分数阶微分型黏弹性地基上变厚度矩形板的动力响应分析

赵凤群; 张瑞平; 王小侠

doi:10.13433/j.cnki.1003-8728.2016.1008

分数阶微分型黏弹性地基上变厚度矩形板的动力响应分析

doi: 10.13433/j.cnki.1003-8728.2016.1008

1.
西安理工大学理学院, 西安 710054

基金项目:

陕西省自然科学资金项目（2011JM1013）与陕西科学技术攻关项目（2015GY004）资助

详细信息

作者简介:
赵凤群(1963-),教授,博士,研究方向为动力系统振动与稳定性研究,微分方程数值解及其应用研究,zhaofq@xaut.edu.cn

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- 被引次数: 0
出版历程
- 收稿日期: 2014-10-10
- 刊出日期: 2016-10-05

Dynamic Response Analysis of Variable Thickness Rectangular Plates on Viscoelastic Foundation with Fractional Derivative

1.
School of Sciences, Xi'an University of Technology, Xi'an 710054, China

摘要

摘要: 研究了黏弹性地基上变厚度矩形薄板的动力响应。采用分数阶微分的Kelvin-voigt模型描述地基的黏弹性特征，基于弹性板的基本假设，对于小变形问题，建立了黏弹性地基上变厚度矩形薄板的动力控制微分方程。针对该分数阶变系数偏微分方程，采用Galerkin法和Haar小波配点法进行数值求解。分析了四边简支板的动力响应特性，得到了均布载荷作用下线性模型、抛物线模型板中心挠度曲线，讨论了变厚度矩形板的厚度比、长宽比、分数阶导数的阶数、地基弹簧系数、粘滞系数、水平剪切系数等参数变化对板动力特性的影响。
- 变厚度矩形板 /
- 黏弹性地基 /
- 动力响应 /
- 分数阶微分方程 /
- Haar小波法
Abstract: This paper analyzes the dynamic response of a variable thickness rectangular thin plate on a viscoelastic foundation. The viscoelastic characteristic of the foundation is described with Kelvin-Voigt model with fractional order differential. The governing differential equation of variable thickness rectangular plate on a viscoelastic foundation is established based on the basic hypothesis of elastic plate. The numerical solution of the fractional order differential equation with variable coefficient is obtained with the Galerkin method and the Haar wavelet collocation method. The dynamic response characteristics of the simply supported plate are analyzed, and the central deflection curves of linear model and the parabola model plate under uniform loading are obtained. The influences of length-width ratio and thickness ratio of the rectangular variable thickness plate, and the fractional order, spring coefficient, viscosity coefficient and horizontal shear parameter of the foundation on the dynamic characteristics of the plate are discussed.
- variable thickness rectangular plate /
- viscoelastic foundation /
- dynamic response /
- fractional differential equation /
- Haar wavelet method

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参考文献(15)

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