Application of radial basis functions and sinc method for solving the forced vibration of fractional viscoelastic beam

Permoon, M.R.; Rashidinia, Jalil; Parsa, Ali; Haddadpour, H.; Salehi, Rezvan

doi:10.1007/s12206-016-0306-3

Cited by 23 publications

(8 citation statements)

References 25 publications

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“…Methods for solving fractional visco-elastic beams in the time domain include the finite element method [21,22], multi-scale method [23], Galerkin method [24] and the variational iteration method [25] which have been found in the literature. But so far, the numerical solutions of the displacement and the stress of fractional visco-elastic rotating beams in time domain has not been studied.…”

Section: Introductionmentioning

confidence: 99%

Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam

Wang

Chen

2020

Chaos, Solitons & Fractals

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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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Section: Introductionmentioning

confidence: 99%

Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam

Wang

Chen

2020

Chaos, Solitons & Fractals

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“…The conclusion is that the coefficient of the fractional derivative affects the stability of natural frequencies and vibration amplitudes. Permoon et al [21] used the Galerkin method to discretize the motion equation into a set of linear ordinary differential equations and then studied the forced vibration of beams. Martinez-Agirre et al [22] studied the harmonic response of the constrained layer damped cantilever beam and analyzed the damping structure system by using the complex modal superposition method.…”

Section: *Manuscript Click Here To View Linked Referencesmentioning

confidence: 99%

Numerical analysis of fractional partial differential equations applied to polymeric visco-elastic Euler-Bernoulli beam under quasi-static loads

Wang

Chen

Cheng

et al. 2020

Chaos, Solitons & Fractals

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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“…Therefore, the development of effective and easy‐to‐use numerical schemes for solving such equations acquires an increasing interest. While several numerical techniques have been proposed to solve many different problems (see, for instance [22–49], and references therein), there have been few research studies that developed numerical methods to solve DOFDEs (see [50–58]). The development, however, for efficient numerical methods to solve DOFDEs is still an important issue [51].…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach

Maleknejad

Rashidinia

Eftekhari

2020

Numerical Methods Partial

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In this paper, a numerical method is presented to obtain and analyze the behavior of numerical solutions of distributed order fractional differential equations of the general form in the time domain with the Caputo fractional derivative. The suggested method is based on the Müntz-Legendre wavelet approximation. We derive a new operational vector for the Riemann-Liouville fractional integral of the Müntz-Legendre wavelets by using the Laplace transform method. Applying this operational vector and collocation method in our approach, the problem can be reduced to a system of linear and nonlinear algebraic equations. The arising system can be solved by the Newton method. Discussion on the error bound and convergence analysis for the proposed method is presented. Finally, seven test problems are considered to compare our results with other well-known methods used for solving these problems. The results in the tabulated tables highlighted that the proposed method is an efficient mathematical tool for analyzing distributed order fractional differential equations of the general form.

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Application of radial basis functions and sinc method for solving the forced vibration of fractional viscoelastic beam

Cited by 23 publications

References 25 publications

Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam

Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam

Numerical analysis of fractional partial differential equations applied to polymeric visco-elastic Euler-Bernoulli beam under quasi-static loads

Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach

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