基于积分方程方法的弹性波多重散射计算

运用积分方程方法计算了含多个随机分布椭圆柱型孔洞的随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。首先,建立了散射位移场满足的积分方程,推导了单个椭圆柱孔洞的散射截面计算公式。接着分析了在含多个随机分布椭圆柱型孔洞的随机非均匀介质中弹性波的多重散射,给出在统计平均意义下的相干波的波速和衰减系数计算公式。然后用Matlab进行了编程,给出了一个数值算例,并将计算结果与波函数展开法进行了比较,分析了随机空隙介质的频散特征及其孔洞椭圆偏心率和材料空隙率的影响。

Multiple scattering computations of elastic waves based on integral equation method

The phase velocities and attenuation coefficients of coherent waves propagating through random medium,in which circular or elliptical column holes are distributed randomly in a matrix material,are studied in this paper.First,the specific integral equation to determine the scattering displacement vector is deduced.The equations to compute the scattering cross-section of one elliptical column hole are also deduced.Secondly,the multiple scattering in the random medium with randomly distributed column holes is analyzed and the equations to compute the phase velocities and attenuation coefficients of coherent waves with statistical average significance are given.Next,a numerical example is given and the numerical results are compared with that obtained by Wave Function extension Method.At last,the influence of the elliptical eccentricity and the porosity on the phase velocity and attenuation coefficient of coherent wave are discussed.