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] 闫启方[2] 

机构地区：[1]上海市应用数学和力学研究所,上海200444 [2]信阳师范学院建筑工程系,河南信阳464000

出　　处：《噪声与振动控制》2009年第4期27-30,共4页Noise and Vibration Control

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,必须建立准确的本构模型。在分数导数理论、粘弹性理论、应力波理论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。Research results indicated that concrete piles have viscoelastic properties. In order to accurately analyze dynamic properties of viscoelastic piles, an accurate constitutive model is established in this paper. The dynamic governing equations for viscoelastic piles based on the fractional derivative model with viscoelastic theory and stress wave theory are established. The Zhang-Shimizu numerical integration method of fractional derivative is employed for the numerical solution of the governing equations. Result indicates that the order of fractional dervative operator and the viscosity-to-elasticity ratio have great influence on the speed of decay and period of attenuation of the pile＇s end.

关 键 词：振动与波 分数导数 粘弹性 应力波 数值积分 

分 类 号：O317[理学—一般力学与力学基础]