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与Aviles等学者的多重散射隔振理论相比较,采用更为完整的Fourier-Bessel函数系的级数展开表达式来研究弹性波入射下的多重散射问题。引入Graf加法定理,并结合位移和应力边界条件,推导了无限均匀弹性介质中任意分布的多个弹性圆柱体对于平面水平向剪切波(SH波)入射时散射系数的理论解析解。随后,取圆柱体分布于两条相互平行的直线上,则问题演变为双排弹性桩屏障对于弹性波的隔离问题。引入无量纲位移(屏障后土体总的位移与仅由入射平面水平向剪切波引起的位移的比值)和透射系数(屏障宽度范围内无量纲位移的几何平均值)的概念来研究屏障的隔振效果。重点讨论了双排桩间距h以及桩土的剪切模量比ξ对于屏障整体隔振效果的影响,阐述了双排桩屏障的隔振性状。特别地,当h=0时,该问题退化为常见的单排非连续屏障的隔振问题。
Compared with the multiple scattering and isolation theory by Aviles et al., The more complete Fourier-Bessel function series expansion expression is used to study the multi-scattering problem with elastic wave incident. By introducing Graf addition theorem and combining displacement and stress boundary conditions, the theoretic analytical solution of the scattering coefficient of plane random shear waves (SH waves) incident on multiple elastic cylinders randomly distributed in an infinitely uniform elastic medium is deduced. Subsequently, taking the cylinder distributed in two parallel straight lines, the problem evolved into the double elastic column barrier for the elastic wave isolation problem. The concept of non-dimensional displacement (the ratio of the total displacement of a soil after a barrier to the displacement caused by shear waves only horizontally from the plane of incidence) and the transmission coefficient (the geometric mean of dimensionless displacements within the barrier width) are introduced Vibration isolation effect. The influence of double-row pile spacing h and the shear modulus ratio of pile-soil on the overall vibration isolation effect of the barrier is discussed, and the vibration isolation characteristics of the double-row pile barrier are expounded. In particular, when h = 0, the problem degenerates into the common problem of vibration isolation of a single row of discontinuous barriers.