Thus the resistance factor and vibration modes of the soil layer are obtained and used to analysis the pile response . by considering the interaction between the soil layer and the pile with boundary condition of continuity of displacement and equilibrium of force at the interface of soil layer and pile , the dynamic equilibrium equation of pile is solved and an analytical solution for the pile response in frequency domain is yielded , which is used to define complex stiffness and mobility at the level of the pile head . based on the convolution theorem and inverse fourier transform , a semi - analytical solution of velocity response in time - domain subjected to a semi - sine exciting force is given 首先通過(guò)引入勢(shì)函數(shù)方法對(duì)土體位移進(jìn)行分解,從而將土體動(dòng)力平衡方程解耦,求解得到了土層的振動(dòng)模態(tài)和阻抗因子,然后利用該解以小應(yīng)變條件下樁土接觸面上力平衡和位移連續(xù)條件來(lái)考慮樁土耦合作用,求解樁的動(dòng)力平衡方程,得到了樁頂?shù)念l域響應(yīng)解析解、復(fù)剛度和速度導(dǎo)納,利用卷積定理和傅里葉逆變換,求得了半正弦脈沖激振力作用下樁頂速度時(shí)域響應(yīng)半解析解。