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

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Abstract

In this paper, the forced vibrations of the fractional viscoelastic beam with the Kelvin-Voigt fractional order constitutive relationship is studied. The equation of motion is derived from Newton’s second law and the Galerkin method is used to discretize the equation of motion in to a set of linear ordinary differential equations. For solving the discretized equations, the radial basis functions and Sinc quadrature rule are used. In order to show the effectiveness and accuracy of this method, some test problem are considered, and it is shown that the obtained results are in very good agreement with exact solution. In the following, the proposed numerical solution is applied to exploring the effects of fractional parameters on the response of the beam and finally some conclusions are outlined.

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Authors and Affiliations

  1. Aerospace Engineering Dept., Sharif University of Tech., Azadi Ave., Tehran, 11155-8639, Iran

    M. R. Permoon & H. Haddadpour

  2. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 168613114, Iran

    J. Rashidinia, A. Parsa & R. Salehi

Authors
  1. M. R. Permoon
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  2. J. Rashidinia
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  3. A. Parsa
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  4. H. Haddadpour
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  5. R. Salehi
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Corresponding author

Correspondence to H. Haddadpour.

Additional information

Recommended by Associate Editor Eung-Soo Shin

Hassan Haddadpour received his B.Sc. in Mechanical Engineering in 1993 from Abadan Institute of Technology in Iran. He also graduated from the M.Sc. degree program and Ph.D. for Mechanical Engineering in the applied design course from University of Tehran. He joined Sharif University of Technology in 2002. Currently, he is a professor in the Department of Aerospace Engineering of Sharif University of Technology. His research interests are Aeroelasticity, Reduced Order Modeling and Structural Dynamics.

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Permoon, M.R., Rashidinia, J., Parsa, A. et al. Application of radial basis functions and sinc method for solving the forced vibration of fractional viscoelastic beam. J Mech Sci Technol 30, 3001–3008 (2016). https://doi.org/10.1007/s12206-016-0306-3

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  • DOI: https://doi.org/10.1007/s12206-016-0306-3

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