Ray Method for Sound‐Wave Reflection in an Open‐Ended Circular Pipe
Ray Method for Sound‐Wave Reflection in an Open‐Ended Circular Pipe
复制标题
开口圆管中声波反射的射线法
DOI：
10.1121/1.1911193
复制
发表时间：
1968
影响因子：
2.4
通讯作者：
H. Yee
中科院分区：
文献类型：
--
作者：
L. Felsen;H. Yee
计算了在一种传播模式下半无限带法兰和无法兰硬壁圆管的模态反射系数和耦合系数。通过射线法进行计算，其中入射模式被分解为撞击在边缘上的局部平面波。由此产生的衍射效应建立了反射波，并等价地表示为来自非各向同性环形源的辐射，环形源的辐射模式由边缘的局部散射特性决定。将非各向同性环形光源所发射的、经管壁反复反射的射线求和为模态形式，并与各向同性环形光源的精确解进行比较，提高了渐近模态级数的质量。反射系数和耦合系数是由模态振幅提供的，并确定了由于入射模式引起的初级衍射和由于管口相互作用引起的多重衍射。与薄壁管的精确计算比较表明，多重相互作用的射线声计算不仅在高频，而且在主导模式下也具有很高的精度。数据也提出了没有精确的解决方案可用的法兰终端。
Modal reflection and coupling coefficients are calculated for a semi‐infinite flanged and unflanged hard‐wall circular tube excited by one of the propagating modes. The calculation is performed by a ray method wherein the incident mode is decomposed into local plane waves impinging on the rim. Consequent diffraction effects establish the reflected waves and are represented equivalently in terms of radiation from a nonisotropic ring source having a radiation pattern determined by the local scattering properties of the rim. The rays emitted by the nonisotropic ring source and reflected repeatedly from the tube wall are summed into modal form, the quality of the resulting asymptotic mode series being improved by comparison with the exact solution for an isotropic ring source. Reflection and coupling coefficients are provided by the modal amplitudes in this representation and are determined for primary diffraction due to the incident mode only and also for multiple diffraction due to interaction across the mouth of the tube. Comparison with exact computations for the thin‐walled tube shows that the multiple interaction ray‐acoustical calculation is capable of high accuracy not only at high frequencies but even in the dominant mode regime. Data are also presented for flanged terminations for which no exact solution is available.