The Fractal Timoshenko Beam Equation

Fractal and Fractional 2026 Open access

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Authors: Helvio P. Mollinedo, Ernesto Pineda León, David De-León, Andriy Kryvko, Israel Miguel-Andrés, Didier Samayoa, Lucero Damián-Adame
DOI: 10.3390/fractalfract10010065
Cited by: 1
References: 45

Abstract

A fractal approach for the Timoshenko beam theory by applying differential vector calculus in a three-dimensional continuum with a fractal metric is developed. First, a summary of the tools needed, mathematical relationships, and background of fractal continuum mechanics is presented. Then, the static and dynamical parts of the Timoshenko beam equation are extended to fractal manifolds. Afterwards, an intrafractal beam constructed as a Cartesian product is suggested and the fractal dimensionalities of the Balankin beam are scrutinized. This allows comparing both intrafractal beams when they have the same Hausdorff dimension but different connectivity. Finally, the effects of fractal attributes on the mechanical properties of the deformable fractal medium are highlighted. Some applications of the developed tools are briefly outlined.

Fields of Study & Subjects

Nonlocal and gradient elasticity in micro/nano structures Fractional Differential Equations Solutions Advanced Mathematical Theories and Applications

Publication details

Journal / source
Fractal and Fractional
Publisher
MDPI AG
Volume
10
Issue
1
Pages
65–65
Publication date
18 January 2026
Language
EN