A quasi-analytical solution to longitudinal vibration of pile with variable sections and its application

The vibration problem of finite length pile with any variable sections under exciting force is developed,in which the influence of the soil under pile toe and surrounding pile is taken into account.With Laplace transform,the transmit functions of a pile about velocity and displacement are derived.Then,by means of Fourier transform,a quasi analytical solution for the velocity response of pile subjected to a semi sine wave exciting force is developed.Based on the solution,the vibrant properties of pile with sharp reduced or expanded section or continuous variable sections are studied.