School of Electrical and Computer Engineering, National Technical University of Athens, Athens 15773, Greece.
J Acoust Soc Am. 2011 Jan;129(1):24-31. doi: 10.1121/1.3514519.
Green's function in the interior of penetrable bodies with inhomogeneous compressibility by sources placed inside them is evaluated through a Schwinger-Lippmann volume integral equation. In the case of a radial inhomogeneous sphere, the radial part of the unknown Green's function can be expanded in a double Dini's series, which allows analytical evaluation of the involved cumbersome integrals. The simple case treated here can be extended to more difficult situations involving inhomogeneous density as well as to the corresponding electromagnetic or elastic problem. Finally, numerical results are given for various inhomogeneous compressibility distributions.
通过一个施温格-李普曼体积积分方程,评估了位于其内的源置于可穿透体内部时的可压缩性不均匀体的格林函数。在各向异性球体的情况下,未知格林函数的径向部分可以展开为双迪尼级数,这允许对所涉及的繁琐积分进行分析评估。此处处理的简单情况可以扩展到更复杂的情况,包括不均匀密度以及相应的电磁或弹性问题。最后,给出了各种不均匀压缩性分布的数值结果。