软式非线性同步振动沉桩系统的动力学分析
Dynamic Analysis of a Flexible Nonlinear Synchronous Vibration Pile System

对软式非线性同步振动沉桩系统进行动力学特性研究。首先，建立同步振动沉桩系统的软式非线性振动模型，采用一次近似解的幅频特性方程判定系统周期解稳定性问题；然后，利用选取的参数分析系统幅频特性关系，并且根据幅频特性曲线确定系统多解处的稳定解问题，以及讨论沉桩系统参数(激振频率、土的刚度和阻尼、激振器的偏心距等)对系统动力学特性的影响；最后，基于Matlab/Simulink采用四阶龙格 库塔法运算程序进行数值仿真确定系统周期解稳定性。通过理论和仿真系统地分析了系统周期解的稳定性特性，以及系统各参数对系统周期解的影响。
The dynamic characteristics of the flexible nonlinear synchronous vibration pile system were studied. The nonlinear dynamic models of the system were proposed to analyze the nonlinear stiffness of the soil, which were induced by the relationship between the nonlinear stress and the strain in the soil. The periodic solutions of the system were investigated using Lyapunov function of the amplitude-frequency characteristic equation for the nonlinear models. The amplitude-frequency characteristics were analyzed through the selected parameters. The dynamic characteristics of the system were presented for the changes of system parameters (including the vibrating frequency, the stiffness of the soil and the damping of the soil, the radius of the eccentric block), which are induced by the amplitude-frequency characteristics. Finally, the stable solution of multiple periodic solutions can be obtained by the different initial conditions, using Runge-Kutta method. The stability of periodic solutions was theoretically analyzed by theory and verified by simulation, and the influence of different parameters on the periodic solution was presented.