Fractional Euler-Bernoulli beams: theory, numerical study and experimental validation

TL;DR

This paper introduces fractional Euler-Bernoulli beams, extending classical theory with non-local fractional calculus, validated through experiments on micro-beams showing size effects and supported by numerical solutions.

Contribution

It develops a fractional calculus-based reformulation of Euler-Bernoulli beam theory, providing a new non-local model validated with experimental and numerical methods.

Findings

Significant size effects observed in micro-beam experiments.

Model parameters successfully identified from AFM data.

Numerical solutions effectively solve fractional differential equations.

Abstract

In this paper the classical Euler-Bernoulli beam (CEBB) theory is reformulated utilising fractional calculus. Such generalisation is called fractional Euler-Bernoulli beams (FEBB) and results in non-local spatial description. The parameters of the model are identified based on AFM experiments concerning bending rigidities of micro-beams made of the polymer SU-8. In experiments both force as well as deflection data were recorded revealing significant size effect with respect to outer dimensions of the specimens. Special attention is also focused on the proper numerical solution of obtained fractional differential equation.