Fractional Euler–Bernoulli beams: Theory, numerical study and experimental validation

• Fractional Euler–Bernoulli beams.
• Fractional calculus.
• Non-local models.
• AFM experiments concerning bending rigidities of micro-beams.

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.