采用非匹配网格离散的快速边界元-有限元宽频声振耦合分析

Solving Broadband Vibroacoustic Problems with Fast Boundary ElementFinite Element Method Divided by Non-Matching Meshes

为构造出性能优异的声振耦合仿真系统,采用直接耦合方法建立了声振问题的边界元-有限元耦合方程,并对其求解方案的选取进行了详细讨论,最终实现了大规模耦合线性方程组的快速求解;考虑更具一般意义的耦合界面上声场边界元网格和结构有限元网格不匹配的情形,采用加权余量法构造了高阶非匹配单元之间的数据交换矩阵,实现了耦合界面上各物理场之间的高精度数据交换;介绍了适用于宽频问题的快速定向算法的实现原理,并将其引入声振耦合方程,在全频段内实现了对常规边界元矩阵的有效压缩,提高了声振耦合方法的计算效率;通过解析算例和自由度超过40万的大规模复杂算例,验证了本文方法的正确性和性能,特别是与现有同类方法相比,本文方法在保证高精度的同时,适用频段明显更宽,可达现有方法的3～4倍。

Modeling vibroacoustic problems with coupled fast boundary element method and finite element method(BEM-FEM)can maximize the advantages of the various numerical methods,hence can get a vibroacoustic simulation system with excellent performance.The direct coupling scheme is used to establish the vibroacoustic equation,and the selected scheme is discussed in detail to achieve a fast solution for a large-scale coupling system.Then the common mismatch between the sound field meshes and the structural meshes on the coupling interface is considered,and the data-exchange matrices between higher-order non-matching meshes are constructed with weight residual method to realize the highly accurate data exchange.The implementation theory for fast directional algorithm(FDA)suitable for broadband issues is introduced,and the traditional BEM matrices in BEM-FEM matrix are compressed efficiently in entire band by FDA.The correctness and effectiveness of this method are validated by introducing analytical examples and a large-scale complex example over 400,000 degrees of BEM-FEM freedom.In particular,this method is of higher accuracy and suitable for a broader band,which is 3 to 4 times that of the existing similar methods.