声辐射模态和球谐波函数在球源声场重建中的比较

Comparison of acoustic radiation modes and spherical harmonic functions in the acoustic field reconstructions of spherical sources

声辐射模态和球谐波函数在球源声场重建中均有应用,两者具有很多相似性,都具有相同的多极子辐射模式和"群组"分布特性。有观点认为球形声源的声辐射模态向量即为球谐波函数,但两者的内在关系一直缺乏有效的证明。为分析两种基函数的相似性及在球源声场重建领域的差异,在理论上建立了两者的内在联系,在应用上比较研究了基于两种基函数的声场重建方法的有效性和可靠性。数值算例结果表明,在中高频段时基于两种函数的声场重建效果相当,但在低频段尤其是存在干扰源的非自由场条件下的声场重建应用中,基于声辐射模态的声场重建方法能得到更高的重建精度。可见,声辐射模态具有较为明显的声场重建优越性,这为利用声辐射模态和球谐波函数进行球源声场重建提供了理论参考。

Acoustic radiation modes and spherical harmonic functions, which have been both applied in the acoustic field reconstructions of spherical sources, are very similar in the multi-pole radiation pattern and ＂group＂ distribution features. Some researchers regard that the acoustic radiation modes of spherical sources as spherical harmonic functions, nevertheless, it has not been theoretically proved yet. In order to analyze the similarities and differences of these two primary functions in acoustic field reconstruction, the inherent relations between them are established in theory, and the effectiveness and reliability in acoustic field reconstruction are compared. The numerical examples results show that the reconstruction results of the two methods are quite same at middle and high excitation frequencies. However, the method based on spherical acoustic radiation modes achieves better reconstruction accuracy at low excitation frequencies, in particular, in a non-free field with interference sources. The conclusion can be made that the acoustic radiation modes has more advantages, which are instructional for selecting acoustic radiation modes or spherical harmonic functions in the acoustic field reconstructions of spherical sources.