Effects of Hausdorff Dimension on the Static and Free Vibration Response of Beams with Koch Snowflake-like Cross Section

被引：3

作者：

Samayoa, Didier ^{[1
]}

Mollinedo, Helvio ^{[2
]}

Alfredo Jimenez-Bernal, Jose ^{[1
]}

del Carmen Gutierrez-Torres, Claudia ^{[1
]}

机构：

[1] Inst Politecn Nacl, SEPI ESIME Zacatenco, Unidad Profes Adolfo Lopez Mateos, Mexico City 07738, Mexico

[2] Inst Politecn Nacl, UPIITA, Engn Dept, Ave IPN 2580,Col Laguna Ticoman,Gustavo A Made, Mexico City 07340, Mexico

来源：

FRACTAL AND FRACTIONAL | 2023年 / 7卷 / 02期

关键词：

Euler-Bernoulli beam; Hausdorff dimension; transversal displacement; vibration modes; EULER-BERNOULLI;

D O I：

10.3390/fractalfract7020153

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this manuscript, static and free vibration responses on Euler-Bernoulli beams with a Koch snowflake cross-section are studied. By applying the finite element method, the transversal displacement in static load condition, natural frequencies, and vibration modes are solved and validated using Matlab. For each case presented, the transversal displacement and natural frequency are analyzed as a Hausdorff dimension function. It is found that the maximum displacement increases as the Hausdorff dimension increases, with the relationship y(max)=k(0.79lndH+0.37), being k the iteration number of pre-fractal. The natural frequencies increase as omega similar to M-2.51, whereas the bending stiffness is expressed as EI=1165.4ln(d(H)+k). Numerical examples are given in order to discuss the mechanical implications.

引用

页数：8

共 47 条

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