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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Autores principales:	Hossein Talebi Rostami, Maryam Fallah Najafabadi, Davood Domiri Ganji
Formato:	article
Lenguaje:	EN
Publicado:	SAGE Publishing 2021
Materias:	Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/a0e58f5ece1e4e8988a9ef42e3b03b9e
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spelling	oai:doaj.org-article:a0e58f5ece1e4e8988a9ef42e3b03b9e2021-12-02T03:33:41ZAnalysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method1687-814010.1177/16878140211060982https://doaj.org/article/a0e58f5ece1e4e8988a9ef42e3b03b9e2021-11-01T00:00:00Zhttps://doi.org/10.1177/16878140211060982https://doaj.org/toc/1687-8140This 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.Hossein Talebi RostamiMaryam Fallah NajafabadiDavood Domiri GanjiSAGE PublishingarticleMechanical engineering and machineryTJ1-1570ENAdvances in Mechanical Engineering, Vol 13 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mechanical engineering and machinery TJ1-1570
spellingShingle	Mechanical engineering and machinery TJ1-1570 Hossein Talebi Rostami Maryam Fallah Najafabadi Davood Domiri Ganji Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method
description	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.
format	article
author	Hossein Talebi Rostami Maryam Fallah Najafabadi Davood Domiri Ganji
author_facet	Hossein Talebi Rostami Maryam Fallah Najafabadi Davood Domiri Ganji
author_sort	Hossein Talebi Rostami
title	Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method
title_short	Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method
title_full	Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method
title_fullStr	Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method
title_full_unstemmed	Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method
title_sort	analysis of timoshenko beam with koch snowflake cross-section and variable properties in different boundary conditions using finite element method
publisher	SAGE Publishing
publishDate	2021
url	https://doaj.org/article/a0e58f5ece1e4e8988a9ef42e3b03b9e
work_keys_str_mv	AT hosseintalebirostami analysisoftimoshenkobeamwithkochsnowflakecrosssectionandvariablepropertiesindifferentboundaryconditionsusingfiniteelementmethod AT maryamfallahnajafabadi analysisoftimoshenkobeamwithkochsnowflakecrosssectionandvariablepropertiesindifferentboundaryconditionsusingfiniteelementmethod AT davooddomiriganji analysisoftimoshenkobeamwithkochsnowflakecrosssectionandvariablepropertiesindifferentboundaryconditionsusingfiniteelementmethod
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Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

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