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Journal of Scientific Computing

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01-05-2023

A viscoelastic Timoshenko Beam Model: Regularity and Numerical Approximation

Authors: Yiqun Li, Hong Wang, Xiangcheng Zheng

Published in: Journal of Scientific Computing | Issue 2/2023

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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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Title: A viscoelastic Timoshenko Beam Model: Regularity and Numerical Approximation
Authors: Yiqun Li
Hong Wang
Xiangcheng Zheng
Publication date: 01-05-2023
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2023
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-023-02187-5

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