改进计算对称壳体声辐射的边界积分方程法

An Improved Method for Calculating Sound Radiation from Axisymmetric Shells with Boundary Integral Equation

用边界积分方程法计算轴对称振动表面的声辐射时,必须处理好特征频率下表面Helmholtz方程无唯一解的问题和奇点附近区域上的奇异积分问题。本文把表面Helmholtz方程与关于内点的补充方程联立组成线性方程组,用最小二乘法求解,并采用极坐标变换将奇异积分转换成普通积分,从而可以方便地计算任意形状轴对称体在各个频率下的声辐射。

When we use the boundary integral equation to calculate the soundradiation from symmetric vibrating shells, two problems must be solved: oneis that the surface Helmholtz equation has no definite solutions at characteristicfrequencies and the other is the singular integration that exists at the visinityof the singular points. In this article, a definite solution can be obtained byusing the least square method to solve linear equations which are composed ofsurface Hemholtz equations and additional equations of the inner points.Singular integration can be changed to ordinary integration by adopting polarcoordinates. Thus the sound radiation field from arbitrary shaped axisymmetricshells can easily be obtained at any frequency.