 A finite element approximation to a viscoelastic Euler–Bernoulli beam with internal dampingYiqun Li and Hong Wang Mathematics and Computers in Simulation (MATCOM), 2023, vol. 212, issue C, 138-158 Abstract: We analyze a finite element approximation to a viscoelastic Euler–Bernoulli beam with internal damping that undergoes vibrations under external excitation. We prove the wellposedness of the problem and regularity estimates of the exact solution to the model. We then utilize these results to prove an optimal-order error estimate of the numerical approximation assuming only the regularity of the data of the model but not that of the exact solution. Because the model exhibits its salient features that are different from those of conventional elastic Euler–Bernoulli beams, a new estimate technique is used in the analysis. We finally carry out numerical experiments to substantiate the error estimate and to investigate the dynamic response of the viscoelastic Euler–Bernoulli beam, in comparison with the conventional Euler–Bernoulli beam. Keywords: Viscoelastic Euler–Bernoulli beam; Variable-order time fractional PDE; Regularity estimate; Finite element approximation; Error estimate (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:212:y:2023:i:c:p:138-158 DOI: 10.1016/j.matcom.2023.04.031 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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