三维半空间中竖向集中力与膨胀点源的动力格林函数  

Dynamic Green's function of concentrated vertical load and dilatational point source in 3-D half-space

作　　者：刘玉桥[1] 张海[1,2] 张岳文[3] 

机构地区：[1]天津城市建设学院天津市软土特性与工程环境重点实验室,天津300384 [2]天津大学建筑工程学院,天津300072 [3]河北工程大学土木工程学院,河北邯郸056038

出　　处：《世界地震工程》2009年第3期81-85,共5页World Earthquake Engineering

基　　金：国家自然科学基金项目(50378063);教育部博士点基金项目(20070056120)

摘　　要：通过积分变换的方法,引入三维轴对称情况时的势函数,首先推导了全空间中竖向集中力的动力格林函数,然后给出了半空间作用地表竖向集中力的动力格林函数,对半空间中埋置竖向集中力和膨胀点源,通过在地表上方对称位置虚拟一个同样大小的集中力或膨胀点源,消除地表剪应力,把残余地表正应力反加到半空间上,给出了频域内三维弹性半空间中埋置竖向集中力和埋置膨胀点源的动力格林函数。数值结果表明:随着位置远离荷载作用点,动力响应衰减明显,另外随着激励频率的增大,动力响应随空间变化更为复杂。Through introducing the axisymmetric potential function and the method of integral transformation, the dynamic Green＇ s function of the concentrated vertical force in the whole three-dimensional space is derived firstly, and secondly, the Green＇ s function of the concentrated vertical force acting on the surface of the three-dimensional half-space is given. For the Green＇ s function of concentrated vertical force and a dilatational point source embed- ded in the three-dimensional half-space, the virtual concentrated vertical force or the dilatational point source is in- troduced, and this leads to non-shear stress and a reduced vertical stress, and then the Green＇ s function of the concentrated vertical force and the dilatational point source is given by acting the minus reduced vertical stress on the half-space. The numerical results show that responses are attenuated as increasing distance, and the responses become more complex as increasing the exciting frequency.

关 键 词：动力格林函数 集中力 膨胀点源 半空间 

分 类 号：TB123[理学—工程力学] TU435[理学—力学]