CAJ | 학술논문

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。
연구료지진작용하비선성지기중장기적3차초해파공진문제。종지기장중추상출역학모형，고필지기적비선성인소，운용 Hamilton 변분원리건립료장기적비선성공제방정。이용 Galerkin 방법리산상술방정，기우다척도섭동법연구료지진작용하비선성지기중장적3차초해파공진문제。이모감암원형장위례，연구료지기토층후도、전절파속도급빈솔비대지진력적영향，수치모의료비선성지기장적3차초해파공진향응，탐토료지진력、지기탄성급비탄성계수대초해파폭빈향응적영향，최후연구장기산생3차초해파공진시적시간역정곡선。결과표명，당지진파빈솔약등우장기고유빈솔적1／3시，용역격발장적3차초해파공진향응；장기적3차초해파공진향응수착지진력、비탄성계수적증대이변득경가현저，수착탄성계수적증대이축점변소。
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.