Elastic instability and free vibration analyses of axially functionally graded Timoshenko beams with variable cross-section

In this paper, the critical buckling loads and natural frequencies of axially functionally graded non-prismatic Timoshenko beam with different boundary conditions are acquired using the Finite Difference Method (FDM). In the recent years, the use of functionally graded materials (FGMs) has been incr...

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Autores principales:	Masoumeh Soltani, Behrouz Asgarian, Vahid jafari Deligani
Formato:	article
Lenguaje:	FA
Publicado:	Iranian Society of Structrual Engineering (ISSE) 2020
Materias:	tapered timoshenko beam axially functionally graded material natural frequency critical buckling load finite difference method Bridge engineering TG1-470 Building construction TH1-9745
Acceso en línea:	https://doaj.org/article/e98c32eaa9b74a7a95e232acc6cca42a
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spelling	oai:doaj.org-article:e98c32eaa9b74a7a95e232acc6cca42a2021-11-08T15:54:03ZElastic instability and free vibration analyses of axially functionally graded Timoshenko beams with variable cross-section2476-39772538-261610.22065/jsce.2019.143692.1627https://doaj.org/article/e98c32eaa9b74a7a95e232acc6cca42a2020-10-01T00:00:00Zhttps://www.jsce.ir/article_81588_cf6f63a0f3bf7c15b19f6376d893aefe.pdfhttps://doaj.org/toc/2476-3977https://doaj.org/toc/2538-2616In this paper, the critical buckling loads and natural frequencies of axially functionally graded non-prismatic Timoshenko beam with different boundary conditions are acquired using the Finite Difference Method (FDM). In the recent years, the use of functionally graded materials (FGMs) has been increasing in different mechanical components due to their conspicuous characteristics such as high strength, thermal resistance and optimal distribution of weight. The designer can thus produce structures with favorable stability and manage the distribution of material properties. In this study, the material properties of non-prismatic Timoshenko beams such as Young’s modulus of elasticity and density of material are described by a power-law formulation along the beam axis. Contemplating elastic behavior, the system of equilibrium equations of non-uniform Timoshenko beam and the related boundary conditions are coupled in terms of the vertical displacement and the bending rotation of the cross-section. Afterwards, the system of second-order differential equations with variable coefficients and end conditions are discretized by finite difference formulations with second-order accuracy. Finally, the system of finite difference equations culminates in a set of simultaneous and linear equations and the critical buckling loads and natural frequencies are calculated by solving an eigenvalue problem of the obtained algebraic system. In order to demonstrate the accuracy and reliability of this approach to calculate elastic buckling loads and natural frequencies of functionally graded (FG) Timoshenko beams, one comprehensive example including axially non-homogeneous and homogeneous members with non-uniform cross-section is expressed. The numerical results in clamped-clamped, simply supported and fixed-free boundary conditions are accomplished. Moreover, the effect of various parameters such as volume fraction index, end conditions and the section variation on the elastic buckling and free vibration behavior of AFG Timoshenko beam are investigated in detail.Masoumeh SoltaniBehrouz AsgarianVahid jafari DeliganiIranian Society of Structrual Engineering (ISSE)articletapered timoshenko beamaxially functionally graded materialnatural frequencycritical buckling loadfinite difference methodBridge engineeringTG1-470Building constructionTH1-9745FAJournal of Structural and Construction Engineering, Vol 7, Iss شماره ویژه 3, Pp 185-202 (2020)
institution	DOAJ
collection	DOAJ
language	FA
topic	tapered timoshenko beam axially functionally graded material natural frequency critical buckling load finite difference method Bridge engineering TG1-470 Building construction TH1-9745
spellingShingle	tapered timoshenko beam axially functionally graded material natural frequency critical buckling load finite difference method Bridge engineering TG1-470 Building construction TH1-9745 Masoumeh Soltani Behrouz Asgarian Vahid jafari Deligani Elastic instability and free vibration analyses of axially functionally graded Timoshenko beams with variable cross-section
description	In this paper, the critical buckling loads and natural frequencies of axially functionally graded non-prismatic Timoshenko beam with different boundary conditions are acquired using the Finite Difference Method (FDM). In the recent years, the use of functionally graded materials (FGMs) has been increasing in different mechanical components due to their conspicuous characteristics such as high strength, thermal resistance and optimal distribution of weight. The designer can thus produce structures with favorable stability and manage the distribution of material properties. In this study, the material properties of non-prismatic Timoshenko beams such as Young’s modulus of elasticity and density of material are described by a power-law formulation along the beam axis. Contemplating elastic behavior, the system of equilibrium equations of non-uniform Timoshenko beam and the related boundary conditions are coupled in terms of the vertical displacement and the bending rotation of the cross-section. Afterwards, the system of second-order differential equations with variable coefficients and end conditions are discretized by finite difference formulations with second-order accuracy. Finally, the system of finite difference equations culminates in a set of simultaneous and linear equations and the critical buckling loads and natural frequencies are calculated by solving an eigenvalue problem of the obtained algebraic system. In order to demonstrate the accuracy and reliability of this approach to calculate elastic buckling loads and natural frequencies of functionally graded (FG) Timoshenko beams, one comprehensive example including axially non-homogeneous and homogeneous members with non-uniform cross-section is expressed. The numerical results in clamped-clamped, simply supported and fixed-free boundary conditions are accomplished. Moreover, the effect of various parameters such as volume fraction index, end conditions and the section variation on the elastic buckling and free vibration behavior of AFG Timoshenko beam are investigated in detail.
format	article
author	Masoumeh Soltani Behrouz Asgarian Vahid jafari Deligani
author_facet	Masoumeh Soltani Behrouz Asgarian Vahid jafari Deligani
author_sort	Masoumeh Soltani
title	Elastic instability and free vibration analyses of axially functionally graded Timoshenko beams with variable cross-section
title_short	Elastic instability and free vibration analyses of axially functionally graded Timoshenko beams with variable cross-section
title_full	Elastic instability and free vibration analyses of axially functionally graded Timoshenko beams with variable cross-section
title_fullStr	Elastic instability and free vibration analyses of axially functionally graded Timoshenko beams with variable cross-section
title_full_unstemmed	Elastic instability and free vibration analyses of axially functionally graded Timoshenko beams with variable cross-section
title_sort	elastic instability and free vibration analyses of axially functionally graded timoshenko beams with variable cross-section
publisher	Iranian Society of Structrual Engineering (ISSE)
publishDate	2020
url	https://doaj.org/article/e98c32eaa9b74a7a95e232acc6cca42a
work_keys_str_mv	AT masoumehsoltani elasticinstabilityandfreevibrationanalysesofaxiallyfunctionallygradedtimoshenkobeamswithvariablecrosssection AT behrouzasgarian elasticinstabilityandfreevibrationanalysesofaxiallyfunctionallygradedtimoshenkobeamswithvariablecrosssection AT vahidjafarideligani elasticinstabilityandfreevibrationanalysesofaxiallyfunctionallygradedtimoshenkobeamswithvariablecrosssection
_version_	1718441621011300352

Elastic instability and free vibration analyses of axially functionally graded Timoshenko beams with variable cross-section

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