Title of article
CalculatinglatentfrequenciesofsystemswithlocaldampingOriginalResearchArticle
Author/Authors
FerencKolonits، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2005
Pages
6
From page
2003
To page
2008
Abstract
Modalanalysisofdampedsystemsoftencannotproceedwithcommonreal-eigenvaluetechniques.Thesystemofequilibriumequationsleadstoamatrixwithelementsbeingquadraticfunctionsofaparameterλ.Thevaluesofthatwhichmakethematrixsingulararethelatentroots,whilethesolutionsoftheassociatedhomogenousequationarethelatentvectors.Theyarethe(generallycomplex)characteristicfrequenciesandthemodeshapesofthesystem,respectively.Althoughthetheoryiswelldeveloped,thenumericalapplicationisopentorefinementsyet.Areductiontobetter-knownreal-domainsubtasksdeservesattention.WithatheoremofPopperandGáspár,an×nλ-matrixproblemcanbecutintwo:inton-sizeasymmetricrealmatriceshavingaseigenvaluesthenlowerandnupperlatentroots,rankedbyabsolutevalue.Thisapproachmaybeofuseforsystemswithhighnumberofdegreesoffreedomwhiledampedbyarelativelyfewconcentrateddevices.Itmightfitalsoanearthquakeanalysis,wherethelowerportionofeigenvaluesiscustomarilywhatcounts.Thedampersappearinthesplittingalgorithmasrestricted-sizemodifications,readyforusebytheSherman–Morrison–Woodburyidentity.Thetaskisre-tracedthiswaytoamoreusualreal-asymmetriceigenproblem.Arequirementofconvergenceisthattheloweranduppern-setoflatentvaluesmustbedistinct.Withodd-numberdegreesoffreedomandneitherover-damped,i.e.alllatentrootsbeingcomplex,thisconditionissurelyviolated.Forsuchcases,asupplementalalgorithmisproposed.
Journal title
Nuclear Engineering and Design Eslah
Serial Year
2005
Journal title
Nuclear Engineering and Design Eslah
Record number
895923
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