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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

赵凤群, 张瑞平, 王小侠. 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[J]. 机械科学与技术, 2016, 35(10): 1520-1524. doi: 10.13433/j.cnki.1003-8728.2016.1008
引用本文: 赵凤群, 张瑞平, 王小侠. 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[J]. 机械科学与技术, 2016, 35(10): 1520-1524. doi: 10.13433/j.cnki.1003-8728.2016.1008
Zhao Fengqun, Zhang Ruiping, Wang Xiaoxia. Dynamic Response Analysis of Variable Thickness Rectangular Plates on Viscoelastic Foundation with Fractional Derivative[J]. Mechanical Science and Technology for Aerospace Engineering, 2016, 35(10): 1520-1524. doi: 10.13433/j.cnki.1003-8728.2016.1008
Citation: Zhao Fengqun, Zhang Ruiping, Wang Xiaoxia. Dynamic Response Analysis of Variable Thickness Rectangular Plates on Viscoelastic Foundation with Fractional Derivative[J]. Mechanical Science and Technology for Aerospace Engineering, 2016, 35(10): 1520-1524. 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
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

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

  • 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。
  • [1] Mansfield E H. On the analysis of elastic plates of variable thickness[J]. The Quarterly Journal of Mechanics & Applied Mathematics, 1962,15(2):167-192
    [2] Alipour M M, Shariyat M. Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations[J]. Mechanics Research Communications, 2011,38(8):594-601
    [3] Hosseini-Hashemi Sh, Taher H R D, Akhavan H. Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations[J]. Composite Structures, 2010,92(7):1734-1743
    [4] 滕兆春,丁树声,郑鹏君.弹性地基上变厚度矩形板自由振动的GDQ法求解[J].应用力学学报,2014,31(2):236-242 Teng Z C, Ding S S, Zheng P J. Free vibration analysis of rectangular plates with variable thickness on elastic foundation by using GDQ method[J]. Chinese Journal of Applied Mechanics, 2014,31(2):236-242(in Chinese)
    [5] 杨柳,彭建设,谢刚,等.Winkler地基上变厚度矩形板弯曲的微分求积解[J].成都大学学报(自然科学版),2011,30(2):131-133 YANG L, PENG J S, XIE G, et al. Differential quadrature solutions for bending problem of rectangular plates with variable thickness on Winkler foundation[J]. Journal of Chengdu University (Natural Science Edition), 2011,30(2):131-133(in Chinese)
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    [10] Meral F C, Royston T J, Magin R. Fractional calculus in viscoelasticity:an experimental study[J]. Communications in Nonlinear Science and Numerical Simulation, 2010,15(4):939-945
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    [12] 寇磊.分数阶微分型双参数黏弹性地基矩形板受荷响应[J].力学季刊,2013,34(1):154-160 Kou L. Response of rectangular plate on fractional derivative two-parameter viscoelastic foundation[J]. Chinese Quarterly of Mechanics, 2013,34(1):154-160(in Chinese)
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    [14] 王苗苗,赵凤群,李娜,等.分数阶微分方程的Haar小波算法研究[J].计算力学学报,2013,30(1):156-160 Wang M M, Zhao F Q, Li N, et al. Study on the Haar wavelet algorithm of fractional differential equations[J]. Chinese Journal of Computational Mechanics, 2013,30(1):156-160(in Chinese)
    [15] Li Y L, Zhao W W. Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations[J]. Applied Mathematics and Computation, 2010,216(8):2276-2285
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出版历程
  • 收稿日期:  2014-10-10
  • 刊出日期:  2016-10-05

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