Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions

Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions

In practice, due to the fact that the phenomenon of drawing self-excited vibration can be deemed as one of the hunting phenomena of the mechanical system, this study focuses on investigating the drawing self-excited vibration process through proposing the fractional differential equation model of hu...

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Main Authors: Jiaquan Xie, Yongjiang Zheng, Zhongkai Ren, Tao Wang, Guangxian Shen
Format: Article
Language:English
Published: Hindawi-Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/9234586
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spelling doaj-5ff78b239ea84f3b92d33f172ac0a9d22020-11-24T21:23:01ZengHindawi-WileyComplexity1076-27871099-05262019-01-01201910.1155/2019/92345869234586Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre FunctionsJiaquan Xie0Yongjiang Zheng1Zhongkai Ren2Tao Wang3Guangxian Shen4College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, ChinaSchool of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, ChinaCollege of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, ChinaCollege of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, ChinaSchool of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, ChinaIn practice, due to the fact that the phenomenon of drawing self-excited vibration can be deemed as one of the hunting phenomena of the mechanical system, this study focuses on investigating the drawing self-excited vibration process through proposing the fractional differential equation model of hunting phenomenon of the mechanical system. The fractional Legendre functions together with their fractional differential operational matrices are used to numerically solve the model. In this way, the numerical solutions of vibration displacement of the model are obtained. At the end, the proposed model and algorithm are proved to be effective via analyzing the numerical results and phase position.http://dx.doi.org/10.1155/2019/9234586
collection DOAJ
language English
format Article
sources DOAJ
author Jiaquan Xie
Yongjiang Zheng
Zhongkai Ren
Tao Wang
Guangxian Shen
spellingShingle Jiaquan Xie
Yongjiang Zheng
Zhongkai Ren
Tao Wang
Guangxian Shen
Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions
Complexity
author_facet Jiaquan Xie
Yongjiang Zheng
Zhongkai Ren
Tao Wang
Guangxian Shen
author_sort Jiaquan Xie
title Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions
title_short Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions
title_full Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions
title_fullStr Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions
title_full_unstemmed Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions
title_sort numerical vibration displacement solutions of fractional drawing self-excited vibration model based on fractional legendre functions
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2019-01-01
description In practice, due to the fact that the phenomenon of drawing self-excited vibration can be deemed as one of the hunting phenomena of the mechanical system, this study focuses on investigating the drawing self-excited vibration process through proposing the fractional differential equation model of hunting phenomenon of the mechanical system. The fractional Legendre functions together with their fractional differential operational matrices are used to numerically solve the model. In this way, the numerical solutions of vibration displacement of the model are obtained. At the end, the proposed model and algorithm are proved to be effective via analyzing the numerical results and phase position.
url http://dx.doi.org/10.1155/2019/9234586
work_keys_str_mv AT jiaquanxie numericalvibrationdisplacementsolutionsoffractionaldrawingselfexcitedvibrationmodelbasedonfractionallegendrefunctions
AT yongjiangzheng numericalvibrationdisplacementsolutionsoffractionaldrawingselfexcitedvibrationmodelbasedonfractionallegendrefunctions
AT zhongkairen numericalvibrationdisplacementsolutionsoffractionaldrawingselfexcitedvibrationmodelbasedonfractionallegendrefunctions
AT taowang numericalvibrationdisplacementsolutionsoffractionaldrawingselfexcitedvibrationmodelbasedonfractionallegendrefunctions
AT guangxianshen numericalvibrationdisplacementsolutionsoffractionaldrawingselfexcitedvibrationmodelbasedonfractionallegendrefunctions
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