Variational principle and bifurcations in stability analysis of panels
dc.contributor.author | Banichuk, Nikolay | |
dc.contributor.author | Barsuk, Alexander | |
dc.contributor.author | Tuovinen, Tero | |
dc.contributor.author | Jeronen, Juha | |
dc.date.accessioned | 2014-12-17T10:23:38Z | |
dc.date.available | 2014-12-17T10:23:38Z | |
dc.date.issued | 2014 | |
dc.identifier.other | oai:jykdok.linneanet.fi:1453772 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/44934 | |
dc.description.abstract | In this paper, the stability of a simply supported axially moving elastic panel is considered. A complex variable technique and bifurcation theory are applied. As a result, variational equations and a variational principle are derived. Anal- ysis of the variational principle allows the study of qualitative properties of the bifurcation points. Asymptotic behaviour in a small neighbourhood around an arbitrary bifurcation point is analyzed and presented. It is shown analytically that the eigenvalue curves in the (ω, V0) plane cross both the ω and V0 axes perpendicularly. It is also shown that near each bifur- cation point, the dependence ω(V0) for each mode approximately follows the shape of a square root near the origin. The obtained results complement existing numerical studies on the stability of axially moving materials, especially those with finite bending rigidity. From a rigorous mathematical viewpoint, the presence of bending rigidity is essen- tial, because the presence of the fourth-order term in the model changes the qualitative behaviour of the bifurcation points. | fi |
dc.format.extent | Verkkoaineisto (14 s.) | |
dc.language.iso | eng | |
dc.publisher | Jyväskylän yliopisto | |
dc.relation.ispartofseries | Reports of the Department of Mathematical Information Technology / University of Jyväskylä. Series B, Scientific computing | |
dc.subject.other | bifurkaatio | |
dc.subject.other | variational principle | |
dc.subject.other | bifurcation | |
dc.subject.other | stability analysis | |
dc.title | Variational principle and bifurcations in stability analysis of panels | |
dc.type | book | |
dc.identifier.urn | URN:ISBN:978-951-39-6018-6 | |
dc.type.dcmitype | Text | en |
dc.relation.issn | 1456-436X | |
dc.relation.numberinseries | 8/2014 | |
dc.rights.accesslevel | openAccess | fi |
dc.subject.yso | lujuusoppi | |
dc.subject.yso | dynamiikka | |
dc.subject.yso | vakavuus | |
dc.subject.yso | kimmoisuus | |
dc.subject.yso | matemaattiset mallit | |
dc.subject.yso | variaatiolaskenta |