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具有分数导数本构关系的粘弹性 Timoshenko 梁的静动力学行为分析
引用本文:朱正佑,李根国,程昌钧.具有分数导数本构关系的粘弹性 Timoshenko 梁的静动力学行为分析[J].应用数学和力学,2002,23(1):1-10.
作者姓名:朱正佑  李根国  程昌钧
作者单位:1. 上海大学,上海市应用数学和力学研究所,上海,200072上海大学数学系,上海200072
2. 上海超级计算中心,上海,201203
3. 上海大学,上海市应用数学和力学研究所,上海,200072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 (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:利用粘弹性材料的三维分数导数型本构关系,建立粘弹性Timoshenko梁的静、动力学行为研究的数学模型;分析了Timoshenko梁在阶跃载荷下的准静态力学行为,得出了问题的解析解,考察了一些材料参数对梁的挠度的影响。基于模态函数讨论了粘弹性Timoshenko梁在横向简谐激励作用下的动力响应,并考察了剪切和转动惯性对梁振动响应的影响。

关 键 词:粘弹性Timoshenko梁  分数导数型本构关系  弱奇异性Volterra积分-微分方程  动力响应
文章编号:1000-0887(2002)01-0001-10

Quasi-Static and Dynamical Analysis for Viscoelastic Timoshenko Beam With Fractional Derivative Constitutive Relation
ZHU Zheng_you ,LI Gen_guo ,CHENG Chang_jun.Quasi-Static and Dynamical Analysis for Viscoelastic Timoshenko Beam With Fractional Derivative Constitutive Relation[J].Applied Mathematics and Mechanics,2002,23(1):1-10.
Authors:ZHU Zheng_you    LI Gen_guo  CHENG Chang_jun
Institution:ZHU Zheng_you 1,2,LI Gen_guo 3,CHENG Chang_jun 1,4
Abstract:The equations of motion governing the quasi_static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three_dimensional fractional derivative constitutive relation. The quasi_static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained. The influence of material parameters on the deflection is investigated. The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions. And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.
Keywords:viscoelastic Timoshenko beam  fractional derivative constitutive relation  weakly singular Volterra integro_differential equation  dynamical response
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