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

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.

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Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

Applied Mathematical Modelling ◽

10.1016/j.apm.2019.12.011 ◽

2020 ◽

Vol 81 ◽

pp. 159-176 ◽

Cited By ~ 3

Author(s):

Yuanhui Wang ◽

Yiming Chen

Keyword(s):

Dynamic Analysis ◽

Fractional Order ◽

Legendre Polynomials ◽

Order Model ◽

Shifted Legendre Polynomials ◽

Fractional Order Model ◽

Pipes Conveying Fluid ◽

Conveying Fluid

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Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2021.10.007 ◽

2021 ◽

Author(s):

Lin Sun ◽

Yiming Chen ◽

Rongqi Dang ◽

Gang Cheng ◽

Jiaquan Xie

Keyword(s):

Numerical Analysis ◽

Fractional Order ◽

Legendre Polynomials ◽

Viscoelastic Plate ◽

Order Model ◽

Shifted Legendre Polynomials ◽

Fractional Order Model

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Numerical analysis of viscoelastic pipe with variable fractional order model based on shifted Legendre polynomials algorithm

10.22541/au.162254089.97058087/v1 ◽

2021 ◽

Author(s):

Suhua Jin ◽

Yiming Chen ◽

Yuanhui Wang

Keyword(s):

Fractional Order ◽

Legendre Polynomials ◽

System Of Equations ◽

Order Model ◽

Shifted Legendre Polynomials ◽

Fractional Order Model ◽

Governing System ◽

The Time Domain ◽

Dynamics Problems

In this paper, an valid numerical algorithm is presented to solve variable fractional viscoelastic pipes conveying pulsating fluid in the time domain and analyze dynamically the vortex-induced vibration of the pipes. Firstly, Coimbra variable fractional derivative operators are introduced. Meanwhile, using Hamilton’s principle and a nonlinear variable fractional order model, the governing system of equations is established. The unknown functions of the system of equations are approximated with shifted Legendre polynomials. Then, convergence analysis and numerical example investigate the effectiveness and accuracy of the proposed algorithm. Finally, the influences of different parameters on the dynamic response of the viscoelastic pipe are studied. The influencing factors and their ranges of the transient and long-term chaotic states of the pipe are analyzed. In addition, the proposed algorithm shows enormous potentials for solving the dynamics problems of viscoelastic pipes with the variable fractional order models.

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Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

Nonlinear Engineering ◽

10.1515/nleng-2016-0059 ◽

2017 ◽

Vol 6 (2) ◽

Cited By ~ 4

Author(s):

Karthikeyan Rajagopal ◽

Anitha Karthikeyan ◽

Prakash Duraisamy

Keyword(s):

Permanent Magnet ◽

Fractional Order ◽

Dynamic Properties ◽

Synchronous Generator ◽

Adaptive Controller ◽

Control Technique ◽

Order Model ◽

Permanent Magnet Synchronous Generator ◽

Chaos Suppression ◽

Fractional Order Model

AbstractIn this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

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