粘弹性地基中有限长桩横向受迫振动问题解析解

基于动力Winkler模型(BDWF)对粘弹性地基中有限长桩的动力响应进行求解，得到了其在桩顶受水平循环荷载作用下的简单形式的时域解析解。通过迭加原理得到了半正弦激振条件下的瞬态解析解，经过简单的数学运算得到了桩头动力阻抗系数。通过对稳态激振时幅频曲线和相频曲线的分析，讨论了桩侧土阻尼系数和刚度系数对共振频率和共振峰值的影响规律。并讨论了桩底边界条件对水平动力响应的影响。本文为单桩的动力分析提供了一种简单的解析分析方法，可为工程设计提供初步参考。

An analytical solution for lateral vibration of a pile with finite length pile in viscoelastic subgrade

The Beam-on-Dynamic-Winkler-Foundation (BDWF) model was utilized to determine the lateral dynamic response of a pile with finite length in a viscoelastic subgrade. An analytical solution was obtained with the simple form in the time domain for a laterally cyclic force applied at the pile head. Based on the solution, the transient response of the pile loaded by semi-sine force was acquired with superposition principle. At the same time, the dynamic impedance parameters at the head of pile were also obtained through some straightforward algebra. Then by the analysis of the amplitude-frequency and phase-frequency curves for the steady-state motion, the influence of dimensionless stiffness coefficient and damp coefficient on resonance frequency and peak values during the resonance was mvestigated. Finally, the influence of tip conditions of pile on the lateral dynamic response was also discussed. The theory developed herein presents an analytical method for the dynamic analysis of a single pile and may be used as a preliminary reference in engineering design.