有质量弹簧振子的弹簧内力  

THE SPRING'S INTERNAL FORCE OF THE VIBRATOR WITH A MASSIVE SPRING

作　　者：陈奎孚[1] 黄峰[1] 蒋晓[2] 赵建柱[3] 

机构地区：[1]中国农业大学理学院,北京100083 [2]北京农业职业学院机电工程学院,北京102208 [3]中国农业大学工学院,北京100083

出　　处：《物理与工程》2016年第5期6-11,15,共7页Physics and Engineering

基　　金：2015年度北京高等学校教育教学改革立项项目(编号:2015-ms049;名称:以工程教育认证为导向的车辆工程专业实践教学改革研究与实践)

摘　　要：文章分析了有质量弹簧振子的弹簧内力,并用Matlab工具进行图形化展示.分析表明:弹簧质量不可忽略时,弹簧各断面上内力是断面位置的函数;对振子均匀拉伸-释放所建立的振动,弹簧内力随时间的变化规律不再是简谐波;随着弹簧质量的增加,内力偏离简谐波越来越明显;质点质量为零时,内力随时间的变化规律为周期性方波.The spring＇s internal force of a vibrator with a light spring is trivially a constant,while the case with a massive spring is much sophisticated.This problem was investigated in detail,and was visualized by the mathematical tool Matlab.This study shows,firstly,that the spring＇s internal force varies along the spring＇s length for a massive spring case.Secondly,the vibration established by uniformly stretching and releasing the spring is not a simple harmonic motion;as a result,the spring＇s internal force deviates from the simple harmonic pattern.Thirdly,the deviation is more and more significant as the spring mass increases.Finally,the internal force lends itself to be a square wave when the lumped mass is null.

关 键 词：弹簧振子 波动 偏微分方程 内力 

分 类 号：O32-4[理学—一般力学与力学基础] G642[理学—力学]