ON THE APPEARANCE OF THE FRACTIONAL DERIVATIVE IN THE BEHAVIOR OF REAL MATERIALS
ON THE APPEARANCE OF THE FRACTIONAL DERIVATIVE IN THE BEHAVIOR OF REAL MATERIALS
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DOI：
10.1115/1.3167615
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发表时间：
1984-01-01
影响因子：
2.6
通讯作者：
BAGLEY, RL
中科院分区：
文献类型：
--
作者：
TORVIK, PJ;BAGLEY, RL
本文提出了粘弹性材料的广义本构关系，其中整数阶时间导数用分数阶导数代替。在这一点上，这种模型的理由在于它们在描述真实的材料的行为方面是有效的。在这项工作中，分数阶导数是自然出现在牛顿流体的某些运动的描述。我们声称，这提供了一些理由使用特设的关系，其中包括分数阶导数。这样的本构关系的预测的瞬态响应的频率依赖性材料的应用包括在内。
Generalized constitutive relationships for viscoelastic materials are suggested in which the customary time derivatives of integer order are replaced by derivatives of fractional order. To this point, the justification for such models has resided in the fact that they are effective in describing the behavior of real materials. In this work, the fractional derivative is shown to arise naturally in the description of certain motions of a Newtonian fluid. We claim this provides some justification for the use of ad hoc relationships which include the fractional derivative. An application of such a constitutive relationship to the prediction of the transient response of a frequency-dependent material is included.