摘要
研究了地震作用下非线性地基中桩基的3次超谐波共振问题.从地基桩中抽象出力学模型,考虑地基的非线性因素,运用Hamilton变分原理建立了桩基的非线性控制方程.利用Galerkin方法离散上述方程,基于多尺度摄动法研究了地震作用下非线性地基中桩的3次超谐波共振问题.以某嵌岩圆形桩为例,研究了地基土层厚度、剪切波速度及频率比对地震力的影响,数值模拟了非线性地基桩的3次超谐波共振响应,探讨了地震力、地基弹性及非弹性系数对超谐波幅频响应的影响,最后研究桩基产生3次超谐波共振时的时间历程曲线.结果表明,当地震波频率约等于桩基固有频率的1/3时,容易激发桩的3次超谐波共振响应;桩基的3次超谐波共振响应随着地震力、非弹性系数的增大而变得更加显著,随着弹性系数的增大而逐渐变小.
The 3 super-harmonic response of pile foundation under earthquake action was investigated. Based on Hamilton Variational Principle, the nonlinear equations of motion on pile under earthquake action were estab- lished. Then the Galerkin method was used to discrete the governing equation. The 3 super-harmonic response of pile was studied by using the multi-scale method. The effects of the soil thickness, the shear wave velocity and the frequency ratio on the seismic force were studied, and the effects of the seismic force, elasticity coefficient and inelasticity coefficient on the frequency-response curves were studied. The results are as follows： the 3 super- harmonic resonance may be excited when the earthquake frequency and the pile frequency are in an almost 1：3 ratio, the 3 super-harmonic responses of pile increase with the increase of seismic force and non-elastic coeffi- cient, but decrease with the increase of elastic coefficient.
出处
《动力学与控制学报》
2015年第4期278-282,共5页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(51378220)~~
关键词
桩
地震力
非线性地基
3次超谐波
pile, earthquake action, nonlinear foundation, 3rd super harmonic resonance
