Asymptotic Approximations of the Solution for a Traveling String under Boundary Damping
Transversal vibrations of an axially moving string under boundary damping are investigated. Mathematically, it represents a homogenous linear partial differential equation subject to nonhomogeneous boundary conditions. The string is moving with a relatively (low) constant speed, which is considered...
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Shahid Chamran University of Ahvaz
2019-10-01
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doaj-ad6e7acab81047979b5de63e52746aa42020-11-25T01:13:43ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362383-45362019-10-015591892510.22055/jacm.2019.28331.147714288Asymptotic Approximations of the Solution for a Traveling String under Boundary DampingRajab A. Malookani0Sanaullah Dehraj1Sajad H. Sandilo2Department of Mathematics and Statistics, Faculty of Science, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah, 67480, Sindh, PakistanDepartment of Mathematics and Statistics, Faculty of Science, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah, 67480, Sindh, PakistanDepartment of Mathematics and Statistics, Faculty of Science, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah, 67480, Sindh, PakistanTransversal vibrations of an axially moving string under boundary damping are investigated. Mathematically, it represents a homogenous linear partial differential equation subject to nonhomogeneous boundary conditions. The string is moving with a relatively (low) constant speed, which is considered to be positive. The string is kept fixed at the first end, while the other end is tied with the spring-dashpot system. The asymptotic approximations for the solution of the equations are obtained by application of two time-scale perturbation technique and the characteristic coordinates method. The vertical displacement of the moving system under boundary damping is computed by using specific initial conditions. It is shown that how the introduced damping at the boundary may affect the vertical displacement of the axially moving system.http://jacm.scu.ac.ir/article_14288_a94764af63010312a7e43c6d36a1c4cd.pdfAxially moving stringBoundary dampingTwo time-scale perturbationCharacteristic coordinates |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Rajab A. Malookani Sanaullah Dehraj Sajad H. Sandilo |
spellingShingle |
Rajab A. Malookani Sanaullah Dehraj Sajad H. Sandilo Asymptotic Approximations of the Solution for a Traveling String under Boundary Damping Journal of Applied and Computational Mechanics Axially moving string Boundary damping Two time-scale perturbation Characteristic coordinates |
author_facet |
Rajab A. Malookani Sanaullah Dehraj Sajad H. Sandilo |
author_sort |
Rajab A. Malookani |
title |
Asymptotic Approximations of the Solution for a Traveling String under Boundary Damping |
title_short |
Asymptotic Approximations of the Solution for a Traveling String under Boundary Damping |
title_full |
Asymptotic Approximations of the Solution for a Traveling String under Boundary Damping |
title_fullStr |
Asymptotic Approximations of the Solution for a Traveling String under Boundary Damping |
title_full_unstemmed |
Asymptotic Approximations of the Solution for a Traveling String under Boundary Damping |
title_sort |
asymptotic approximations of the solution for a traveling string under boundary damping |
publisher |
Shahid Chamran University of Ahvaz |
series |
Journal of Applied and Computational Mechanics |
issn |
2383-4536 2383-4536 |
publishDate |
2019-10-01 |
description |
Transversal vibrations of an axially moving string under boundary damping are investigated. Mathematically, it represents a homogenous linear partial differential equation subject to nonhomogeneous boundary conditions. The string is moving with a relatively (low) constant speed, which is considered to be positive. The string is kept fixed at the first end, while the other end is tied with the spring-dashpot system. The asymptotic approximations for the solution of the equations are obtained by application of two time-scale perturbation technique and the characteristic coordinates method. The vertical displacement of the moving system under boundary damping is computed by using specific initial conditions. It is shown that how the introduced damping at the boundary may affect the vertical displacement of the axially moving system. |
topic |
Axially moving string Boundary damping Two time-scale perturbation Characteristic coordinates |
url |
http://jacm.scu.ac.ir/article_14288_a94764af63010312a7e43c6d36a1c4cd.pdf |
work_keys_str_mv |
AT rajabamalookani asymptoticapproximationsofthesolutionforatravelingstringunderboundarydamping AT sanaullahdehraj asymptoticapproximationsofthesolutionforatravelingstringunderboundarydamping AT sajadhsandilo asymptoticapproximationsofthesolutionforatravelingstringunderboundarydamping |
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1725160444424880128 |