Abstract: According to the mechanism of vibratory pile driving and non-linear stress-strain relation of soil, a nonlinear dynamic model for vibratory pile driving was established. In this model, the action of soil to the pile was represented by a soft nonlinear spring and a linear damper. The first approximate solution of the system in primary resonance case was obtained by using the method of multiple scales. Amplitude-frequency characteristic for steady primary resonance of the system was analyzed by selecting appropriate parameters. The initial displacement intervals in which the primary resonance had stable solutions in multi-solution frequency band were determined by using Matlab. Finally, the effects of construction parameters on amplitude-frequency characteristics for the primary resonance were discussed. The results of this research provide guidelines for vibratory pile driving construction.

Key words: vibration and wave, vibratory pile driving, nonlinear, method of multiple scales, primary resonance

摘要： 根据振动沉桩机理，结合土壤的非线性应力―应变关系，提出把土壤对桩的作用看作一个软式非线性弹簧和一个线性阻尼器。建立振动沉桩非线性动力学模型，利用多尺度法得到系统主共振情况下的一次近似解。选取适当的参数，分析系统稳态主共振幅频特性，并且借助Matlab确定主共振在多解频带上取稳定解的初始位移区间。最后讨论施工参数变化对主共振幅频特性的影响。研究结果对振动沉桩的现场施工具有指导作用。

关键词: 振动与波, 振动沉桩, 非线性, 多尺度法, 主共振