动态法测量杨氏模量的理论分析与Matlab辅助研究  

Theoretical analysis of measuring Young's modulus using dynamic method based on Matlab

作　　者：王龙 李东霞 马红章 李书光 王晓萌 

机构地区：[1]中国石油大学(华东)理学院,山东青岛266580

出　　处：《大学物理》2015年第10期39-42,共4页College Physics

基　　金：中国石油大学(华东)重点教学研究与改革项目(JY-A201402)资助

摘　　要：由动态法测量杨氏模量的实验思想,从杆横振动偏微分方程的建立出发,通过分离变量法推导出其通解,并根据自由振动的边界条件,确定出满足边界条件的超越方程及通解的各项系数.采用Matlab7.0软件,基于图解法先获得近似值后获得高精度数值解的方式,进行了数值计算求解,最终确定并计算出了杆横振动的前三阶振动固有频率和对应的振动模态及振动节点的位置,与教材及参考文献中给出的理论值是一致的.According to the idea of measuring Young＇ s modulus using dynamic method, we establish the partial differential equation of transverse vibration of the bar. By using variable separation method, the general solution is obtained. On the analysis of boundary conditions of free vibration, we present a transcendental equation and the coefficients of the general solution. Also, by using graphic method in Matlab 7.0 environment, we obtain the approximate solution and high precision numerical solution to the first three order natural frequencies of the transverse vibration of the bar. The first three order vibration modes and nodes location are given by graphic, which consistent with the theoretical values in the textbook.

关 键 词：横振动 固有频率 图解法 振动模态 

分 类 号：O4-33[理学—物理] O4-39