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

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)

Quasi-Static and Dynamical Analysis for Viscoelastic Timoshenko Beam With Fractional Derivative Constitutive Relation

1.
Shanghai Institute of Applied Mathematics and Mechancis, Shanghai University, Shanghai 200072, P R China;
2.
Department of Mathematics, Shanghai University, Shanghai 200072, P R China;
3.
Shanghai Supercomputer Center, Shanghai 201203, P R China;
4.
Department of Mechanics, Shanghai University, Shanghai 200072, P R China

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Timoshenko梁在阶跃载荷作用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。
- 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
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 paraeters 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.
- viscoelastic Timoshenko beam /
- fractional derivative constitutive relation /
- weakly singular Volterra integro-differential equation /
- dynamical response

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