板式结构声辐射特性研究

发布时间：2018-05-18 19:11

本文选题：Mindlin板理论 + 声辐射　；参考：《中北大学》2014年硕士论文

【摘要】：板式结构作为一种基本结构形式，在国防、民用等行业产品中广泛应用，它不仅在受到激励作用下会向外辐射噪声，，而且也可用于控制噪声的传播。因此，对板式结构的振动声辐射研究不仅具有理论研究意义，也有较大的工程应用价值。本文针对板式结构的振动声辐射特性展开了研究，并对表面大量采用板式结构的发动机模型进行了声场求解分析。本文的主要研究工作有：（1）基于弹性力学及有限元的相关理论,结合Mindlin板弯曲理论,探究了单元应变位移关系、位移函数同应变阵的关系以及应力与应变之间的关系。对板式结构在不同载荷情况下的振动响应情况进行了理论分析。基于振动响应结果，研究了板结构振动所激发的声学响应，推导得到了边界积分方程的离散形式。（2）介绍了以三次B样条函数作为单元型函数的研究方法来分析薄板的弯曲、振动问题。建立基于Helmholtz边界方程的边界元模型，采用基于三次B样条函数的耦合有限元法-边界元法对在空气介质中的矩形钢板进行了辐射声功率的数值计算，同采用Matlab编制的Rayleigh积分公式计算矩形钢板辐射声功率的结果对比，由此来验证基于三次B样条函数的耦合FEM-BEM方法在计算板式结构辐射声功率上的精度和准确性。（3）探讨了以下板式结构参数对其声辐射特性的影响：1）平板、加肋板、梯形板、三角形板和梯形板这五种不同的板式结构形状；2）加肋板中肋条的布置方案；3）20种不同组合的边界约束条件；4）在等厚板中不同的厚度值、在厚度值线性变化的变厚度中不同的倾斜角；5）不同的长宽比。（4）针对边界元法在计算大规模问题时耗时、耗计算空间甚至出现无法计算的问题，文章应用快速多极边界元算法，并以此为理论基础对表面结构大量采用板式结构的某型发动机模型进行了声辐射求解，并同采用常规边界元算法进行了对比，验证了快速多极边界元法在计算大规模问题时的准确性和高效性。
[Abstract]:Plate structure, as a basic structure form, is widely used in industries such as national defense, civil industry, etc. It not only radiates noise but also can be used to control the propagation of noise. Therefore, the study of vibration and acoustic radiation of plate structure is not only of theoretical significance, but also of great engineering application value. In this paper, the characteristics of vibration sound radiation of plate structure are studied, and the acoustic field of engine model with plate structure is analyzed. The main research work of this paper is as follows: 1) based on the theory of elastic mechanics and finite element, combined with Mindlin plate bending theory, the relationship between strain displacement, displacement function and strain matrix, and the relationship between stress and strain are discussed. The vibration response of plate structure under different loads is theoretically analyzed. Based on the results of vibration response, the acoustic response of plate structure excited by vibration is studied, and the discrete form of boundary integral equation is derived. In this paper, the method of using cubic B-spline function as element function to analyze the bending and vibration of thin plate is introduced. A boundary element model based on Helmholtz boundary equation is established. The coupled finite element method based on cubic B-spline function and the boundary element method are used to calculate the radiated sound power of rectangular steel plate in air media. The accuracy and accuracy of the coupled FEM-BEM method based on cubic B-spline function in calculating the radiated sound power of plate structures are verified by comparing the results of the calculation of the radiated sound power of rectangular steel plate with the Rayleigh integral formula compiled by Matlab, which proves that the coupled FEM-BEM method based on cubic B-spline function is accurate and accurate in calculating the radiated sound power of plate structure. The influence of the following structure parameters on the acoustic radiation characteristics of the plate is discussed. (1) flat plate, stiffened plate, trapezoidal plate, Triangular plate and trapezoidal plate are five different plate structural shapes. The arrangement of rib in ribbed plate is divided into 20 kinds of boundary constraint conditions. (4) different thickness values in equal thickness plate. In the variable thickness with linearly varying thickness, the slanting angle is 5) and the aspect ratio is different. In this paper, the fast multipole boundary element algorithm is applied to solve the problem that the boundary element method is time-consuming and even can not be calculated in the computation of large scale problems. On the basis of this theory, the acoustic radiation of a certain engine model with a large number of plate structures is solved and compared with the conventional boundary element algorithm. The accuracy and efficiency of the fast multipole boundary element method for large scale problems are verified.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB53

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