固体媒质中异质球形散射体的声散射特性

Acoustic Wave Scattering from Spherical Scatterers Embedded in a Matrix

复合材料的物理性能和基材中填充物的复合状态有着密切的关系 .应用声散射方法研究复合材料复合状态是材料评价的常用方法之一 .在许多情况下 ,基材中的填充物呈现球状 ,因此对基材中球形填充物的散射研究是人们十分重视的研究课题 .然而以前的研究中 ,大多数讨论了纵波或横波入射时单一球形固体、流体或真空腔体的散射特性 ,对同一基材中不同性质材料球形散射体的散射谱特性及影响散射谱的因素较少涉及 .而后者对复合材料的评价很有意义 .首先介绍了固体中异质球形散射体的声散射理论模型 ,然后数值计算了同一基材中不同材质的球形散射体对入射平面声纵波的散射谱特性 .结果表明 ,散射体的归一化散射截面谱同基材和散射体的声速在速度状态图上的相对位置有直接的关系 ;散射截面随频率的变化规律在低频区的特性主要反映了散射横波的性质 。

Some composite materials are made of matrix and spherical fillers. The physical characteristics of the composites are closely related to the properties of the composite constituents. To evaluate the composites nondestructively, various methods are adopted and the acoustic wave scattering method is proven to be most promising. Therefore, the scattering from spherical scatterers embedded in a matrix has gained much interest of many investigators. As early as in 1956, Ying and Truell initiated the study on scattering of a plane longitudinal wave by a spherical obstacle in isotropic elastic solid. In 1980, Flax and berall introduced a resonant theory of elastic wave scattering from spherical solid inclusion. Experimental investigation of ultrasonic scattering by a solid sphere embedded in a isotropic medium was carried out only recently by Sessarego et al to verify the theories of sound scattering and to find applications in ultrasonic nondestructive evaluation (NDE) of composite materials. In previous studies, the acoustic wave scattering from single solid and liquid sphere or cavity in a matrix with the incidence of longitudinal or transverse wave has been thoroughly studied. However, the scattering from different scatterers embedded in the same matrix and how these scatterers affect the scattering somehow attracts little attention. In this paper, we briefly introduce the theory of acoustic longitudinal wave scattering from spherical scatterers embedded in a matrix by using the elastic wave equation in isotropic solids and the expansion method of normal modes in a spherical coordinate as well as the boundary conditions at the interface between the matrix and spherical scatterer. The relation between the acoustic propagation attenuation and scattering cross section of a spherical scatterer is given. Following the theoretical formulation, we have made some numerical computations of the scattering cross sections of scatterers with different density and elastic constants in the same matrix (Ge) at certain frequency range. The numerical results reveal that the magnitude of normalized scattering cross section depends on the relative position of scatterers and matrix in the state diagram of acoustic velocity. At lower frequency range the variation of normalized scattering cross section against frequency is mainly associated with the scattered transverse wave, while at high frequency range it reflects the scattered longitudinal wave properties. These results may be very useful for ultrasonic NDE of composites with different spherical fillers in the same matrix.