Fractal Continuum Calculus of Functions on Euler-Bernoulli Beam - Didier Samayoa; Andriy Kryvko; Gelasio Velázquez; Helvio Mollinedo (Fractal and Fractional, 2022)
A new approach for solving the fractal Euler-Bernoulli beam equation is proposed. The mapping of fractal problems in non-differentiable fractals into the corresponding problems for the fractal continuum applying the fractal continuum calculus (<semantics><msubsup>FdH3</msubsup></semantics>-CC) is carried out. The fractal Euler-Bernoulli beam equation is derived as a generalization using <semantics><msubsup>FdH3</msubsup></semantics>-CC under analogous assumptions as in the ordinary calculus and then it is solved analytically. To validate the spatial distribution of self-similar beam response, three different classical beams with several fractal parameters are analysed. Some mechanical implications are discussed.