室内低频声场边界元法应用缺陷的数值模拟和分析

毕业设计说明书（论文）中文摘要边界元法具有计算简单、适应性强和精度高的优点，其应用广泛存在于应力分析、传热学等工程计算领域。利用边界元法求解室内声场问题，为室内声场的特征分析提供了依据。然而工程实际和相关文献表明边界元法在处理低频问题过程，由于静稳态场在边界处的移动导致的放射与原来的场耦合的情形使得计算结果出现严重误差。因此，本论文基于二文边界元法对室内声场进行模拟，分析频率变化，导致的算法精度的变化规律。针对室内声场问题，建立了二文边界元模型。简要给出Morse 简正理论，最终，利用c++编写了边界元程序对室内声场进行了模拟，分析频率变化，导致的算法精度的变化规律。6481
关键词边界元法室内声场数值模拟算法精度
毕业设计说明书（论文）外文摘要
Title Numerical Simulation and Analysis of Boundary element
method application defects in the indoor and low-frequency sound field

Abstract
The boundary Element Method (BEM) is widely applied to engineering
problems, such as stress analysis and thermodynamics, due to its simple
computation, strong adaptability and high accuracy. It provides a basis
for the characteristic analysis to solve room acoustic problems by BEM.
However, engineering practice and relevant literature suggests that the
boundary element method in dealing with the process of low-frequency
problem, due to radiation caused by the static steady-state field in the
boundary of the moving coupling with the original, it makes to serious
calculation error .Therefore, based on two-dimensional boundary element
method to simulate the indoor sound field and analysis of the variation
of the algorithm accuracy caused by the frequency changes.
For the indoor sound field, I build up the two-dimensional boundary element
model, and briefly give Morse theory .At last, use C + + to write the
boundary element program to simulate the indoor sound field and analysis
of the variation of the algorithm accuracy, caused by the frequency change.
Keywords    Boundary Element Method Room Acoustics Numerical Simulation
Algorithm Accuracy
        本科毕业设计说明书（论文）    第 I 页   共 I 页
目次
1绪论：    1
1.1 选题背景    1
1.2 研究现状    1
1.3 本文的研究路线和内容安排    3
2.内部声学的边界元模型 4
2.1 边界积分方程的建立    4
2.2 边界积分方程的离散化    5
2.3 Green函数及性质. 6
2.4 边界单元的划分    7
2.5 边界积分的计算    8
2.51直线单元的边界积分    8
2.52奇异积分的计算    9
2.6 方程求解 10
3室内声场的计算 . 12
3.1 Morse简正理论 12
3.2 声学边界条件 . 13
4.室内声场的数值模拟. 15
4.1 考虑同一点 1-100Hz频率范围 . 16
4.2 同一高度不同距离点 . 17
4.3 同一距离不同高度点 . 18
结论. 19
致谢. 20
参考文献. 21 1 绪论：
1.1 选题背景
室内声学是研究室内声音的传播和听闻效果的学科，是建筑声学的重要组成部分。
其目的是为室内音质设计提供理论依据和方法。声音在室内的传播与房间的形状、
尺寸、构造和吸声材料布置有关。为了满足人们对声学特征的要求，通常在室内环境室内低频声场边界元法应用缺陷的数值模拟和分析:http://www.751com.cn/shuxue/lunwen_4058.html