TY - JOUR
T1 - Effects of Hausdorff Dimension on the Static and Free Vibration Response of Beams with Koch Snowflake-like Cross Section
AU - Samayoa, Didier
AU - Mollinedo, Helvio
AU - Jiménez-Bernal, José Alfredo
AU - Gutiérrez-Torres, Claudia del Carmen
N1 - Publisher Copyright:
© 2023 by the authors.
PY - 2023/2
Y1 - 2023/2
N2 - 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 (Formula presented.), being k the iteration number of pre-fractal. The natural frequencies increase as (Formula presented.), whereas the bending stiffness is expressed as (Formula presented.). Numerical examples are given in order to discuss the mechanical implications.
AB - 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 (Formula presented.), being k the iteration number of pre-fractal. The natural frequencies increase as (Formula presented.), whereas the bending stiffness is expressed as (Formula presented.). Numerical examples are given in order to discuss the mechanical implications.
KW - Euler–Bernoulli beam
KW - Hausdorff dimension
KW - transversal displacement
KW - vibration modes
UR - http://www.scopus.com/inward/record.url?scp=85148901910&partnerID=8YFLogxK
U2 - 10.3390/fractalfract7020153
DO - 10.3390/fractalfract7020153
M3 - Artículo
AN - SCOPUS:85148901910
SN - 2504-3110
VL - 7
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 2
M1 - 153
ER -