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Large deflection of viscoelastic beams using fractional derivative model

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Abstract

This paper deals with large deflection of viscoelastic beams using a fractional derivative model. For this purpose, a nonlinear finite element formulation of viscoelastic beams in conjunction with the fractional derivative constitutive equations has been developed. The four-parameter fractional derivative model has been used to describe the constitutive equations. The deflected configuration for a uniform beam with different boundary conditions and loads is presented. The effect of the order of fractional derivative on the large deflection of the cantilever viscoelastic beam, is investigated after 10, 100, and 1000 hours. The main contribution of this paper is finite element implementation for nonlinear analysis of viscoelastic fractional model using the storage of both strain and stress histories. The validity of the present analysis is confirmed by comparing the results with those found in the literature.

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Authors and Affiliations

  1. School of Mechanical Engineering, Shiraz University, Shiraz, Iran

    Seyed Masoud Sotoodeh Bahraini, Mohammad Eghtesad, Mehrdad Farid & Esmaeal Ghavanloo

Authors
  1. Seyed Masoud Sotoodeh Bahraini
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  2. Mohammad Eghtesad
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  3. Mehrdad Farid
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  4. Esmaeal Ghavanloo
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Corresponding author

Correspondence to Mohammad Eghtesad.

Additional information

Recommended by Associate Editor Seong Beom Lee

Seyed Masoud Sotoodeh Bahraini received his B.S. degree from Shahid Bahonar University of Kerman, Iran (2009), M.S. degree from Shiraz University, Iran (2012), all in Mechanical Engineering. His research interests include viscoelastic materials, finite element analysis, vibration analysis and control, and fractional calculus.

Mohammad Eghtesad received his Ph.D. from University of Ottawa (1996), Professor of Mech. Eng. (2010). Dr. Eghtesad joined the Department of Mechanical Engineering at Shiraz University in 1997. He has taught and done research in the areas of robotics, mechatronics and control. His research includes both theoretical and experimental studies.

Mehrdad Farid received his Ph.D. from University of Calgary (1997). He is currently an Associate Professor in the Department of Mechanical Engineering at Shiraz University. His research interests include applied mechanics, computational mechanics and vibrations.

Esmaeal Ghavanloo received his B.Sc. and M.Sc. degrees in Mechanical Engineering from Shiraz University in 2007 and 2009, respectively. He is currently a Ph.D. candidate at Shiraz University. His research interests focus on the mechanics of nanostructures, fluid-structure interaction problems, pliable structures and viscoelastic materials.

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Bahraini, S.M.S., Eghtesad, M., Farid, M. et al. Large deflection of viscoelastic beams using fractional derivative model. J Mech Sci Technol 27, 1063–1070 (2013). https://doi.org/10.1007/s12206-013-0302-9

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  • DOI: https://doi.org/10.1007/s12206-013-0302-9

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