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Open AccessArticle

Dynamic Analysis of the Viscoelastic Pipeline Conveying Fluid with an Improved Variable Fractional Order Model Based on Shifted Legendre Polynomials

by Yuanhui Wang 1 and Yiming Chen 1,2,3,*
1
College of Sciences, Yanshan University, Qinhuangdao 066004, China
2
LE STUDIUM RESEARCH FELLOW, Loire Valley Institute for Advanced Studies, 45000 Orléans, France
3
INSA Center Val de Loire-88, Boulevard Lahitolle, 18000 Bourges, France
*
Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(4), 52; https://doi.org/10.3390/fractalfract3040052
Received: 10 October 2019 / Revised: 6 November 2019 / Accepted: 14 November 2019 / Published: 17 November 2019
(This article belongs to the Special Issue 2019 Selected Papers from Fractal Fract’s Editorial Board Members)
Viscoelastic pipeline conveying fluid is analyzed with an improved variable fractional order model for researching its dynamic properties accurately in this study. After introducing the improved model, an involuted variable fractional order, which is an unknown piecewise nonlinear function for analytical solution, an equation is established as the governing equation for the dynamic displacement of the viscoelastic pipeline. In order to solve this class of equations, a numerical method based on shifted Legendre polynomials is presented for the first time. The method is effective and accurate after the numerical example verifying. Numerical results show that how dynamic properties are influenced by internal fluid velocity, force excitation, and variable fractional order through the proposed method. More importantly, the numerical method has shown great potentials for dynamic problems with the high precision model. View Full-Text
Keywords: improved model; shifted Legendre polynomial; viscoelastic pipeline conveying fluid; variable fractional order equation; numerical solution; dynamic response improved model; shifted Legendre polynomial; viscoelastic pipeline conveying fluid; variable fractional order equation; numerical solution; dynamic response
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Wang, Y.; Chen, Y. Dynamic Analysis of the Viscoelastic Pipeline Conveying Fluid with an Improved Variable Fractional Order Model Based on Shifted Legendre Polynomials. Fractal Fract 2019, 3, 52.

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