边界元法计算已知振速封闭面的声辐射

BOUNDARY ELEMENT METHOD FOR CALCULATING ACOUSTIC RADIATION FROM,CLOSED SURFACES WITH PRESCRIBED VELOCITY DISTRIBUTION

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。

The application of BEM to the calculation of acoustic radiation from closed surfaces in an infinite acoustic medium has the advantages of less memory space, higher accuracy and faster calculating speed. However, the singular integrals and the nonuniqueness problem of surface Helmholtz equation at characteristic frequencies .should be dealt with. We suggest in this paper combination of the interior Helmholtz equation and its derivatives with respect to the coordinates of an interior point to form an extra equation, in order to solve the problems of acoustic radiation at various frequencies with surface Helmholtz equation; on the area which includes singular point, singular integrals are converted to ordinary ones by polar coordinate transformation. As an example, the acoustic radiation field of closed axisymmetric surfaces with prescribed surface velocity distribution is calculated in the paper.