Semi-analytical solution for vibration of pile with variable section in layered soil

Assuming that pile is an elastic member and soil represented by a series of vertical springs and dashpots, the mathematical model of vibration of pile with several various sections is established taking account of pile and layered-soil interaction. Using the method of integral transform, semi-analytical solution for a pile response under exciting force in the head of pile is gained. The expression of the pile top response when subjected to transient force is given, and the effects of exciting force and degree of variable section on the pile top velocity response are studied respectively.