基于拉格朗日方程导出的三模耦合模理论及实验验证  

Theory and Experimental Verification of Three-Mode Coupled Mode Based on Lagrange Equation

作　　者：张亚博 丁中正 彭雪城[1] 黄万霞[1] 黄时中[1] ZHANG Ya-bo;DING Zhong-zheng;PENG Xue-cheng;HUANG Wan-xia;HUANG Shi-zhong(School of Physics and Electronic Infbrmation and Anhui Key Laboratory of Optoelectronic Materials Science and Technology,Anhui Normal University,Wuhu 241002,China)

机构地区：[1]安徽师范大学物理与电子信息学院安徽省光电材料科学和技术重点实验室,安徽芜湖241002

出　　处：《安徽师范大学学报（自然科学版）》2022年第3期227-236,共10页Journal of Anhui Normal University(Natural Science)

基　　金：安徽省自然科学基金项目(2108085MA23);安徽省高等学校省级质量工程项目(2019mooc066).

摘　　要：通过近几年对耦合系统的研究,在双模耦合系统中已经很广泛的进展。本文扩展到对三模耦合系统进行探究,从拉格朗日方程出发,建立更完善的音叉耦合系统的动力学方程,再利用久期微扰理论将动力学方程退化为耦合模理论的主方程(一阶微分方程),搭建由弹簧连接的音叉耦合受迫振动系统进行了实验和理论研究。研究结果表明理论与实验符合的很好,并且相对于两模耦合系统,三模耦合系统存在更多的可调参数,在耦合体系理论研究中有一定的指导意义。Through the research in the coupling system in recent years,there has been extensive progress in the dual-mode coupling system.This paper is extended to explore the three-mode coupling system.Starting from the Lagrange equation,a more complete dynamic equation of the tuning fork coupling system is established,and then the duration perturbation theory is used to degenerate the dynamic equation into the master equation of the coupled-mode theory(First-order differential equation),experimental and theoretical studies were carried out by building a tuning fork coupled forced vibration system connected by a spring.The research results show that the theory and experiment are in good agreement,and compared with the dual-mode coupling system,the three-mode coupling system has more adjustable parameters,which has certain guiding significance in the theoretical research of the coupling system.

关 键 词：三模耦合 拉格朗日方程 耦合模理论 久期微扰理论 

分 类 号：O4-33[理学—物理]