基于林德斯泰特-庞加莱法的双节拍器耦合系统同步规律研究  

RESEARCH ON SYNCHRONIZATION OF DOUBLE METRONOME COUPLING SYSTEM BASED ON LINDSTEDT-POINCARÉMETHOD

作　　者：谭景芳 王成会[1] 莫润阳[1] TAN Jingfang;WANG Chenghui;MO Runyang(School of Physics and information Technology,Shaanxi Normal University,Xi'an,Shaanxi 710119)

机构地区：[1]陕西师范大学物理学与信息技术学院,陕西西安710119

出　　处：《物理与工程》2023年第5期46-52,共7页Physics and Engineering

基　　金：教育部高等学校物理学类专业教学指导委员会项目“师范专业认证背景下基于OBE理念的力学课程教学模式研究”(2018-ZDGH-201);师范专业认证背景下师范院校教师教育课程设置研究(JSJY2021019);陕西师范大学课程思政示范课建设项目“理论力学”。

摘　　要：本文在双节拍器耦合系统动力学方程的基础上,利用Runge-Kutta(龙格-库塔)法对振动系统进行数值分析,通过摆杆摆角随时间演化的曲线图像,讨论影响系统同步性质的因素。利用L-P(林德斯泰特-庞加莱)法研究相同双节拍器耦合系统的系统参数对于摆杆摆动振幅和摆动频率的影响,得到无耦合双节拍器系统的近似解,结合数值分析比较系统参数对同步周期和振幅的影响;在理论分析得到的近似同步周期中设定同步系数q值,并通过拟合函数进行拟合,拟合后得到的同步周期与数值分析的周期基本一致。本文能为更好地理解耦合系统的同步性质提供参考,也能为学生进行双节拍器同步物理实验提供一些理论参考,增强学生理论联系实际的能力。In this paper,we used dynamics equation of the coupled system of double metronome to analyze the vibration system numerically by Runge-Kutta method,and discussed the factors affecting the synchronization of the system by using the curve image of the pendulum angle evolution with time.L-P(Lindstedt-Poincare)method was used to study the influence of system parameters of the same double metronome coupling system on the pendulum amplitude and frequency,and obtained the approximate solution of the uncoupled double metronome system,compared with numerical analysis to discuss the effects of system parameters on synchronization period and amplitude.The approximate synchronization period is obtained by theoretical analysis,we set q as synchronization coefficient,and used fitting function to fit q value.After fitting,the synchronization period is basically consistent with the period of numerical analysis.This paper can provide a reference for better understanding the synchronization properties of coupled systems,and also provide some theoretical references for students to conduct the physical experiment of double metronome synchronization,enhance students'ability to combine theory with practice.

关 键 词：耦合同步 振动系统 频率响应 

分 类 号：O32[理学—一般力学与力学基础]