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.
出处
《应用数学和力学》
EI
CSCD
北大核心
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)
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
viscoelastic column
fractional derivative constitutive relation
averaging method
weakly singular Volterra integro_differential equation
dynamical stability
