【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。更多还原

【Abstract】 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 nth-order 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 solution 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.更多还原