非连续弹性圆柱实心桩屏障对弹性波的隔离

Discontinuous barrier used a row of elastic piles for incident elastic waves

采用波函数展开法和Graf加法定理,根据桩土界面处位移和应力连续的边界条件,得到了非连续弹性圆柱实心桩屏障对入射平面P波和SH波散射系数的理论解,通过引入无量纲位移,即屏障后某处土体内由入射波和散射波引起的总的纵向位移和水平位移与未设屏障时由入射平面P波和SH波在该处土体内单独引起的位移幅值的比值,根据求得的散射系数的理论解,绘制了平面P波和SH波单独入射情况下,弹性圆柱实心桩屏障后不同位置的无量纲位移、不同剪切模量的弹性圆柱实心桩屏障后的无量纲位移等值线和透射系数随桩间距的变化曲线,通过研究这些图件进而分析了屏障后不同位置、剪切模量、桩间距和入射频率对非连续弹性圆柱实心桩屏障的隔离效果的影响,为非连续弹性屏障的隔振设计提供了理论依据。

The expansion method of wave functions and Graf addition theorem were adopted, the displacements and stresses were considered as continuous boundary of elastic piles and soils, and a theoretical solution of scattering coefficients for incident plane P wave and SH wave by the barrier of a row of elastic piles was obtained. The normalized longitudinal and horizontal displacements were introduced, which are the ratio of total longitudinal and horizontal displacement amplitudes of soils behind the barrier caused by the incident wave and scattered wave to the displacement amplitude of soils at the same place only caused by incident P wave or SH wave, the normalized longitudinal and horizontal displacements at different places behind the barrier of elastic piles, the contours of the normalized longitudinal and horizontal displacements behind the harrier of elastic piles with different shear modulus, the curves of transmissibility index changing with the distance between the piles were drawn according to the theoretical solutions and their trends were studied. The influences of the distance between the elastic piles, shear modulus of elastic piles, different places behind the barrier and normalized frequencies on the isolation effect of the barrier for incident P wave and SH wave were analyzed, which provides a theoretical basis for the design of discontinuous barrier for vibration isolation.