Title
Comparative analysis of beam responses via Hencky and fractional models under different mass distributions
Authors
[ 1 ] Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ P ] employee
Scientific discipline (Law 2.0)
Year of publication
2025
Published in
Article type
scientific article
Publication language
english
Keywords
EN
- Hencky beam
- Nonlocality
- Fractional modeling
- Symmetric caputo derivative
- Free vibration
Abstract
EN This study presents a comparative analysis of the mechanical responses of beams modeled using Hencky and fractional approaches under various mass distribution conditions. The beam models considered in this study are composed of rigid segments connected by rotational springs, with three distinct mass distribution schemes analyzed: masses concentrated at the joints, masses located at the midpoints of each rigid part, and masses uniformly distributed along each segment. The developed model converges to the Euler–Bernoulli beam theory in the continuum limit, as the number of rigid segments tends to infinity. Closed-form expressions for natural frequencies are derived for simply supported boundary conditions. To approximate the dynamic response of these discrete models and capture their scale-dependent effects, corresponding nonlocal fractional continuum models are formulated using the symmetric Caputo derivative. These models enable precise fractional parameter calibration based on discrete systems’ dispersion relations. The analysis reveals a strong influence of the mass distribution on the dynamic behavior, with stiffening or softening effects emerging depending on the mass arrangement. The proposed fractional framework successfully replicates the dispersion characteristics of each discrete Hencky model and confirms that the accurate selection of fractional derivative parameters effectively models the vibrational behavior of microstructured beams.
Date of online publication
11.09.2025
Pages (from - to)
104511-1 - 104511-6
Comments
Article Number: 104511
License type
CC BY (attribution alone)
Open Access Mode
czasopismo hybrydowe
Open Access Text Version
final published version
Date of Open Access to the publication
in press
Ministry points / journal
70
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