Effect of Winkler Elastic Foundation on Free Vibration of Tapered Beam Based on Non-Local Elasticity Theory

In this paper, the influence of Winkler type elastic foundation on the free vibration behavior of non-local Euler-Bernoulli beam with varying cross-section is semi-analytically investigated. For this purpose, the governing equation of motion is derived based on nonlocal elasticity Eringen’s model an...

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Autores principales:	Masoumeh Soltani, Masooma Mohammadi, Behrouz Asgarian
Formato:	article
Lenguaje:	FA
Publicado:	Iranian Society of Structrual Engineering (ISSE) 2021
Materias:	natural frequency non local elasticity theory tapered beam elastic foundation power series method Bridge engineering TG1-470 Building construction TH1-9745
Acceso en línea:	https://doaj.org/article/857a5abe10e34436bf697ce74f84117a
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spelling	oai:doaj.org-article:857a5abe10e34436bf697ce74f84117a2021-11-08T15:54:55ZEffect of Winkler Elastic Foundation on Free Vibration of Tapered Beam Based on Non-Local Elasticity Theory2476-39772538-261610.22065/jsce.2019.176357.1807https://doaj.org/article/857a5abe10e34436bf697ce74f84117a2021-07-01T00:00:00Zhttps://www.jsce.ir/article_99200_2223b7370ec984ce3dfd6e1d6798d0ef.pdfhttps://doaj.org/toc/2476-3977https://doaj.org/toc/2538-2616In this paper, the influence of Winkler type elastic foundation on the free vibration behavior of non-local Euler-Bernoulli beam with varying cross-section is semi-analytically investigated. For this purpose, the governing equation of motion is derived based on nonlocal elasticity Eringen’s model and Hamilton’s principle. The power series approximation is applied to solve the fourth order differential equation, since in the presence of variable cross-section, stiffness quantities are not constant. Based on this semi-analytical methodology, displacement component and cross-section properties should be expanded in terms of power series of a known degree. The natural frequencies of non-local beam with variable cross-section are then derived by imposing the boundary conditions and solving the eigenvalue problem. The results of this research are compared with the obtained results by other researchers and there is a good agreement. At the end, the effects of different parameters such as: end conditions, nonlocal Eringen’s parameter, tapering ratio and Winkler spring constant on non-dimensional natural frequency of nano-beam are studied in detail. The outcomes of this study indicate that the increase of nonlocal parameter and non-uniformity ratio causes to decrease the dimensionless natural frequency. However, with increasing the Winkler elastic constant, the non-local frequencies increase. Furthermore, it is shown that the effect of Winkler elastic foundation is predominate than the tapering ratio and Eringen’s parameter on the natural frequency of nano-beams.Masoumeh SoltaniMasooma MohammadiBehrouz AsgarianIranian Society of Structrual Engineering (ISSE)articlenatural frequency nonlocal elasticity theory tapered beam elastic foundation power series methodBridge engineeringTG1-470Building constructionTH1-9745FAJournal of Structural and Construction Engineering, Vol 8, Iss 5, Pp 237-259 (2021)
institution	DOAJ
collection	DOAJ
language	FA
topic	natural frequency non local elasticity theory tapered beam elastic foundation power series method Bridge engineering TG1-470 Building construction TH1-9745
spellingShingle	natural frequency non local elasticity theory tapered beam elastic foundation power series method Bridge engineering TG1-470 Building construction TH1-9745 Masoumeh Soltani Masooma Mohammadi Behrouz Asgarian Effect of Winkler Elastic Foundation on Free Vibration of Tapered Beam Based on Non-Local Elasticity Theory
description	In this paper, the influence of Winkler type elastic foundation on the free vibration behavior of non-local Euler-Bernoulli beam with varying cross-section is semi-analytically investigated. For this purpose, the governing equation of motion is derived based on nonlocal elasticity Eringen’s model and Hamilton’s principle. The power series approximation is applied to solve the fourth order differential equation, since in the presence of variable cross-section, stiffness quantities are not constant. Based on this semi-analytical methodology, displacement component and cross-section properties should be expanded in terms of power series of a known degree. The natural frequencies of non-local beam with variable cross-section are then derived by imposing the boundary conditions and solving the eigenvalue problem. The results of this research are compared with the obtained results by other researchers and there is a good agreement. At the end, the effects of different parameters such as: end conditions, nonlocal Eringen’s parameter, tapering ratio and Winkler spring constant on non-dimensional natural frequency of nano-beam are studied in detail. The outcomes of this study indicate that the increase of nonlocal parameter and non-uniformity ratio causes to decrease the dimensionless natural frequency. However, with increasing the Winkler elastic constant, the non-local frequencies increase. Furthermore, it is shown that the effect of Winkler elastic foundation is predominate than the tapering ratio and Eringen’s parameter on the natural frequency of nano-beams.
format	article
author	Masoumeh Soltani Masooma Mohammadi Behrouz Asgarian
author_facet	Masoumeh Soltani Masooma Mohammadi Behrouz Asgarian
author_sort	Masoumeh Soltani
title	Effect of Winkler Elastic Foundation on Free Vibration of Tapered Beam Based on Non-Local Elasticity Theory
title_short	Effect of Winkler Elastic Foundation on Free Vibration of Tapered Beam Based on Non-Local Elasticity Theory
title_full	Effect of Winkler Elastic Foundation on Free Vibration of Tapered Beam Based on Non-Local Elasticity Theory
title_fullStr	Effect of Winkler Elastic Foundation on Free Vibration of Tapered Beam Based on Non-Local Elasticity Theory
title_full_unstemmed	Effect of Winkler Elastic Foundation on Free Vibration of Tapered Beam Based on Non-Local Elasticity Theory
title_sort	effect of winkler elastic foundation on free vibration of tapered beam based on non-local elasticity theory
publisher	Iranian Society of Structrual Engineering (ISSE)
publishDate	2021
url	https://doaj.org/article/857a5abe10e34436bf697ce74f84117a
work_keys_str_mv	AT masoumehsoltani effectofwinklerelasticfoundationonfreevibrationoftaperedbeambasedonnonlocalelasticitytheory AT masoomamohammadi effectofwinklerelasticfoundationonfreevibrationoftaperedbeambasedonnonlocalelasticitytheory AT behrouzasgarian effectofwinklerelasticfoundationonfreevibrationoftaperedbeambasedonnonlocalelasticitytheory
_version_	1718441581131857920

Effect of Winkler Elastic Foundation on Free Vibration of Tapered Beam Based on Non-Local Elasticity Theory

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