ANALYTICAL SOLUTION OF THE NEAR FIELD VIBRATION ISOLATION EFFECT OF PIPE PILE BARRIERS UNDER A CYLINDRICAL WAVE SOURCE
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摘要: 基于波函数展开法表示柱面波源自由场，首次提出了一种求解柱面波源下管桩屏障对弹性波隔振效应的解析方法。方法首先考虑柱面波源与管桩屏障的位置关系，采用波函数展开法对入射柱面波进行了0阶Hankel展开表示，并采用任意坐标系间变换的Graf加法定理在任意桩体坐标系中表示，将入射波场和散射波场叠加后通过满足所有桩体的边界条件以求解所有桩体的散射波场。该解析方法分析了柱面波源入射下群桩屏障的隔振效果，首次在排桩隔振问题中考虑了入射波曲率的影响，为柱面波的散射问题提供了理论解答。该文重点讨论了入射波曲率、管桩个数和桩排数等因素对管桩隔振效果的影响，结果表明：整体上管桩屏障对柱面P波的隔振效果优于柱面SV波；柱面波源距离管桩屏障更近时排桩后场地的位移反应显著增大；相比平面波，柱面波源作用下排桩数量的提升对隔振效果的影响较小；三排管桩屏障比两排管桩屏障隔振效果更强，更宜采用三排管桩屏障进行柱面波源的隔振。Abstract: Based on the wave function expansion method of expressing the free field of cylindrical wave source, an analytical method for solving the vibration isolation effect of pipe pile barriers on elastic waves under a cylindrical wave source is proposed for the first time. In the method, considering the position relationship between the cylindrical wave source and the pipe pile barrier, the incident cylindrical wave was expressed by the 0-order Hankel expansion using the wave function expansion method, and expressed in any pile coordinate system using Graf addition theorem of transformation between arbitrary coordinate systems. After superposing the incident wave field and the scattered wave field, the scattered wave field of all piles was solved by satisfying the boundary conditions of all piles. The analytical method is used to analyze the vibration isolation effect of pile group barriers under the incidence of cylindrical wave source. The influence of the incident wave curvature is considered in the vibration isolation problem of row piles for the first time, which provides a theoretical solution for the scattering problem of cylindrical waves. The results show that the isolation effect of pipe pile barrier on cylindrical P-waves is generally better than that on cylindrical SV waves; When the cylindrical wave source is closer to the pipe pile barrier, the displacement response of the pile behind the pile increases significantly; Compared with a plane wave source, the number of piles under the action of a cylindrical wave source decreases; The isolation effect of three-row pipe pile barriers is stronger than that of two-row pipe pile barriers, so three-row pipe pile barrier is more suitable for the vibration isolation of a cylindrical wave source.
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图 1 管桩屏障对柱面P波、SV波的散射分析模型
Figure 1. Analysis model of P and SV wave scattering by pipe pile barrier
图 2 任意两个坐标系间的内域Graf加法公式形式
Figure 2. Form of Graf addition formula in internal domain between any two coordinate systems
图 6 柱面P波入射时管桩隔振频谱图
Figure 6. Spectra of pipe pile vibration isolation under cylindrical P-wave incidence
图 7 柱面SV波入射时管桩隔振频谱图
Figure 7. Spectra of pipe pile vibration isolation under cylindrical SV-wave incidence
图 8 柱面P波下不同入射波曲率的位移等值线图
Figure 8. Displacement contour map of different incident wave curvatures under cylindrical P-waves
图 9 柱面SV波下不同入射波曲率的位移等值线图
Figure 9. Displacement contour map of different incident wave curvatures under cylindrical SV-waves
图 10 桩个数对排桩隔振效果影响的位移等值线图
Figure 10. Displacement contour map of influence of pile number on vibration isolation effect of row piles
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