰动后响应呈现随机性的不稳定同步;当转子工作在系统近谐振区时,同步恢复能力最强.仿真结论可为更复杂振动系统的自同步现象研究提供参考.The single-degree-of-freedom two-rotor system,as the most classical self-synchronous system,is widely used in engineering.In this paper,a dynamics model of the single-degree-of-freedom two-rotor system is established using Lagrange’s equation,and a MATLAB/Simulink simulation model is constructed based on the dynamics model.Firstly,a numerical simulation is carried out with completely symmetric system parameters to analyze the Sommerfeld effect of the system.Then,by applying disturbances to the system with different sets of system parameters in the numerical simulation,the self-synchronization phenomenon under different system parameters is studied,system stability after disturbance is investigated,and the ability of the system to recover self-synchronization is evaluated.Finally,the self-synchronization phenomena appearing in the simulation were classified,and how the system parameters will affect the system’s synchronization recovery capability is also given.The results of numerical simulation and analysis show that,with different system parameters,the self-synchronization phenomena can be classified into three categories:stable self-synchronization with in-phase synchronization in the near-resonant region and anti-phase synchronization in the far resonant region,as well as unstable self-synchronization with randomness response after being disturbance when working in the violent resonance region of the system.The result also shows the system’s self-synchronization capability is strongest when the rotor is operated in the near-resonance region of the system.The results of this study can provide a reference for the study of self-synchronization phenomena in more complex vibration systems.

关 键 词：索末菲效应 自同步 双转子系统 振动系统 稳定性 

分 类 号：TH113[机械工程—机械设计及理论]