粘弹性桩的混沌运动分析

研究了在轴向载荷和周期性横向载荷共同作用下非线性粘弹性嵌岩桩的混沌运动情况。假定桩和土体分别满足Leaderman非线性粘弹性和线性粘弹性本构关系，得到的运动方程为非线性偏微分．积分方程；利用Galerkin方法将方程简化为非线性常微分一积分方程，同时利用非线性动力系统中的数值方法，进行了数值计算，得到了不同载荷参数、几何参数、材料参数时粘弹性桩发生周期运动、多周期运动及混沌运动的时程曲线、相图、功率谱、Poincare截面图，同时得到了挠度-载荷、挠度-几何参数、挠度-材料参数等分叉图，考察了各种参数的影响。数值结果表明非线性粘弹性桩在一定的条件下可以通过倍周期分叉的方式进入混沌运动状态，且桩的载荷参数、几何参数、材料参数对其运动状态有较大的影响。

Analysis of Chaotic Motion on Piles with Nonlinear Viscoelastic Materials

The chaotic motion of a nonlinear viscoelastic rigid basic pile subjected to an axial force and a periodic horizontal force was investigated. Assume that the pile material is one of nonlinear viscoelastic materials and obeys Leaderman constitutive relation and that the soil obeys the linear viscoelastic constitutive relation. The motion equation of pile was derived as a nonlinear integro-partial differential equation and it was simplified into a nonlinear integro-ordinary differential equation by Galerkin method. The numerical results were presented by using the methods in nonlinear dynamic systems. Time history curves, power spectrum figures, phase plane portraits, Poincare maps for the periodic motion, multi-periodic motion and chaotic motion of the pile as well as different bifurcation plots were given. The numerical results indicate that the chaotic motion will appear through period double bifurcation in nonlinear viscoelastic piles and the influence of the material parameter, the load parameter, the geometric parameter on the dynamic behavior of the pile is obvious.