TY - JOUR
T1 - Fractal Continuum Calculus of Functions on Euler-Bernoulli Beam
AU - Samayoa, Didier
AU - Kryvko, Andriy
AU - Velázquez, Gelasio
AU - Mollinedo, Helvio
N1 - Publisher Copyright:
© 2022 by the authors.
PY - 2022/10
Y1 - 2022/10
N2 - 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 ((Formula presented.) -CC) is carried out. The fractal Euler-Bernoulli beam equation is derived as a generalization using (Formula presented.) -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.
AB - 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 ((Formula presented.) -CC) is carried out. The fractal Euler-Bernoulli beam equation is derived as a generalization using (Formula presented.) -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.
KW - Euler-Bernoulli beam
KW - Hausdorff dimension
KW - fractal continuum calculus
KW - transversal displacement
UR - http://www.scopus.com/inward/record.url?scp=85140597717&partnerID=8YFLogxK
U2 - 10.3390/fractalfract6100552
DO - 10.3390/fractalfract6100552
M3 - Artículo
AN - SCOPUS:85140597717
SN - 2504-3110
VL - 6
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 10
M1 - 552
ER -