| 具有分数导数型本构关系的粘弹性柱的动力稳定性 |
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| 引用本文： | 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[J].应用数学和力学,2001,22(3):250-258. |
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| 作者姓名： | 李根国 朱正佑 程昌钧 |
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| 作者单位： | 上海市应用数学和力学研究所, |
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| 基金项目： | 国家自然科学基金资助项目 !(19772 0 2 7)，上海市科学技术发展基金 !(98JC14 0 32 )，上海市教委发展基金资助项目!(99A0 1) |
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| 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，克服了存在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。
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| 关 键 词： | 粘弹性柱 分数导数型本构关系 平均化方法 微分方程 动力稳定性 |
| 文章编号： | 1000-0887(2001)03-0250-09 |
| 修稿时间： | 2000年1月25日 |
Dynamical Stability of Viscoelastic Column With Fractional Derivative Constitutive Relation |
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| LI Gen-guo,Zhu Zheng-you,Cheng Chang-jun.Dynamical Stability of Viscoelastic Column With Fractional Derivative Constitutive Relation[J].Applied Mathematics and Mechanics,2001,22(3):250-258. |
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| Authors: | LI Gen-guo Zhu Zheng-you Cheng Chang-jun |
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| Institution: | LI Gen_guo 1,2,ZHU Zheng_you 1,2,CHENG Chang_jun 1,3 |
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| 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_differential 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. |
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| Keywords: | viscoelastic column fractional derivative constitutive relation averaging method weakly singular Volterra integro_differential equation dynamical stability |
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