二维稳态辐射声场的光滑有限元-完美匹配层解法

摘要

Aiming at the problem of low accuracy of finite element method （FEM） for exterior acoustics analysis, the smoothed finite element method-perfectly matched layer （SFEM-PML） method is proposed for the analysis of two-dimensional steady-state acoustic radiation problem. In SFEM-PML, the computational region, truncated by perfectly matched layer（PML）, is discreted into four-node isoparametric elements. The mapping relation between the PML＇s parameter coordinates and Cartesian coordinates is implemented by using the exponential absorbing function. In order to recast the domain integrals involving shape function gradients to the boundary integrals involving only shape functions, the radiant acoustic stiffness matrix is calculated by using the smoothed acoustic pressure gradient matrix. Numerical example of a two-dimensional radiation field of acoustic cavity of automobile is presented, which shows that SFEM-PML achieves better absorbing effect in PML, and higher accuracy in the computational region as compared with FEM-PML. Hence the SFEM- PML can be well applied in solving two dimensional acoustic radiation problems, and has a wide application foreground.%针对外场声学有限元计算精度偏低的问题，将光滑有限元技术引入二维稳态辐射声场预测中，提出了光滑有限元-完美匹配层解法．该解法采用完美匹配层截断声场计算域，并将其离散为等参四边形单元，采用指数吸收函数实现完美匹配层内参数坐标和笛卡尔坐标的映射关系，采用光滑声压梯度技术计算辐射声场刚度矩阵，将形函数梯度的域内积分转换为形函数域边界积分．某汽车二维声腔辐射声场的数值分析结果表明，与标准有限元-完美匹配层相比，光滑有限元-完美匹配层解法在完美匹配层内的声波吸收效果更好，在计算域内的数值计算精度更高，具有良好的工程应用前景．