地震作用下桩基的1/3次亚谐波共振分析

建立了均匀地基下桩基础的非线性运动方程。运用Galerkin方法对运动方程进行一阶模态截断,得到离散的非线性振动方程。利用多尺度法求得该系统1/3次亚谐波共振的一阶近似解。分析了频率比、剪切波速度及土层厚度等参数对地震惯性力和亚谐波共振幅频响应的影响,并通过与非共振硬激励情况对比分析1/3次亚谐波共振对系统实际动力反应的影响。研究结果表明:在软弱土层中,剪切波速度及土层厚度对地震惯性力影响显著;1/3次亚谐波共振区域对外激励幅值敏感;阻尼大于一定值后,系统将不出现1/3次亚谐波共振响应;1/3次亚谐波共振显著增大系统稳态动力响应位移。

1/3 sub-harmonic response analysis of Pile Foundation under earthquake action

The nonlinear vibration of piles in uniform foundation under horizontal earthquake action is investigated in the present paper. Based on the established nonlinear equations of motion of pile foundation under horizontal earthquake action, the approximate solution of piles for the case of the 1/3 sub-harmonic resonance is obtained by using the Galerkin method and the multi-scale method. To illustrate the characteristics of the 1/3 sub-harmonic resonance, the effects of the frequency ratio, the shear wave velocity, the soil thickness and damping coefficient on the frequency-response curves of the pile in uniform foundation are studied. The effect of the 1/3 sub-harmonic resonance on the actual dynamic response of this system is analyzed with the contrast to the non-resonant situation. The numerical results show that Shear wave velocity and soil thickness have significant effect on the seismic inertia force; the excitation amplitude has significant impact on the 1/3 sub-harmonic resonance region; the resonance of the pile on elastic foundation will not appear when the damping coefficient is greater than a certain value; the 1/3 sub-harmonic resonance significantly increases the displacement of the stationary response.