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

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 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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