Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model |
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| Institution: | 1. College of Sciences, Yanshan University, Qinhuangdao 066004, Hebei, China;2. LE STUDIUM RESEARCH FELLOW, Loire Valley Institute for Advanced Studies Orléans & Tours, France;3. PRISME (INSA-Institut National des sciences appliqués)-88, Boulevard Lahitolle, Bourges 18000, France;1. College of Mechanical Engineering, Yangzhou University, Yangzhou 225127, China;2. Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering, College of Mechanical Engineering and Applied Electronics, Beijing University of Technology, Beijing 100124, China;1. Department of Mathematics, Shiraz University of Technology, Shiraz, Iran;2. Department of Applied Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, Jiangsu 215123, China;1. Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, P.O. Box-71555-313, Iran;2. Departments of Mathematics, Shiraz University of Technology, Shiraz, P.O. Box-71555-313, Iran |
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| Abstract: | The dynamic analysis of viscoelastic pipes conveying fluid is investigated by 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 convergence analysis and numerical example verify 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 under the variable fractional order model. |
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