Mathematical Sciences: Multiple Scattering by Elastic Spheres in an Elastic Half-Space Bounded by an Elastic Penetrable Interface

数学科学：由弹性可穿透界面界定的弹性半空间中弹性球的多次散射

• 批准号: 8910594
• 负责人: Dieudonne Phanord
• 金额: $ 1.2万
• 依托单位: University of Alabama in Huntsville
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-10-01 至 1991-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8910594&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multiple; Scattering; Elastic

Dr. Phanord will extend to elasticity the work done by Richard Solakiewicz under the guidance of Professor Victor Twersky on acoustic scattering by an obstacle in a half-space bounded by a penetrable interface. With the elastic extension of the solution for the single object in isolation, Dr. Phanord will construct the multiple scattering solution for a distribution of identical spheres. He will use the self-consistent procedure to obtain integral equations for the multiple scattering amplitudes of the composite media in terms of the scattering amplitudes of the single obstacle. From the ensemble average of the integral equations and the equivalent medium approach, he will derive a pair of dispersion relations which provide a means to obtain the bulk propagation parameters of the composite media from those of the isolated single scatterer. To compute multiple scattering cross-sections, Dr. Phanord will establish new reciprocity relations corresponding to multiple elastic scattering for different combinations of the incident waves.

Phanord博士将把Richard Solakiewicz在Victor Twersky教授的指导下所做的关于以可穿透界面为界的半空间中障碍物的声波散射的工作扩展到弹性。通过对孤立的单个物体的解的弹性扩展，法诺德博士将为相同球体的分布构造多重散射解。他将使用自洽程序，以单一障碍物的散射振幅来获得复合介质的多重散射振幅的积分方程。从积分方程的系综平均和等效介质方法中，他将推导出一对色散关系，为从孤立的单个散射体的色散参数中获得复合介质的体传播参数提供了一种方法。为了计算多重散射截面，Phanord博士将建立新的互易关系，对应于入射波的不同组合的多重弹性散射。