求助，求Journal of Acoustical Society of America上的一篇论文，作者E. D. Scheirer，年份1998

英文
A self‐consistent method of estimating effective macroscopic elastic constants for inhomogeneous materials with spherical inclusions is formulated based on elastic‐wave scattering theory. The method for general ellipsoidal inclusions will be presented in the second part of this series. The case of spherical inclusions is particularly simple and therefore provides an elementary introduction to the general method. The self‐consistent effective medium is determined by requiring the scattered, long‐wavelength displacement field to vanish on the average. The resulting formulas are simpler to apply than previous self‐consistent scattering theories due to the reduction from tensor to vector equations. In the limit of long wavelengths, our results for spherical inclusions agree with statically derived self‐consistent moduli of Hill and Budiansky. Our self‐consistent formulas are also compared both to the estimates of Kuster and Toksöz and to the rigorous Hashin–Shtrikman bounds. (For spherical inclusions and long wavelengths, the Kuster–Toksöz effective moduli are known to be identical to the Haskin–Shtrikman bounds.) A result of Hill for two‐phase composites is generalized by proving that the self‐consistent effective moduli always lie between the Haskin–Shtrikman bounds for n‐phase composites. Numerical examples for a two‐phase medium with viscous fluid and solid constituents show that the real part of our self‐consistent moduli always lie between the rigorous bounds, in agreement with the analytical results. Some of the practical details in the numerical solution of the coupled, nonlinear self‐consistency equations are discussed. Examples of velocities and attenuation coefficients estimated when the solid constituent possesses intrinsic absorption are also presented.PACS
Scattering of acoustic waves
中文
一个自我提供一致的种估计方法有效的宏观弹性常数对非球形夹杂物材料制定提供基于弹性波散射理论。一般椭圆夹杂的方法将展示这个系列的第二部分。球形夹杂物的情况下非凡简单,因此提供了一个基本介绍的一般方法。提供有效的媒介的自我是由一致要求分散的、长波长位移场,终于消失在平均水平。结果应用该公式是比以前更简单的自我终于由于散射理论相一致,从矢量方程组张量减少。在长波长的限制,我们的结果为球形夹杂物终于同意静态导出常数等自我希尔和Budiansky一致。我们的自我提供一致的公式作了比较分析两者是对的估计和Toksoz Kuster和严谨的Hashin-Shtrikman界限。(为球形夹杂物的长波长,Kuster-Toksoz和有效模被认为是完全相同的Haskin-Shtrikman界限。)由于希尔终于为两相复合材料,证明了广义一致有效自我终于Haskin-Shtrikman模之间的界限总是撒谎对于n终于相复合材料。以两个数值例子与粘性介质提供相流体和固体成分显示,实际的一部分,我们总是自我提供一致的模隔了严格的界限,在协议与分析结果的可靠性。一些细节上的实用的数值解耦合、非线性自我一致性方程终于进行了讨论。实例的速度和衰减系数估计当固体成分具有内在的吸收进行了研究。