Fractional Euler-Bernoulli beams: theory, numerical study and experimental validation
arXiv:1502.01525 · doi:10.1016/j.euromechsol.2015.07.002
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.
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Cited by in corpus (4)
- A Ritz-based Finite Element Method for a Fractional-Order Boundary Value Problem of Nonlocal Elasticity
- Geometrically Nonlinear Response of a Fractional-Order Nonlocal Model of Elasticity
- Thermodynamics of fractional-order nonlocal continua and its application to the thermoelastic response of beams
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