On Stability Analysis of Linear Axially Moving Damped Beam with Elastic Foundation

This study investigates the dynamical behavior of an axially moving beam with elastic foundation under viscous damping. The beam is taken to be simply supported at the ends. Axial speed of beam is assumed to be time-dependent function about a relatively low mean constant speed. The motion of axially...

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Main Authors: Ghulam Yameen Mallah, Rajab Ali Malookani, Sajad Hussain Sandilo, Sanaullah Dehraj
Format: Article
Language:English
Published: Wiley 2024-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2024/8893138
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author Ghulam Yameen Mallah
Rajab Ali Malookani
Sajad Hussain Sandilo
Sanaullah Dehraj
author_facet Ghulam Yameen Mallah
Rajab Ali Malookani
Sajad Hussain Sandilo
Sanaullah Dehraj
author_sort Ghulam Yameen Mallah
collection DOAJ
description This study investigates the dynamical behavior of an axially moving beam with elastic foundation under viscous damping. The beam is taken to be simply supported at the ends. Axial speed of beam is assumed to be time-dependent function about a relatively low mean constant speed. The motion of axially moving beam in the term of transverse vibrations is expressed in the fourth-order linear and homogeneous partial differential equations with variable coefficients. The governing equations of motion are solved by using the two timescales perturbation method together with the Fourier expansion method. The sum and difference-type resonances are taken to examine the stability of the system. The influence of the parameters such as damping and stiffness of foundation on the transverse amplitude response of the system is seen. It is found out that the system is stable with the increase in damping.
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institution Kabale University
issn 1687-9651
language English
publishDate 2024-01-01
publisher Wiley
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series International Journal of Differential Equations
spelling doaj-art-47dfb683358a4e5aa76087daae08a99e2025-02-03T01:30:23ZengWileyInternational Journal of Differential Equations1687-96512024-01-01202410.1155/2024/8893138On Stability Analysis of Linear Axially Moving Damped Beam with Elastic FoundationGhulam Yameen Mallah0Rajab Ali Malookani1Sajad Hussain Sandilo2Sanaullah Dehraj3Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsThis study investigates the dynamical behavior of an axially moving beam with elastic foundation under viscous damping. The beam is taken to be simply supported at the ends. Axial speed of beam is assumed to be time-dependent function about a relatively low mean constant speed. The motion of axially moving beam in the term of transverse vibrations is expressed in the fourth-order linear and homogeneous partial differential equations with variable coefficients. The governing equations of motion are solved by using the two timescales perturbation method together with the Fourier expansion method. The sum and difference-type resonances are taken to examine the stability of the system. The influence of the parameters such as damping and stiffness of foundation on the transverse amplitude response of the system is seen. It is found out that the system is stable with the increase in damping.http://dx.doi.org/10.1155/2024/8893138
spellingShingle Ghulam Yameen Mallah
Rajab Ali Malookani
Sajad Hussain Sandilo
Sanaullah Dehraj
On Stability Analysis of Linear Axially Moving Damped Beam with Elastic Foundation
International Journal of Differential Equations
title On Stability Analysis of Linear Axially Moving Damped Beam with Elastic Foundation
title_full On Stability Analysis of Linear Axially Moving Damped Beam with Elastic Foundation
title_fullStr On Stability Analysis of Linear Axially Moving Damped Beam with Elastic Foundation
title_full_unstemmed On Stability Analysis of Linear Axially Moving Damped Beam with Elastic Foundation
title_short On Stability Analysis of Linear Axially Moving Damped Beam with Elastic Foundation
title_sort on stability analysis of linear axially moving damped beam with elastic foundation
url http://dx.doi.org/10.1155/2024/8893138
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AT rajabalimalookani onstabilityanalysisoflinearaxiallymovingdampedbeamwithelasticfoundation
AT sajadhussainsandilo onstabilityanalysisoflinearaxiallymovingdampedbeamwithelasticfoundation
AT sanaullahdehraj onstabilityanalysisoflinearaxiallymovingdampedbeamwithelasticfoundation