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A viscoelastic Timoshenko Beam Model: Regularity and Numerical Approximation

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Abstract

We derive a fully-discrete finite element scheme to a fractional Timoshenko beam model, which characterizes the mechanical responses of viscoelastic beams, thick beams and beams subject to high-frequency excitations by properly considering the effects of both transverse shear and rotational inertia. We prove high-order regularity of the solutions to the model and then accordingly prove error estimates of the numerical scheme. Numerical experiments are performed to substantiate the numerical analysis results and to demonstrate the effectiveness of the fractional Timoshenko beam model in modeling the mechanical vibrations of different beams, in comparison with its integer-order analogue and the widely-used integer-order and fractional Euler-Bernoulli beam models.

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Acknowledgements

The authors would like to express their most sincere thanks to the referees for their very constructive and helpful comments and suggestions, which greatly improved the quality of this paper. This work was partially supported by the National Science Foundation under Grant No. DMS-2012291 and the National Natural Science Foundation of China under Grant No. 11971272. Enquiries about data availability should be directed to the authors.

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Yiqun Li & Hong Wang

  2. School of Mathematics, Shandong University, Jinan, 250100, China

    Xiangcheng Zheng

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  1. Yiqun Li
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  2. Hong Wang
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Correspondence to Xiangcheng Zheng.

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Li, Y., Wang, H. & Zheng, X. A viscoelastic Timoshenko Beam Model: Regularity and Numerical Approximation. J Sci Comput 95, 57 (2023). https://doi.org/10.1007/s10915-023-02187-5

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