基于复模态法的粘弹性基桩横向振动研究

Research on Lateral Free Vibration of Viscoelastic Piles by Complex Model Method

假定基桩及桩周土材料满足非线性弹性和线性粘弹性本构关系,导出了分析基桩线性横向振动的非线性偏微分方程。在假设基桩和土的非线性比较弱的情况下,忽略非线性因素影响,用复模态法得到了一端铰支、另一端轴向自由横向铰支的端部条件下方程的解析解,并给出了数值算例,考察了参数的影响。结果表明:粘性系统的频率随着桩周土刚度增大而非线性增大,随着桩顶静载荷的增大而减少,静止桩是振动桩的一种特殊形式,桩周土的存在大大增加了基桩的承载力,土抗力调整系数对基桩承载力的影响也较大,硬土比软土更能提高基桩的承载力。

Assuming that the materials of the pile and the soil around the pile comply with nonlinear viscoelastic constitutive relation,the partial differential equation governing the lateral vibration of piles was firstly derived.In the case that the viscous characters of materials of the pile and the soil are weak without consideration of nonlinear factors,the exact solution of the equation has been obtained,with boundary condition of one end fixed,the other free in axial direction and hinged support in lateral direction,by the complex model method.Numerical example is given.As a result,it is found that the bigger the rigidity of soil,the bigger the natural frequency of pile;and that the bigger the load on the top of pile,the smaller the natural frequency of pile.The bearing capacity is largely improved because of the existence of soil around pile,the hard soil is more effectively improving the bearing capacity of pile than the soft soil.