具有分数导数型本构关系的粘弹性柱的动力稳定性

李根国; 朱正佑; 程昌钧

具有分数导数型本构关系的粘弹性柱的动力稳定性

李根国^1,2,
朱正佑^1,2,
程昌钧^1,3

1.
上海市应用数学和力学研究所, 上海 200072;
2.
上海大学(嘉定校区)数学系, 上海 201800;
3.
上海大学力学系, 上海 200072

基金项目: 国家自然科学基金资助项目(19772027);上海市科学技术发展基金(98JC14032);上海市教委发展基金资助项目(99A01)

详细信息

作者简介:
李根国(1969- ),男,甘肃古浪人,博士;朱正佑(1937- ),男,浙江海盐人,教授,博士生导师.

中图分类号: O165.6;O345
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- 被引次数: 0
出版历程
- 收稿日期: 2000-01-25
- 修回日期: 2000-12-19
- 刊出日期: 2001-03-15

Dynamical Stability of Viscoelastic Column With Fractional Derivative Constitutive Relation

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China;
2.
Department of Mathematics, Shanghai University, Shanghai 201800, P R China;
3.
Department of mechanics, Shanghai University, Shanghai 200072, P R China

摘要

摘要: 研究简支的受轴向周期激励的粘弹性柱动力稳定性,柱的材料满足分数导数型本构关系.建立了描述粘弹性柱动力学行为的弱奇异性Volterra积分-偏微分方程,利用Galerkin方法将其化归为弱奇异性Volterra积分-常微分方程.利用平均化方法的思想给出了粘弹性柱运动稳定状态的存在性条件.给出一种新的计算方法,克服了存储整个响应历史数据的困难,并给出了数值算例,计算结果与解析方法的结论比较吻合.
- 粘弹性柱 /
- 分数导数型本构关系 /
- 平均化方法 /
- 弱奇异性Volterra积分-微分方程 /
- 动力稳定性
Abstract: The dynamic stability of simple supported viscoelastic column,subjected to a periodic axial force,is investigated.The viscoelastic material was assumed to obey the fractional derivative constitutive relation.The governing equation of motion was derived as a weakly singular Volterra integro- partial-differential equation,and it was simplified into a weakly singular Volterra integro-ordinary-di-f ferential equation by the Galerkin method.In terms of the averaging method,the dynamical stability was analyzed.A new numerical method is proposed to avoid storing all history data.Numerical examples are presented and the numerical results agree with the analytical ones.
- viscoelastic column /
- fractional derivative constitutive relation /
- averaging method /
- weakly singular Volterra integro-differential equation /
- dynamical stability

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参考文献(10)

[1]	Cederbaum G,Mond M.Stability properties of a viscoelastic column under a periodic force[J].J Appl Mech,1992,59(16):16-19.
[2]	程昌钧,张能辉.粘弹性矩形板的混沌与超混沌行为[J].力学学报,1998,30(6):690-699.
[3]	Bagley R L,Torvik P J.Fractional calculus——a different approach to the analysis of viscoelastically damped structures[J].AIAA J,1983,21(5):741-748.
[4]	Bagley R L.A theoretical basis for the application of fractional calculus to viscoelasticity[J].J Rheol,1983,27(3):201-210.
[5]	黄文虎,王心清,张景绘,等.航天柔性结构振动控制的若干进展[J].力学进展,1997,27(1):5-18.
[6]	Enelund M,Mahler L,Runesson K,et al.Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws[J].Int J Solids Strut,1999,36(7):1417-1442.
[7]	Drozdov A D.Fractional differential models in finite viscoelasticity[J].Acta Mech,1997,124(1):155-180.
[8]	Samko S G,Kilbas A A,Marricher O Z.Fractional Integrals and Derivatives:Theory and Application[M].New York:Gordon and Breach Science Publishers,1993.
[9]	刘延柱,陈文良,陈立群.振动力学[M].北京:高等教育出版社,1998.
[10]	Rossikhin Y A,Shitikova M V.Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solid[J].Appl Mech Rev,1997,50(1):15-67.