具有分数导数型本构关系的粘弹性柱的动力稳定性  

Dynamical Stability of Viscoelastic Column With Fractional Derivative Constitutive Relation

作　　者：李根国[1] 朱正佑[1] 程昌钧[1] 

机构地区：[1]上海市应用数学和力学研究所

出　　处：《应用数学和力学》2001年第3期250-258,共9页Applied Mathematics and Mechanics

基　　金：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)

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 。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.

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 

分 类 号：O345[理学—固体力学]