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Nonlinear modeling and dynamic analysis of bioengineering hyper-elastic tubes based on different material models

Biomechanics and Modeling in Mechanobiology volume 19, pages 971–983 (2020)Cite this article

Abstract

In this research, nonlinear vibrations of a hyper-elastic tube accounting for large deflection and moderate rotation have been examined. The hyper-elastic tube is assumed to be surrounded by a nonlinear hardening elastic medium. Different types of hyper-elastic material models are presented and discussed including neo-Hookean, Mooney–Rivlin, Ishihara and Yeoh models. The efficacy of these models in nonlinear vibration modeling and analysis of hyper-elastic tubes has been examined. Modified von-Karman strain is used to consider both large deflection and moderate rotation. The governing equations are obtained based on strain energy function of above-mentioned hyper-elastic material models. The nonlinear governing equation of the tube contains cubic and quantic terms which is solved via extended Hamiltonian method leading to a closed form of nonlinear vibration frequency. The effect of hyper-elastic models and their material parameters on nonlinear vibrational frequency of tubes has been studied.

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Acknowledgements

The authors would like to thank Fidar Project Qaem (FPQ) for providing the fruitful and useful help.

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Affiliations

  1. Department of Mechanical and Industrial Engineering, Qatar University, P.O. Box 2713, Doha, Qatar

    Seyed Sajad Mirjavadi & Masoud Forsat

  2. Department of Electrical Engineering, Qatar University, Doha, Qatar

    Salman Badnava

Authors
  1. Seyed Sajad Mirjavadi
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  2. Masoud Forsat
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  3. Salman Badnava
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Correspondence to Seyed Sajad Mirjavadi.

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Mirjavadi, S.S., Forsat, M. & Badnava, S. Nonlinear modeling and dynamic analysis of bioengineering hyper-elastic tubes based on different material models. Biomech Model Mechanobiol 19, 971–983 (2020). https://doi.org/10.1007/s10237-019-01265-8

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  • DOI: https://doi.org/10.1007/s10237-019-01265-8

Keywords

  • Bioengineering material
  • Nonlinear vibration
  • Hyper-elastic material
  • Yeoh model
  • Moderate rotation
  • Hamiltonian method