预紧等截面直弦的横向振动分析

摘要等截面直弦的横向振动属于无限自由度系统的振动，常见的吉他弦、二胡弦等的振动都属于等截面直弦的振动。弦振动规律比较复杂。建立物理模型，截取微小段受力分析，利用牛顿第二定律推导弦自由振动的振动方程，求解出弦振动的固有频率与固有振型函数。推导弦受迫振动的振动规律，利用模态叠加法求解弦自由振动的振动位移响应。分析弦振动过程中，各参数对固有频率以及振动位移响应的影响，利用数学软件工具MATLAB将其中的规律用绘制曲线图的形式表示出来。68005

毕业论文关键词固有频率固有振型偏微分方程分离变量法模态叠加

Title The vibration analysis of an pretension straight string with equal section

Abstract

The vibration of an pretension straight string with equal section is unlimited freedom vibration system.Commonly, Vibrations of guitar strings and other Strings etc. all belong to the vibration of the string section straight..The law of vibration is more complex.Establish the physical model and Interception tiny segment with doing Stress Analysis. Derived the law of free vibration of the string vibration equation by using Newton's second law. Solving the natural frequency of vibration and the inherent vibration mode function of the string .Derive the string vibration forced vibration law,using the modal superposition method to solve the free vibration of the string vibration displacement response Analyze.the response of Various parameters on the natural frequencies and vibration displacement during the process of the String vibration ,Using mathematical software tools MATLAB which will be drawn with the law represented in graph form.

Keywords Natural frequency Natural modes Partial Differential Equations Separation of variables Modal superposition

1 绪论 1

1.1课题工程背景 1

1.2 偏微分方程简单介绍 2

1.3 MATLAB简单介绍 3

1.4 本课题工作 6

2 建立物理模型与偏微分方程 6

2.1弦的物理模型 6

2.2利用牛顿第二定律推导振动偏微分方程 8

2.3 分离变量法求解固有振动位移函数 8

2.4 求解固有频率与固有振型函数 9

3 验证固有振型的正交性 10

4 振型叠加法求解自由振动 12

4.1给定初始条件下弦做自由振动的分析 12

4.2 应用固有振型正交性简化振动方程 13

4.3 振动响应曲线的绘制 15

4.4 分析位移响应曲线 18

5 研究弦的受迫振动 18

5.1 建立受迫振动模型 19

5.2 固有振型函数正交性简化受迫振动 19

5.3 简谐激励下的受迫振动分析 20

6 参数对固有频率的影响 21

6.1 弦预紧力T对固有频率的影响 22

6.2 弦线长度L对固有频率的影响预紧等截面直弦的横向振动分析:http://www.751com.cn/wuli/lunwen_76394.html