摘要
本文作者采用一种全新的“高斯函数多项式”来描述活塞声场,用这种方法计算了活塞式声场的轴向分布和远近场的径向分布,与用精确的表达式(瑞利积分)计算结果颇相符合,并证明了这种“函数多项式”或高斯函数组对于某一类函数展开是完备的,这表明轴对称声源可以看作一系列高斯声源的线性叠加。这种方法不仅为了简化声场的数学描述,而且也有利于处理有限束声场的散射、聚焦声场等声学问题。
In this paper, an analytical form is obtained for describing ultrasonic field of piston source by using entirely new 'Gaussian function's polynomial'. By this method, the pressure distribution is calculated along the axis and on cross section in near and far field of the circular piston. The result is in good agreement with the one predicted by Rayleigh's integral, We also demonstrate that the 'function's polynomial' or the set of Gaussian function is complete to the expansion of some functions, and it indicates that all axis -symmetric sources are taken as the superposition of sets of Gaussian source. This method not only simplifies mathematical representation of the sound field but also deals with the problems such as the beam -limited sound field scattering and focusing source etc.
出处
《声学学报》
EI
CSCD
北大核心
1993年第4期249-255,共7页
Acta Acustica
基金
国家自然科学基金
