基于径向积分边界单元法的内场声学分析

由于Helmholtz方程的基本解是频率的函数,传统边界单元法在处理声场特征值问题时具有天生的缺陷.采用Laplace方程基本解生成积分方程,通过径向积分法将在此过程中产生的域积分项转化为边界积分.此方法克服了传统边界单元法系数矩阵对频率的依赖,同时克服了特解积分法和双重互易法对特解的依赖,将内场声学特征值问题转化为广义特征值问题.最后通过内场声辐射分析和声学特征值分析验证了算法的有效性.

Interior acoustic analysis based on radial integration boundary element method

The traditional boundary element method has a well-known difficulty when calculating acoustic eigenvalue problems since the fundamental solution of the Helmholtz equation is dependent on the frequency. The integral equation of acoustics Helmholtz equation is obtained by using the fundamental solution of Laplace equation, and then, the radial integration method is presented to transform domain integrals to boundary integrals. The proposed method eliminates the frequency dependency of the coefficient matrices in the traditional boundary element method and the dependence on particular solutions of the dual reciprocity method and the particular integral method. Eventually, the acoustic eigenvalue analysis procedure based on the radial integration boundary element method resorts to a generalized eigenvalue problem. Interior acoustic radiation analysis and acoustic eigenvalue analysis demonstrate the validity and accuracy of the proposed approach.