Non-linear problems of fractional calculus in modeling of mechanical systems
Non-linear problems of fractional calculus in modeling of mechanical systems
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DOI：
10.1016/j.ijmecsci.2013.02.007
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发表时间：
2013-05-01
影响因子：
7.3
通讯作者：
Zbiciak, Artur
中科院分区：
文献类型：
--
作者：
Grzesikiewicz, Wieslaw;Wakulicz, Andrzej;Zbiciak, Artur
本文提出了用于求解机械系统建模的非线性分数阶微分方程 (FDE) 的数学公式和数值算法。本文提出的方法涉及变分不等式的概念。它适用于相对于分数阶导数呈线性的一项 FDE。还提供了除分数元素外还包含非线性弹性、粘性和塑性元素的流变模型示例。提出了求解初值问题的Euler型和Runge-Kutta型差分时间离散格式。特别关注对沥青骨料混合物的原始弹粘塑性分数模型的分析，该模型是经典 Huet-Sayegh 模型的修改。给出了受到谐波运动激励的机械系统的数值模拟结果。 (C) 2013 Elsevier Ltd. 保留所有权利。
The paper presents mathematical formulation and numerical algorithm for solving non-linear fractional-order differential equations (FDEs) modeling mechanical systems. The method presented in the paper involves the notion of variational inequalities. It is applied to one-term FDEs which are linear with respect to the fractional derivative. The examples of rheological models containing, in addition to fractional elements, the non-linear elastic, viscous and plastic elements are presented. The difference time-discretization schemes of Euler and Runge-Kutta types for solving initial-value problems are proposed. A special attention is paid to analysis of an original elastic-visco-plastic fractional model of asphalt-aggregate mixes being a modification of the classical Huet-Sayegh model. The results of numerical simulations of mechanical systems subjected to harmonic kinematic excitations are presented. (C) 2013 Elsevier Ltd. All rights reserved.