快速多极子边界元法在吸声材料声场计算中的应用

Application of FMBEM to calculation of sound fields in sound-absorbing materials

对快速多极子边界元法中多极子展开式的数值计算进行了研究,建立四点单级传递关系与多级传递关系模型。通过与格林函数及其法向导数理论值的比较,考察两种传递情况下,多极子展开式在吸声材料介质及空气介质中的计算精度。结果表明,复波数展开式的求解精度与截断项数的大小相关,而且当复波数虚部值与展开点间距离乘积过大时,展开式值开始与真值相背离。最后提出了解决此问题的两种方法。此外,以膨胀腔阻性消声器传递损失计算为例,验证了该方法的有效性与可行性。

The numerical calculation of muhipole expansions in FMBEM was investigated, and the models of four points translation relationships at single level and multi-levels were built. According to the variation of theoretical values of Green＇s function and its normal derivative, the computational accuracy of muhipole expansions in sound-absorbing materials and in air medium was compared under the two different translation relationships respectively. The results indicate that, the computational accuracy, which is derived from the calculation of expansions with complex wavenumber, is related to the number of truncated terms. When the product of the wavenumber＇s imaginary part and the distance between transitive points is too big, the expansion＇s value begins to go far away from the true value. Two methods were proposed to solve this problem. Furthermore, tile transmission loss of a silencer with dissipative expansion chamber was calculated as an example and the availability and feasibility of the methods presented were validated.