敷设多孔吸声材料声腔特征值分析的径向积分边界元法

由于Helmholtz方程的基本解是频率的函数,因此传统边界元法在处理声场特征值问题时具有天生的缺陷。本文采用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元法系数矩阵对频率的依赖,同时克服了特解积分法对特解的依赖,并通过对表面声导纳的多项式逼近,将敷设多孔吸声材料声腔特征值问题转化为矩阵多项式,从而避免了复杂的非线性求解。通过数值算例验证了算法的有效性。

Eigenvalue analysis for acoustical cavity covered with porous materials by using the 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.In this paper,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 particular integral method.By using polynomials approximating of surface acoustic admittance,the acoustic eigenvalue analysis procedure for acoustical cavity covered with porous materials resorts to a matrix polynomial problem instead of nonlinear transcendental eigenvalue forms.Several numerical examples are presented to demonstrate the validity and accuracy of the proposed approach.