论文部分内容阅读
应用二级分形有限元方法计算了外域声场。用一人工边界把外域声场分为两部分,人工边界以内使用常规有限元方法,人工边界以外的无限大区域使用分形有限元方法。使用分形有限元方法,一方面形成几何自相似网格使得相邻层之间的单元刚度矩阵和质量矩阵具有非常简单的关系,另一方面引用自动满足无限远辐射条件的全域插值函数把节点自由度变换为一组广义坐标,因而计算量可以大大减少。数值计算结果表明:该方法对于计算无限大外域声场是有效的。
The second-order fractal finite element method is used to calculate the outfield acoustic field. An artificial boundary is used to divide the sound field of the outlying area into two parts. The conventional finite element method is used within the artificial boundary. The infinite area outside the artificial boundary is solved by using the fractal finite element method. The use of fractal finite element method, on the one hand to form a geometric self-similar grid so that the adjacent layer stiffness matrix between the matrix and the mass matrix has a very simple relationship, on the other hand, the reference to automatically meet the infinite radial conditions of the global interpolation function of the node free Degrees transform into a set of generalized coordinates, so the amount of computation can be greatly reduced. The numerical results show that this method is effective in calculating the infinite field sound field.