单排弹性实心桩对SH波的散射求解问题

An approach for solving the scattering of SH waves by elastic solid piles in one row

采用波函数展开法结合格拉夫加法定理分析单排实心弹性桩的SH波散射问题,通过改变单一变量,分析桩土剪切模量之比、桩体个数等因素对排桩隔振的影响效果,得到如下结论:当无量纲频率为低频和中频时,排桩后无量纲位移曲线在无限远处趋于0,随着桩体根数的增加隔振效果逐渐提高;在排桩后0~70 a(a为桩径)范围内无量纲位移之比变化幅度较大,且不稳定,隔振效果较差;当桩土剪切模量之比小于500时,在250a~380a范围内减隔振效果较好;当桩土剪切模量之比大于或等于500时,隔振效果并不会随着其增加而大幅增加,即此时可将桩体认为是刚性桩体。当无量纲频率为中频时,在100a~120a范围内隔振效果较好,之后此范围内无量纲位移之比先骤升后逐渐下降,但当无量纲频率上升为高频时,各桩体根数下排桩隔振效果相差不大,且会在距离排桩更近处就已经达到很好的隔振效果。

The scattering issue of shear horizontal(SH)waves from solid elastic piles in a single row was analyzed using the wave function expansion technique and Graf's addition theorem.By changing a single variable,we analyzed the effects of the pile-soil shear modulus ratio and the number of piles on the vibration isolation capabilities of row piles.Our results show that when dimensionless frequency is low to medium,the dimensionless displacement curve beyond the row piles tends to zero at infinity.As the number of piles increases,the vibration isolation effect also gradually improves.However,the ratio of dimensionless displacement changes greatly in the range of 0-70 a following the piles,leading to unstable and poor vibration isolation performance.When the pile-soil shear modulus ratio is less than 500,the vibration isolation effect within the range of 250 a-380 a proves to be satisfactory.Conversely,when the pile-soil shear modulus ratio is equal to or exceeds 500,there is no substantial increase in the vibration isolation effect.This suggests that the pile can be regarded as a rigid pile at this time.In instances of medium dimensionless frequency,the vibration isolation effect performs well within the 100 a-120 a range.The ratio of dimensionless displacement in this range experiences a sudden increase before gradually decreasing.However,as the dimensionless frequency escalates to high frequencies,the vibration isolation effect shows minor variation with different numbers and exhibits good performance close to the row piles.