无网格FEM-BEM法计算舱室空间声传递函数

Meshless FEM-BEM method for computing sound transfer function in enclosed spaces

对于舱室空间低频声场计算问题,通常采用有限元法(FEM)或者边界元法(BEM),但是当封闭空间内部存在其他物体,又需要考虑外部激励对内场的影响时,直接采用单一的前述方法不能满足建模计算要求,而且这些基于网格的方法在前处理、光顺化处理等方面都存在不足。针对这些问题,将有限元和边界元法结合,并将其无网格化,这对于封闭环境的声场预测是一种新的尝试。首先推导了无网格FEM-BEM计算模型,对微分方程的离散、形函数构造等细节进行了详细阐述,然后以实际算例对提出的方法进行了验证,结果表明,无网格FEM-BEM方法和SYSNOISE的计算结果保持一致;进一步与实测结果的对比表明,该方法在低频率范围内,各测点平均声压级相对误差在5.26%以内。这说明,该方法不仅适用于复杂问题的计算,同时还具有良好的计算精度。

The finite element method（FEM）or boundary element method（BEM）is usually employed in sound field calculation of a cabin space at lower frequency,but a single method can not satisfy computing requirements of complex structures.These methods have some disadvantages,such as,lack of pre-processing and smoothing processing. Aiming at these problems,here,FEM and BEM were combined into a hybrid algorithm,and then transform it was converted into a meshless algorithm.It was a new approach for a sound prediction problem in enclosed environment.At first,the combined meshless FEM-BEM model was derived,and then the specific details including discretization of differential equations,construction of shape functions,nodal disposal,and were combined integral computing scheme were described.Finally,numerical simulations and tests were conducted to verify this method.The simulation results showed that the results using the proposed method agree well with those using SYSNOISE.The test results showed that the average relative error of each position＇s sound pressure of a cabin space is less than 5.26%.These results showed that the proposed method not only is applicable for complex problems,but also has a good computation accuracy.