基于分数导数模型的粘弹性桩振动分析  

Dynamic Analysis of Viscoelastic Piles Based on Fractional Derivative Model

作　　者：刘林超[1] 杨骁[2] 

机构地区：[1]上海市应用数学和力学研究所,上海200072 [2]上海大学土木工程系,上海200072

出　　处：《应用基础与工程科学学报》2009年第2期303-308,共6页Journal of Basic Science and Engineering

基　　金：上海市重点学科建设项目(Y0103)资助;上海市自然科学基金(06ZR14037)

摘　　要：研究成果表明混凝土桩具有粘弹性性质,为了准确分析粘弹性桩的振动特性,必须建立准确的粘弹性本构模型.在分数导数理论、粘弹性理论、应力波理论的基础上建立了基于分数导数模型的粘弹性桩的振动方程,利用Zhang-Shimizu分数导数数值积分法得到了基于分数导数模型的粘弹性桩的振动方程数值解.分析结果表明,分数导数微分算子的阶数和粘弹比对粘弹性桩桩端速度衰减的快慢和衰减周期等有很大的影响.The results show that concrete piles have viscoelastic properties. In order to analyze the vibration characteristics, we must establish the constitutive model exactly. The dynamic equation of viscoelastic piles described by fractional derivative model was developed by fractional derivative theory, viscolestic theory and stress wave theory, and the numerical solution was obtained by using Zhang-Shimizu fractional derivative numerical integration method. Result indicated that the order of fractional derivative operator and visco-elastic ratio had great influence on the speed and period of attenuation of pile＇ s velocity.

关 键 词：分数导数 粘弹性 应力波 数值积分 

分 类 号：TU459[建筑科学—岩土工程]