分数阶Bagley-Torvik方程的研究

An Investigation of Fractional Bagley-Torvik Equation.

作者信息

Zafar Azhar Ali, Kudra Grzegorz, Awrejcewicz Jan

机构信息

Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, Poland.

Department of Mathematics, Government College University, Lahore 54000, Pakistan.

出版信息

Entropy (Basel). 2019 Dec 24;22(1):28. doi: 10.3390/e22010028.

DOI:10.3390/e22010028

PMID:33285803

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7516449/

Abstract

In this article, we will solve the Bagley-Torvik equation by employing integral transform method. Caputo fractional derivative operator is used in the modeling of the equation. The obtained solution is expressed in terms of generalized function. Further, we will compare the obtained results with other available results in the literature to validate their usefulness. Furthermore, examples are included to highlight the control of the fractional parameters on he dynamics of the model. Moreover, we use this equation in modelling of real free oscillations of a one-degree-of-freedom mechanical system composed of a cart connected with the springs to the support and moving via linear rolling bearing block along a rail.

摘要

在本文中，我们将采用积分变换方法求解Bagley-Torvik方程。方程建模中使用了Caputo分数阶导数算子。所得解以广义函数表示。此外，我们将把所得结果与文献中其他可用结果进行比较，以验证其有效性。此外，还给出了示例以突出分数阶参数对模型动力学的控制。此外，我们将此方程用于对一个单自由度机械系统的实际自由振动进行建模，该系统由一个通过弹簧连接到支架并通过线性滚动轴承座沿轨道移动的小车组成。