受迫振动非线性特性的教学拓展

丁红胜, 王佳曦, 张师平, 董军军

doi:10.16854 /j.cnki.1000-0712.200335

大学物理 >

2021 , Vol. 40 >Issue 2: 12 - 17

DOI: https://doi.org/10.16854 /j.cnki.1000-0712.200335

教学研究

受迫振动非线性特性的教学拓展

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1. 北京科技大学数理学院应用物理系，北京100083; 2. 北京科技大学自然科学基础实验中心，北京100083

丁红胜( 1969—) ，男，湖北麻城人，北京科技大学应用物理系教授，博士，从事大学物理及大学物理实验的教学工作.

收稿日期: 2020-07-28

修回日期: 2020-09-21

网络出版日期: 2021-02-22

基金资助

中央高校基本科研业务费专项资金资助项目( FRF-BD-20-12A) 资助

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Teaching development of the nonlinear characteristics of forced vibration

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1. Department of Physics，School of Mathematics and Physics，University of Science and Technology Beijing，Beijing 100083，China;2. Basic Experimental Center for Natural Science，University of Science and Technology Beijing，Beijing 100083，China

Received date: 2020-07-28

Revised date: 2020-09-21

Online published: 2021-02-22

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摘要

受迫振动在大学物理和大学物理实验中均是重点教学内容，为了使学生更加深入理解受迫振动的非线性特性，本文基于波耳共振仪所涉及的非线性因素和实验数据，对受迫振动方程进行非线性修正，利用数值分析探讨其非线性特性.通过引入硬弹簧型杜芬方程，探讨系统由周期性运动进入混沌状态的演化，将受迫振动中相对稳定的平衡点与奇异吸引子进行类比，拓展非线性振动教学内容.

关键词： 受迫振动; 杜芬方程; 数值分析; 混沌

本文引用格式

丁红胜, 王佳曦, 张师平, 董军军 . 受迫振动非线性特性的教学拓展[J]. 大学物理, 2021 , 40(2) : 12 -17 . DOI: 10.16854 /j.cnki.1000-0712.200335

Abstract

Forced vibration is an important teaching content in both college physics and college physics experiments.In order to make students understand the nonlinear characteristics of the forced vibration more deeply，the nonlinear correction of the forced vibration equation is carried out based on the nonlinear factors and experimental data involved in the Pohl resonator，and the nonlinear characteristics are discussed by numerical analysis. By introducing the Duffing equation of hard spring type，the evolution of the system from periodic motion to chaotic state is discussed. The relatively stable equilibrium point in forced vibration is compared with the singular attractor to expand the teaching content of nonlinear vibration.

Key words： forced vibration; Duffing equation; numerical analysis; chaos

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