Fractal Continuum Calculus of Functions on Euler-Bernoulli Beam
FRACTAL AND FRACTIONAL(2022)
摘要
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 (F-dH(3)-CC) is carried out. The fractal Euler-Bernoulli beam equation is derived as a generalization using F-dH(3)-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.
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关键词
fractal continuum calculus,Hausdorff dimension,Euler-Bernoulli beam,transversal displacement
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