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双层壳体结构水下辐射声场数值预报方法研究

Research on the Numerical Prediction of Sound Radiation from Submerged Double Elastic Shell-structures

作者: 专业:声学 导师:商德江 年度:2010 学位:硕士  院校: 哈尔滨工程大学

Keywords

FEM+BEM, Double-layer elastic shell, Singular integrals, CHIEF

        为解决双层弹性壳体结构水下声辐射预报问题,本文自行开发了边界元算法及软件。对于边界元算法中的奇异积分问题,采用了极坐标变换、退化单元法及广义极坐标变换三种方法;并采用了内点法及改进的内点法,有效地解决了边界元算法中特征频率处解不唯一的问题。并通过自编程序解与脉动球声场的解析解、多点源组合的分布声场及基于表面法向振速由Sysnoise计算的结构声场的比对等方式验证了上述各算法的正确性与可行性。此外,在考虑瑞利阻尼系数Alpha,Beta的情况下,本文对流固耦合的有限元算法进行了改进和补充,并对改进后有限元算法的正确性进行了验证。将有限元算法与边界元算法相结合,建立有限元+边界元的算法,解决水下弹性结构的声振耦合问题也是本文的研究工作之一。通过与Sysnoise软件的计算结果的对比,验证了该算法的可行性。最后,在千岛湖进行了双层弹性圆柱壳水下辐射声场的外场试验,验证了自行开发的边界元算法预报水下结构辐射声场的有效性。
    To solve the problem of predicting the acoustic radiation field of the double-layer elastic shell structure submerged in water, in this dissertation, the algorithm and the program of the BEM have been developed independently. Three methods which are the polar coordinate transformation, the transformation of the degenerative element for linear quadrilateral element, and the generalized polar coordinate transformation are adopted for dealing with the singular integrals in the algorithm of the BEM; The non-uniqueness problem of the BEM at characteristic frequencies has been solved effectively in two ways. One is the CHIEF method, the other one is the combination of the interior helmholtz equation and its derivatives to form a new extra equation. To verify the accuracy and feasibility of those methods, the sound field for three kinds of sound sources, including a pulsating sphere, the combination of the point sources and an elastic structure with the known normal velocity on its surface, has been calculated by use of the self-developed algorithm, the analytical method, and by use of Sysnoise software respectively, and very good agreement has obtained.In addition, the fluid-solid coupling FEM algorithm has been improved and complemented in this dissertation on considering the rayleigh damping multiplier Alpha and Beta. The accuracy of the FEM algorithm improved is tested.The algorithm combination of the FEM and the BEM has been constructed to solve the structural-acoustic coupled problem of the elastic structure submerged in water. The validity of the combinated algorithm is tested by means of the comparison between the results calculated by use of the algorithm improved and that by use of Sysnoise.At last, the validity of the self-developed BEM algorithm for predicting the acoustic radiation field of elastic structures submerged in water is tested by an experiment in Qiandao Lake, in which the experimental model is a double-layer cylindrical elastic shell.
        

双层壳体结构水下辐射声场数值预报方法研究

摘要5-6
ABSTRACT6
第1章 绪论9-15
    1.1 论文研究背景及意义9-10
    1.2 弹性结构水下振动声辐射数值研究方法概述10-12
    1.3 国内外有限元加边界元方法研究概况12-13
    1.4 本文的主要内容13-15
第2章 边界元算法的理论推导15-38
    2.1 声学基本方程及Helmholtz 方程15-16
    2.2 外部问题的Helmholtz 声学边界积分方程16-20
        2.2.1 外部Helmholtz 边界积分方程16-18
        2.2.2 表面Helmholtz 边界积分方程18-19
        2.2.3 内部Helmholtz 边界积分方程19-20
    2.3 内部问题的Helmholtz 声学边界积分方程20
    2.4 曲面元与局部坐标系20-22
    2.5 边界Helmholtz 积分方程的数值离散22-26
    2.6 非奇异单元的高斯积分26
    2.7 奇异积分问题的解决26-34
        2.7.1 极坐标变换法27-31
        2.7.2 退化单元法31-32
        2.7.3 广义极坐标变换法32-34
    2.8 特征频率处解不唯一问题的解决34-36
        2.8.1 内点法的矩阵表示(CHIEF 法)35-36
        2.8.2 改进的内点法36
    2.9 算法中的矩阵求广义逆的问题36-37
    2.10 本章小结37-38
第3章 有限元基本理论38-44
    3.1 流固耦合有限元方程推导38-40
    3.2 Ansys 中的阻尼计算问题40-42
    3.3 有限元与边界元算法的结合42-43
    3.4 本章小结43-44
第4章 有限元和边界元算法开发研究44-67
    4.1 边界元算法验证44-55
        4.1.1 与脉动球解析解对比44-49
            4.1.1.1 表面声压验证44-47
            4.1.1.2 场点声压验证47-49
        4.1.2 任意点源分布的验证49-53
        4.1.3 基于Sysnoise 中表面法向振速的验证53-55
    4.2 解决奇异积分的三种方法验证55-57
    4.3 解决特征频率处解不唯一问题的方法验证57-61
        4.3.1 内点法验证58-59
        4.3.2 改进的内点法验证59-61
    4.4 改进的有限元算法验证61-63
    4.5 有限元与边界元结合的整体算法验证63-66
    4.6 本章小结66-67
第5章 边界元声辐射预报试验验证67-75
    5.1 双层壳体模型及测量系统67-70
    5.2 试验数据分析70-74
        5.2.1 试验相关理论的补充70
        5.2.2 试验模型仿真分析70-72
        5.2.3 试验数据处理72-74
    5.3 本章小结74-75
结论75-77
参考文献77-81
致谢81
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