Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method
This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural freque...
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| Auteurs principaux: | , , |
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| Format: | article |
| Langue: | EN |
| Publié: |
SAGE Publishing
2021
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| Sujets: | |
| Accès en ligne: | https://doaj.org/article/a0e58f5ece1e4e8988a9ef42e3b03b9e |
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| Résumé: | This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it. |
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