Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam
In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin–Voigt and fractional derivative element constitutive models, the two governing equations of fractional v...
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| Published in: | Chaos, solitons and fractals Vol. 132; p. 109585 |
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| Language: | English |
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01.03.2020
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| ISSN: | 0960-0779, 1873-2887 |
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| Abstract | In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin–Voigt and fractional derivative element constitutive models, the two governing equations of fractional visco-elastic rotating beams are established. According to the approximation technique of shifted Chebyshev polynomials, the integer and fractional differential operator matrices of polynomials are derived. By means of the collocation method and matrix technique, the operator matrices of governing equations can be transformed into the algebraic equations. In addition, the convergence analysis is performed. In particular, unlike the existing results, we can get the displacement and the stress numerical solution of the governing equation directly in the time domain. Finally, the sensitivity of the algorithm is verified by numerical examples. |
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| AbstractList | In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin–Voigt and fractional derivative element constitutive models, the two governing equations of fractional visco-elastic rotating beams are established. According to the approximation technique of shifted Chebyshev polynomials, the integer and fractional differential operator matrices of polynomials are derived. By means of the collocation method and matrix technique, the operator matrices of governing equations can be transformed into the algebraic equations. In addition, the convergence analysis is performed. In particular, unlike the existing results, we can get the displacement and the stress numerical solution of the governing equation directly in the time domain. Finally, the sensitivity of the algorithm is verified by numerical examples. In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin-Voigt and fractional derivative element con-stitutive models, the two governing equations of fractional visco-elastic rotating beams are established. According to the approximation technique of shifted Chebyshev polynomials, the integer and fractional differential operator matrices of polynomials are derived. By means of the collocation method and matrix technique, the operator matrices of governing equations can be transformed into the algebraic equations. In addition, the convergence analysis is performed. In particular, unlike the existing results, we can get the displacement and the stress numerical solution of the governing equation directly in the time domain. Finally, the sensitivity of the algorithm is verified by numerical examples. |
| ArticleNumber | 109585 |
| Author | Wang, Lei Chen, Yi-Ming |
| Author_xml | – sequence: 1 givenname: Lei surname: Wang fullname: Wang, Lei email: qiqiqiqiha@163.com organization: School of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, PR China – sequence: 2 givenname: Yi-Ming surname: Chen fullname: Chen, Yi-Ming email: chenym@ysu.edu.cn organization: School of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, PR China |
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| Keywords | Fractional visco-elastic rotating beam Fractional governing equation Approximation technique Operator matrix Numerical solution Shifted Chebyshev polynomials |
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| SubjectTerms | Approximation technique Fractional governing equation Fractional visco-elastic rotating beam Mathematics Numerical solution Operator matrix Shifted Chebyshev polynomials |
| Title | Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam |
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