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本文首先求出桩长有限、桩端为弹性支承时，考虑桩侧土作用，桩顶受稳态正弦激振条件下，基桩纵向振动问题的解析解；其次利用迭加原理求得了瞬态半正弦激振条件下的解析解；然后对所得解进行了研究分析，得到了许多重要结论。最后，将瞬态激振条件下得到的理论曲线与反射波法测得的实际曲线进行了拟合对比，结果表明两者吻合很好。
In this paper, firstly, the analytical solution to the longitudinal vibration problem of the pile under the condition of sinusoidal excitation under steady state is considered when the pile length is finite and the pile end is elastically supported. The superposition principle is used to obtain the transient state. Analytical solution under semi-sine-wave excitation conditions; then the resulting solution was studied and analyzed, and many important conclusions were obtained. Finally, the theoretical curves obtained under the transient excitation conditions are compared with the actual curves measured by the reflected wave method. The results show that the two are in good agreement.