基于多时间尺度法的桩基轴向振动分析研究  

Analysis on Axial Vibration of Piles by Multiscale Time Method

作　　者：刘民[1] 陈中学[2] 胡春林[3] 

机构地区：[1]三峡大学机械与材料学院,宜昌443002 [2]中国科学院武汉岩土力学所,武汉430071 [3]武汉理工大学土木工程与建筑学院,武汉430070

出　　处：《长江科学院院报》2009年第12期102-105,共4页Journal of Changjiang River Scientific Research Institute

摘　　要：假定桩基及桩周土的材料满足粘弹性本构关系,导出了分析粘弹性桩基轴向振动的偏微分方程。在桩基和土的粘性都比较弱的情况下,用四阶多时间尺度方法求解了边界条件为一端固定、另一端自由的粘弹性桩基轴向自由振动的n阶固有频率和振动位移的近似表达式,得到:n阶固有频率是粘弹性阻尼、阶数n和桩周土刚度系数的函数;位移与初始位移、相位、固有频率、时间、桩身位置、阻尼系数等有关;将四阶多时间尺度近似解与精确解进行了对比发现,当阻尼比小于0.76时,四阶多时间尺度解与精确解误差很小(小于3%),因此,只要使用较高的阶数,在较低的阻尼比情况下,用多时间尺度法求得的近似解与精确解误差不大,可以用于分析粘弹性桩基轴向振动。On the assumption that the materials of the pile and the soil around the pile comply with visco-elastic constitutive relation, the partial differential equation governing the axial vibration of piles is first derived. In the case that the viscous characters of materials of the pile and the soil are weak, the approximate expressions of the nthorder natural frequency and the vibration displacement are obtained with boundary condition of one end fixed and the other free by the multiscale time analysis method. As a result, it is found that： the nth-order natural frequency is the function of damp, stiffness coefficient of soil around pile ; displacement relates to initial displacement, natural frequency, time, pile body position and damp coefficient. In comparison the 4th-order multiscale approximate solu- tion with exact solution, the error between approximate solution and exact solution is very small （only 3 % ） when damping ratio is less than 0.76. Therefore, under the conditions of higher exponent number and lower damping ratio, multiscale approximate solution is very near to the exact solution, multiscale method can be used for analysing the vibration of viscoelastic pile.

关 键 词：粘弹性桩 轴向自由振动 固有频率 多时间尺度法 

分 类 号：TU473.16[建筑科学—结构工程]