Effects of Hausdorff Dimension on the Static and Free Vibration Response of Beams with Koch Snowflake-like Cross Section-Reference-Cited by-同舟云学术

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

Published:2023-02-04 Issue:2 Volume:7 Page:153
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Samayoa Didier¹^ORCID,Mollinedo Helvio²^ORCID,Jiménez-Bernal José Alfredo¹^ORCID,Gutiérrez-Torres Claudia del Carmen¹^ORCID

Affiliation:

1. SEPI-ESIME Zacatenco, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico

2. Engineering Department, Instituto Politécnico Nacional, UPIITA, Av. IPN, No. 2580, Col. La Laguna Ticoman, Gustavo A. Madero, Mexico City 07340, Mexico

Abstract

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 ymax=k0.79lndH+0.37, being k the iteration number of pre-fractal. The natural frequencies increase as ω∼M2.51, whereas the bending stiffness is expressed as EI=1165.4ln(dH+k). Numerical examples are given in order to discuss the mechanical implications.

Funder

Instituto Politécnico Nacional under the research SIP-IPN

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/2/153/pdf

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