分数导数型粘弹性地基上矩形板的受荷响应  

Response of a Loaded Rectangular Plate on Fractional Derivative Viscoelastic Foundation

作　　者：朱鸿鹄[1] 刘林超[2] 叶肖伟[3] 

机构地区：[1]南京大学地球科学与工程学院,江苏南京210093 [2]信阳师范学院土木工程学院,河南信阳464000 [3]香港理工大学土木及结构工程学系

出　　处：《应用基础与工程科学学报》2011年第2期271-278,共8页Journal of Basic Science and Engineering

基　　金：国家重点基础研究发展计划("973"计划)资助(2011CB710605)

摘　　要：地基上板的受荷变形性状通常具有明显的时间效应.本文采用一种分数导数型Kelvin模型,对粘弹性地基上均匀受荷的矩形板进行准静态分析.根据弹性-粘弹性对应原理,通过拉普拉斯变换将该问题的弹性解推广到以M ittag-Leffler函数表示的分数导数型粘弹性解.算例的分析结果表明,分数导数型粘弹性模型具有比经典粘弹性模型更好的适用性.通过参数分析研究了该模型的参数对地基板挠度-时间关系的影响.结果表明,通过调整粘滞系数和分数阶的取值,地基上板的时效性变形可以用分数导数型Kelvin模型精确模拟.Deformation of a loaded plate on soil foundation will normally exhibit considerable time-dependent behaviour.In this paper,a fractional derivative Kelvin model is proposed to study the quasi-static problem of a rectangular plate rested on a viscoelastic foundation,which is subjected to uniform distributed loads.According to the correspondence principle of elasticity and visco-elasticity,the elastic solution of this problem is extended to the fractional derivative viscoelastic solution in terms of the Mittag-Leffler function using Laplase transform.The study of an example indicates that the fractional derivative visco-elastic model is more adaptive than the classical viscoelastic model.The influence of the model parameters on the plate deflection-time relationship is studied through a parametric study.The analysis results indicate that the time-dependent deformation of the plate can be accurately captured by varying values of the fractional order of differential operator and the coefficient of viscosity.

关 键 词：粘弹性地基 分数导数 KELVIN模型 地基板 拉普拉斯变换 

分 类 号：O343[理学—固体力学] TU433[理学—力学]