边界元法计算已知振速封闭面的声辐射

采用边界元法求解封闭面在无限域声媒质中的辐射声场具有内存小、计算精度高、速度快等优点。但需处理被积函数在边界面上的奇异积分及表面Helmholtz方程在特征频率下无唯一解的问题。本文提出把内部Helmholtz方程与它关于内点坐标取导后的式子构成补充方程式,经与表面Helmholtz方程相结合,可求解任意频率下的声辐射问题;而在奇点附近区域,则提出用极坐标变换消除积分的奇异性。文中以轴对称形封闭面为例,计算了具有已知表面振速分布下的辐射声场。     

三维Helmholtz方程外问题的自然积分方程及其数值解

用文[2,3]提出的自然边界归化方法来处理三维Helmholtz方程的外边值问题。在简要介绍如何用球谐展开的方法得到Helmholtz问题在外球域上的自然积分方程后,给出求解该自然积分方程的一种数值方法及相应的数值算例。     

轴对称体声振耦合的边界子波谱与有限元耦合方法

探讨了子波在Helmholtz积分方程及声振耦合中的应用,在建立了求解轴对称Helmholtz积分方程的子波谱方法的基础上,构造了轴对称子波谱与轴对称有限元的耦合方法,该方法可以处理轴对称问题的任意边界条件.进行了声振耦合问题的模态分析.     

开口/封闭薄壳体声辐射和散射的统一边界积分方程解法

推导了在二维和三维空间下开口和封闭薄壳体在任意阻抗边界条件下声辐射和散射的统一边界积分方程.相对于以前的求解方法,该方程求解声辐射和散射问题具有相同的影响矩阵,能够同时求解薄壳体气动和振动噪声的辐射和散射现象,以及分析壳体声阻抗对声波传播的影响.推导的方程可以应用于叶轮机械、管道等噪声和消声器消声性能的预测等方面.在此方程基础上,可以进一步考虑运动边界和运动介质对声辐射和散射的影响. 关键词： 薄壳体 声阻抗 积分方程 边界元方法     

改进的半空间频率均方声压法计算结构频带振动声辐射

为计算中高频半空间结构频带振动下声辐射问题,推导了基于能量源的半空间频率均方声压法(Frequency Averaged Quadratic Pressure,FAQP),并提出了改进的半空间FAQP法,克服了半空间FAQP法在失效频率下解不唯一的问题。频率带宽为4 Hz的刚性壁面作用下的脉动球和与自由表面相接触的脉动半球的声辐射数值计算,验证了改进的半空间FAQP法对解决失效频率下解不唯一问题的有效性。同时,刚性壁面作用下的脉动球和与自由表面相接触的脉动半球声辐射数值计算结果均表明,在1/3倍频程下,改进的半空间FAQP法与常规边界元方法相比,具有更高的计算精度,更适用于中高频计算。      

结构声辐射的振动模态分析和声辐射模态分析研究

基于辐射声功率的二次型表达式,采用有限元法、Rayleigh积分和边界元法对结构声辐射进行了振动模态分析和声辐射模态分析研究。振动模态间的耦合对辐射声功率影响的研究表明: 结构各阶振动模态自身对结构辐射声功率的贡献是增大结构的辐射声功率,而振动模态间的耦合可能会增大结构辐射声功率,也可能会减小结构辐射声功率,或对辐射声功率没有影响。而且,当振动模态间的耦合作用对辐射声功率的影响不大时,采用振动模态控制可取得较好的减振降噪双重控制效果。将混合的Helmholtz积分方程方法用广义逆引入到三维复杂结构声辐射分析的声辐射模态公式中,解决了特征频率下解不唯一问题。还研究了正方形封闭空间结构声辐射模态的辐射效率和形状,并对结构声辐射的振动模态控制和声辐射模态控制进行了讨论。     

声辐射计算的改进体积源边界点法

对体积源边界点法做了较大的改进,提出了在加权余量意义下,通过在边界结点法线方向(背离分析域)构作的四面体上对Ｈｅｌｍｈｏｌｔｚ方程的基本解进行积分,来对偶地表达系统方程中的系数矩阵,从而求解结构振动声辐射问题。对大量算例和模拟车床主轴箱辐射声场的改进体积源边界点法分析表明:改进的方法在计算速度较原体积源边界点法提高了１０余倍的情况下,在计算精度、计算稳定性、对振动体任意表面几何形状的适应性以及克服解的非唯一性等方面,表现出了良好的性态。     

水下弹性球壳被激振动和辐射声的时域特性研究

本文在时域上对水下球壳在球冠形均匀单频填充脉冲力源作用下的振动和辐射声问题进行分析和计算。结果表明:在长脉冲力作用下,根据填充频率不同,会激起不同模态振动和产生长的共振辐射声或拍频辐射声,但有一部分模态对远场声辐射的贡献甚微;在短脉冲力作用下,脉冲波在球壳上传播一般会发生展宽和变形。文中还应用DAA2方法简化水——壳体耦合关系和边界元方法计算辐射声场。与精确解比较可知,DAA2方法的结果是令人满意的。     

基于Burton-Miller方程的轴对称结构声学边界元方法

提出了一种求取轴对称结构任意边界条件下声辐射特性的边界元方法。采用Burton和Miller改进型公式将高阶奇异项转化为弱奇异项之和,保证声辐射参数的唯一性,且计算简单精确。将结构表面声压与振速按照旋转轴角度进行Fourier级数展开,利用级数的正交性建立各项待定系数的求解公式;然后转化格林函数的法向偏导为切向偏导,方便直接计算各项积分,并将面积分公式表示为沿结构边界的线积分和沿旋转角度的积分;进一步采用二次等参单元离散结构边界线,建立声压与振速的关系矩阵,从而确定结构声辐射参数。以脉动球源和横向振动球源为例计算,与解析解和传统边界元法结果作对比,说明该方法的有效精确性。     

求解本征值问题的改进边界元法

本文提出了一种求解本征值问题的改进边界元技术,它是将Laplace方程对应的基本解用于Helmholtz方程,从而使形成的边界元方程不隐含本征量,这样大大降低了对计算机内存的要求,并提高了求解速度。     

A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method

Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.     

A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions

This paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions. The difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface. This process gives rise to a set of uniquely solvable boundary integral equations. Distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation. The modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only. This implementation allows direct application of standard quadrature formulas over the entire integration domain; that is, the collocation points are exactly the positions at which the integration points are located. Selecting the interior surface is an easy task. Moreover, only a few corresponding interior nodal points are sufficient for the computation. Numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders. Comparisons with analytical solutions are made. Numerical results demonstrate the efficiency and accuracy of the current solution method.     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

流体加载下加肋板结构的声辐射特性研究

本文采用有限元和边界元方法对加肋板结构的声辐射进行了计算分析,研究分析了加肋板结构的板厚、板面积、板边长比、肋骨惯性矩和间距、边界条件以及板材和流体介质等对结构辐射声功率的影响,得到了一些有意义的结论,从而为揭示加板结构声辐射规律,降低结构的声辐射提供了一定的依据。     

A prediction of the acoustic field of a vibrating box by FEM-BEM

I.Mathematicalmodelofacousticfie1dByapplyingtheSommerfeldradiationcondihonThus,anacousticfic1disdescribcdbyHelmholtzformula.Byconsideringaficldpointinthearea,Helmholtzformulaisgivenbythefollowingthreeintegra1equations:(1)Theexternalintcgra1fOrmu1a'(2)Thcintcrnalintegralformu1af(3)Thesurfaceintegralformu1afwhcreP.isthesoundpressureonthcSsurface;rthedistancefrompointqtothee1ementsurfacedSiqtheficldpoint,tuthefrcqucncyoftheacousticradiation;pthedensityofthesurroundingmedium,vsthenormalvibrati…     

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.     

The application of source methods in estimation of an interior sound field

In earlier studies, one has successfully developed three different source methods (SSM, similar source method; IPSM, internal parallel source method; ISM, internal source method) to estimate radiation and scattering sound fields. All these methods are estimations of exterior sound fields. In the present study, the similar source method is modified to estimate an interior sound field. The modification is to move the imaginary sources outside the boundary surface. In addition, general boundary conditions in terms of acoustic admittance or impedance are considered by introducing the suitable least square error functions. Finally, a two-dimensional interior sound field with alternative boundary conditions is evaluated to simulate sound fields inside a car. The results are in agreement with those of boundary integral method.     

An iterative method to solve acoustic scattering problems using a boundary integral equation

In this work, a simple iterative method to solve the acoustic scattering/radiation problems using the boundary integral equation (BIE) formulation is presented. The operator equation obtained in the BIE formulation is converted into a matrix equation using the well-known method of moments solution procedure. The present method requires much fewer mathematical operations per iteration when compared to other available iterative methods. Further, the present iterative method can easily handle multiple incident fields, a highly desirable feature not available in any other iterative method, much the same way as direct solution techniques. Several numerical examples are presented to illustrate the efficiency and accuracy of the method.     

Predict acoustic field of vibrating beams by Helmholtz integral equation and BEM

New method of predicting the acoustic field radiation of vibratingbodies is presented.It is based on the Helmholtz integral equation and bounda-ry element method and applicable to the use of computers.The acoustic field ofthe cantilever beams has been calculated and measured.Test results haveproved the effectiveness of the predicting method.