摘要
首先利用格林函数的双中心球坐标展开式得到了一类球函数加法公式。对于多球体声学系统,可应用该加法公式将空间声场相对于每一个球体中心展开,这样可以很方便地利用每个球体的边界条件来研究多球体系统的声学散射问题。研究了两球体系统在不同边界条件下的散射声场,每个球的散射声场可通过求解由双重级数和耦合的两个无穷方程组得到。最后引入了形函数的定义,计算了两球体系统在平面波入射下的形函数,从而通过与现有文献的数值对比验证了本文理论公式的正确性。
A kind of addition formulae for the spherical wave functions is generated first by using the bicentric expansion of Green function in spherical coordinates. For an acoustic system with multiple spheres, the addition formulae permit the field expansions all referred to the center of one of the spheres, whose boundary conditions can be consequently used to study the acoustic scattering from multiple spheres easily. The two-sphere acoustic system with different boundary conditions is considered and the scattered field by each sphere can be obtained by solving an infinite set of two linear, complex, algebraic equations, whose coefficients are coupled through double sums in the spherical wave functions. Finally, the form functions of two spheres insonified by plane waves at arbitrary angles of incidence are calculated and the addition formulae generated are validated by comparing the corresponding numerical results with those of the existing literature.
出处
《声学学报》
EI
CSCD
北大核心
2004年第3期238-243,共6页
Acta Acustica
基金
国家自然科学基金资助项目(10174037)
