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。

Acoustic boundary element method for axisymmetric structures based on Burton-Miller equation

A boundary element method for obtaining the acoustic radiation characteristics under arbitrary boundary condition of axisymmetric structure is proposed. By using the improved Burton and Miller formulas, the hypersingular term is transformed into the sum of the weak singular terms to ensure the uniqueness of the acoustic radiation parameters and the calculation is simple and accurate. By expanding the surface velocity and pressure in Fourier series with respect to the angle of revolution and using the orthogonality of the series, the undetermined coefficient is established. The normalized operators of the Green function is translated into the tangential operators, which makes it easy to calculate the integrals directly. The surface integral formula is expressed as a line integral along the generator of the body and the integral over the circumferential angle. Furthermore, the relationship between the sound pressure and the vibration velocity is established with quadratic isoparametric elements to determine the acoustic radiation parameters. Taking a pulsating sphere and an oscillating sphere as examples, the results are compared with the analytical results and the results of the traditional boundary element method to illustrate the validity and accuracy of the method.