Uniform Decay for Solutions of an Axially Moving Viscoelastic Beam
The paper deals with an axially moving viscoelastic structure modeled as an Euler–Bernoulli beam. The aim is to suppress the transversal displacement (transversal vibrations) that occur during the axial motion of the beam. It is assumed that the beam is moving with a constant axial speed and it is s...
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| Published in | Applied mathematics & optimization Vol. 75; no. 3; pp. 343 - 364 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.06.2017
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0095-4616 1432-0606 |
| DOI | 10.1007/s00245-016-9334-8 |
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| Abstract | The paper deals with an axially moving viscoelastic structure modeled as an Euler–Bernoulli beam. The aim is to suppress the transversal displacement (transversal vibrations) that occur during the axial motion of the beam. It is assumed that the beam is moving with a constant axial speed and it is subject to a nonlinear force at the right boundary. We prove that when the axial speed of the beam is smaller than a critical value, the dissipation produced by the viscoelastic material is sufficient to suppress the transversal vibrations. It is shown that the rate of decay of the energy depends on the kernel which arise in the viscoelastic term. We consider a general kernel and notice that solutions cannot decay faster than the kernel. |
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| AbstractList | The paper deals with an axially moving viscoelastic structure modeled as an Euler-Bernoulli beam. The aim is to suppress the transversal displacement (transversal vibrations) that occur during the axial motion of the beam. It is assumed that the beam is moving with a constant axial speed and it is subject to a nonlinear force at the right boundary. We prove that when the axial speed of the beam is smaller than a critical value, the dissipation produced by the viscoelastic material is sufficient to suppress the transversal vibrations. It is shown that the rate of decay of the energy depends on the kernel which arise in the viscoelastic term. We consider a general kernel and notice that solutions cannot decay faster than the kernel. |
| Author | Tatar, Nasser-eddine Kelleche, Abdelkarim |
| Author_xml | – sequence: 1 givenname: Abdelkarim surname: Kelleche fullname: Kelleche, Abdelkarim email: kellecheabdelkarim@gmail.com organization: Faculté des Mathématiques, Université des Sciences et de la Technologie Houari Boumediene – sequence: 2 givenname: Nasser-eddine surname: Tatar fullname: Tatar, Nasser-eddine organization: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals |
| BackLink | https://www.osti.gov/biblio/22617044$$D View this record in Osti.gov |
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| CitedBy_id | crossref_primary_10_1007_s12555_019_0592_5 crossref_primary_10_1080_00036811_2016_1277708 crossref_primary_10_1002_mma_6932 crossref_primary_10_3846_13926292_2017_1376295 crossref_primary_10_1002_mma_4452 |
| Cites_doi | 10.1016/j.na.2004.11.007 10.1103/RevModPhys.33.239 10.1016/0016-0032(74)90104-5 10.1137/S0363012901380961 10.1016/0022-0396(70)90101-4 10.4134/JKMS.2005.42.6.1137 10.1115/1.2893942 10.1007/s10440-008-9257-8 10.4134/JKMS.2012.49.5.947 10.1109/3516.891053 10.1002/mma.512 10.1109/9.668828 10.1155/S1048953395000049 10.1137/1.9781611970807 10.1016/j.amc.2009.08.034 10.1007/BF00256456 10.1090/S0033-569X-06-01010-4 10.1007/s00009-012-0177-5 10.1007/s00033-008-8030-1 10.1016/j.aml.2008.04.005 10.1063/1.3533766 10.1109/CDC.1998.762038 10.1002/mma.1018 10.5209/rev_REMA.2001.v14.n1.17057 |
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| DOI | 10.1007/s00245-016-9334-8 |
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| Keywords | Viscoelasticity Nonlinear force Euler–Bernoulli beam Arbitrary decay Moving structure |
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| Snippet | The paper deals with an axially moving viscoelastic structure modeled as an Euler–Bernoulli beam. The aim is to suppress the transversal displacement... The paper deals with an axially moving viscoelastic structure modeled as an Euler-Bernoulli beam. The aim is to suppress the transversal displacement... |
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| SubjectTerms | BEAMS Beams (structural) Boundaries Calculus of Variations and Optimal Control; Optimization CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Constants Control DECAY Decay rate ELASTICITY KERNELS Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models MATHEMATICAL SOLUTIONS Mathematics Mathematics and Statistics NONLINEAR PROBLEMS Numerical and Computational Physics SIMULATION Systems Theory Theoretical VELOCITY Vibration Viscoelasticity VISCOSITY |
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| Title | Uniform Decay for Solutions of an Axially Moving Viscoelastic Beam |
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