Shifted Legendre Polynomials algorithm used to the dynamic analysis of viscoelastic pipes conveying fluid with the variable fractional order model $
Résumé
The dynamic analysis of viscoelastic pipes conveying fluid is investigated with the variable fractional order model in this article. The nonlinear variable fractional order integral-differential equation is established by introducing the model into the governing equation. Then the Shifted Legendre Polynomials algorithm is first presented for dealing with this kind of equations. The numerical example verifies that the algorithm is an effective and accurate technique for addressing this type complicated equation. Numerical results for dynamic analysis of viscoelastic pipes conveying fluid show the effect of parameters on displacement, acceleration, strain and stress. It also indicates that how dynamic properties are affected by the variable fractional order and fluid velocity varying. Most of all, the proposed algorithm has enormous potentials for the problem of high precision dynamics with the variable fractional order model.
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