复振型的物理意义——以两自由度陀螺系统为例  

THE PHYSICAL MEANING OF COMPLEX MODES:AN EXAMPLE OF 2DOF GYROSCOPIC SYSTEM

作　　者：杨晓东[1,2] 商林源 YANG Xiaodong;SHANG Linyuan(Faculty of Materials and Manufacturing,Beijing University of Technology,Beijing 100124,China;School of Aeronautics and Astronautics,Shenyang Aerospace University,Shenyang 110136,China)

机构地区：[1]北京工业大学材料与制造学部,北京100124 [2]沈阳航空航天大学航空宇航学院,沈阳110136

出　　处：《力学与实践》2024年第2期432-434,共3页Mechanics in Engineering

基　　金：国家自然科学基金项目(11972050,12332001)资助。

摘　　要：在传统振动力学教学中,复振型主要用于振动方程解耦的数学操作,对其物理意义阐述不清楚。本文从简单的旋转框架下两自由度线性系统入手,阐述了模态振动中复振型表征各振子位移与速度组合的比例关系,而非实振型所表征的位移比例关系。本文明确了复振型振动的非同时性及伴随性,引导振动力学的初学者深刻理解复振型的直观物理意义。In the traditional teaching of vibration mechanics,the complex modes have been used to decouple the systems as a manipulation tool.The physical meaning of the complex modes is not clearly transferred.In this paper,the relationship between the combo of displacement and velocity of every oscillators have been demonstrated as the system shows the complex modes,illustrated by a 2DOF rotating system.The non-uniform and following features of the complex modes have been discussed,which give visual physical meaning to the beginners of the vibration course.

关 键 词：振动 复振型 陀螺效应 两自由度系统 

分 类 号：O312[理学—一般力学与力学基础]