空沟对平面纵波隔离效果的理论解答

发布时间：2018-11-04 15:46

【摘要】：借助复变函数的保角变换法将有限长度的空沟映射变换为单位圆,根据空沟四周完全自由的边界条件,运用波动函数展开法得到了空沟对纵波(P波)和剪切波(SV波)隔离的理论解答。引入位移比值(屏障后某点由入射波波、散射波产生的总位移与入射波单独产生的位移之比),以入射P波为例,计算了沟宽0.4 m、沟长分别为3.0 m、4.0 m、5.0 m和6.0 m共4条空沟的位移比值,通过比较发现:随着空沟长度的增加,最佳隔振效果明显提高,区域明显增大;当空沟长度达到6.0 m时,靠近空沟的区域的隔振效果超过了70%,隔振效果比较理想。最后对比了空沟和单排柱腔列的隔振效果,结果表明:由于单排柱腔列产生波的透射和绕射,而空沟仅产生波的绕射,6.0 m长空沟的最佳隔振效果与8根半径1.0 m的单排柱腔列相当,因此在场地和施工条件都允许的前提下,宜优先考虑空沟进行隔振。
[Abstract]:With the aid of conformal transformation of complex functions, the finite length gap mapping is transformed into a unit circle, and according to the boundary conditions of complete freedom around the gully, By using wave function expansion method, the theoretical solutions for the separation of P-wave (P-wave) and shearing wave (SV wave) are obtained. The displacement ratio (the ratio of the total displacement produced by the incident wave, the total displacement produced by the scattering wave to the displacement produced by the incident wave alone) at a certain point behind the barrier is introduced. Taking the incident P wave as an example, the width of the channel is 0.4 m, and the length of the ditch is 3.0 mL 4.0 m, respectively. The displacement ratio of 4 empty trenches of 5.0 m and 6.0 m is compared. It is found that with the increase of gap length, the best isolation effect is obviously improved, and the region is obviously increased. When the length of the gully reaches 6.0 m, the isolation effect of the area near the gully is more than 70, and the isolation effect is ideal. The results show that the single row cylindrical cavity train produces wave transmission and diffraction, while the hollow channel only produces wave diffraction. The optimum isolation effect of 6.0m long gully is equivalent to that of 8 single-row cylindrical cavities with a radius of 1.0 m. Therefore, under the condition of site and construction conditions, priority should be given to isolating vibration by emptying ditch.
【作者单位】：郑州大学水利与环境学院;
【基金】：国家自然科学基金(51278467) 河南省高校科技创新人才支持计划(14HASTIT050)
【分类号】：TU435

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