Lie group theory and analytical solutions for the axially accelerating string problem

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dc.contributor.authorÖzkaya E.
dc.contributor.authorPakdemirli M.
dc.date.accessioned2024-07-22T08:25:37Z
dc.date.available2024-07-22T08:25:37Z
dc.date.issued2000
dc.description.abstractTransverse vibrations of a string moving with time-dependent velocity v(t) have been investigated. Analytical solutions of the problem are found using the systematic approach of Lie group theory. Group classification with respect to the arbitrary velocity function has been performed using a newly developed technique of equivalence transformations. From the symmetries of the partial differential equation, the method for deriving exact solutions for the arbitrary velocity case is shown. Special cases of interest such as constant velocity, constant acceleration, harmonically varying velocity and exponentially decaying velocity are investigated in detail. Finally, for a simply supported strip, approximate solutions are presented for the exponentially decaying and harmonically varying cases.
dc.identifier.DOI-ID10.1006/jsvi.1999.2651
dc.identifier.issn0022460X
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/20505
dc.language.isoEnglish
dc.publisherAcademic Press Ltd
dc.subjectAcceleration
dc.subjectApproximation theory
dc.subjectMathematical transformations
dc.subjectNumerical methods
dc.subjectPartial differential equations
dc.subjectVelocity
dc.subjectArbitrary velocity function
dc.subjectAxially accelerating string problem
dc.subjectLie group theory
dc.subjectTime dependent velocity
dc.subjectTransverse vibrations
dc.subjectVibrations (mechanical)
dc.titleLie group theory and analytical solutions for the axially accelerating string problem
dc.typeArticle

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