【作者】 赵志高；

【导师】 黄其柏；

【作者基本信息】 华中科技大学 ， 机械设计及理论， 2005， 博士

【摘要】 本文在分析了结构声辐射数值方法的历史及其现状的基础上,详细推导了结构声辐射的边界积分方程,对声辐射的数值计算方法、声辐射的模态理论以及声辐射的灵敏度分析作了深入详细的探讨。本文以边界元方法作为研究结构声辐射的基础,并针对边界元方法中的两个关键问题,奇异积分与多频计算,提出了有效的数值计算方法;在此基础上,对结构声辐射的机理问题进行了研究,提出了一种对复杂结构声辐射模态与灵敏度计算的方法,对复杂结构声辐射的解耦进行了探讨,最后对所提出方法的有效性与可靠性进行了试验验证。论文回顾了结构声辐射、模态理论以及灵敏度分析的历史与发展现状,阐述了声辐射中需要解决的关键问题,明确了本文的研究目标与主要工作。对结构声辐射的边界积分方程的内部形式与外部形式进行了详细的推导,给出了角点系数的计算方法与边界积分方程的形式,在此基础上,分析了奇异积分产生的原理及其对数值计算的重要性,提出了一种计算奇异积分的非等参单元的变换方法,该方法给Helmholtz 声学边界积分方程中的弱奇异积分与Cauchy 奇异积分的计算以及编程提供了极大便利。阐述了Helmholtz 边界积分方程在进行多频计算时计算量的巨大性,针对如何提高Helmholtz 边界积分方程的计算效率,提出了一种无穷级数展开的方法-SECHIEF,该方法可以极大地提高计算速度。其实质是通过空间来换取速度,对于非唯一性问题,则采用CHIEF 方法来处理,将补充的CHIEF 方程也通过级数展开的方法表示为波数的矩阵幂级数形式。在前几章的基础上,通过结构声辐射的模态理论对结构的声辐射的机理进行了深入地探讨,针对目前声辐射模态的研究对象主要是简单的板和梁类结构,提出了一种计算复杂结构声辐射模态的方法,利用前两章研究所得的结论,将边界元方法与广义特征值的理论结合起来研究了复杂结构的声辐射模态与声辐射效率,先将结构的声辐射功率表示为一个正定的厄米特二次型,运用广义特征值分解求解了复杂结构的声辐射模态,然后利用声辐射模态关于阻抗矩阵与均方速度耦合矩阵的正交性,求解了复杂结构的声辐射效率,最后用具有解析解的脉动球与辐射立方体验证了该方法的有效性。更多还原

【Abstract】 In this dissertation, based on the discussed history of numerical method of structure-born sound radiation, the boundary element integral equation is deduced, and then the numerical method of sound radiation, the theory of radiation modal and the sound radiation sensitivity analysis is discussed in details. The two key problems of BEM, namely singular integral and multi-frequency calculation, are studied in details based on the BEM method, and two valid numerical methods is posted, and sound radiation mode and sensitivity analysis of complex structure is also studied, the theory of sound radiation mode explain the principle of structural sound radiation, last, the validity of those methods is tested by experiments. The history and development of numerical method of sound radiation, modal theory and sensitivity analysis is reviewed, and the key problems about those theories are presented, last, the main studied works of this dissertation are summarized. Then the boundary element integral equation of interior and exterior form is deduced in detail, also the form with corner coefficient. The significance for numerical calculation and principle of the singular integral is analyzed, and a non-isoparametric transformation method is presented to calculate weak singular integral and Cauchy integral, the method presented provides us a very simple way to computer the two kinds of singular integral of Helmholtz boundary integral equation, and it is easy to program in computer. After the difficulty of the calculation for multi-frequency of Helmholtz boundary element is explained, a method named SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation), which is focused on the computational efficiency, is presented. The method can not only provide uniqueness of solution and reduce the computational time but also give accurate results under the coarse elements. The essential of this method is to enhance the computational efficiency by increasing the use of disc space. For the problems of non-uniqueness, the CHIEF method is used to overcome it, and the CHIEF equation is also expanded by series. Based on the previous results, the principle of structral sound radiation is studied by the theory of structrural sound radiation mode. According to the studied results at present, the studied objects are mainly thin plate and beam about sound radiation mode, a method computed sound radiation mode of complex structure is presented in this dissertation, according to the results of the previous two chapter, a theoretical method to solve acoustical radiation mode and acoustical radiation efficiency of complex structure by boundary element method and acoustical radiation theory is posed, the acoustical radiation power is expressed as a Hermitian quadratic form, while the radiation modes is determined by general eigenvalue decomposing, and then the radiation efficiency is computed via the orthodoxy of radiation modes with regard to impedance matrix and average velocity matrix; lastly, the validity of the method is proved by pulsating sphere and radiating cube with analytical results. According to results of the form three chapter, the structure sound radiation sensitivity is studied in detail, the sound radiation power of structure can be expressed as positive Hermitian quadratic form, the sound radiation sensitivity can be expressed as two parts by partial differential with respect to design variable, which are sensitivity of boundary velocity and impedance matrix, combined with the theory of FEM and BEM, the structure sound radiation can be translated to the analysis of structure dynamic sensitivity and impedance matrix sensitivity. The theory posted in this dissertation is tested by the FEM software ANSYS and the software AAS(Advanced Acoustic Simulation) programmed by author. Lastly, the summarization and expectation are given.更多还原