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1、Chapter21Fluid-structureInteractionProblemsRogerOhayonConservatoireNationaldesArtsetM´etiers(CNAM),Paris,FranceWereviewinthispaperreducedordermodelsformodal1Introduction683analysisofelasticstructurescontaininganinviscidfluid2Structural-acousticProblem684(gasorliquid).Thesemethods,basedonRitzGalerk
2、inprojectionusingappropriateRitzvectors,allowusto3Structural-acousticEquations684constructreducedmodelsexpressedintermsofphysical-4IncompressibleHydroelastic-sloshingProblem689displacementvectorfielduinthestructure,andgeneralized-5Hydroelastic-sloshingEquations689displacementvectorrdescribingthebe
3、haviorofthefluid.6Conclusion692Thosereducedmodelsleadtounsymmetric(CraggsandReferences692Stead,1976;SungandNefske,1986)orsymmetricgen-FurtherReading693eralizedeigenvaluematrixsystem(MorandandOhayon,1979,1995;Ohayon,2001)involvingareducednumberofdegreesoffreedomforthefluid.Forthispurpose,wecon-struc
4、tsymmetricmatrixmodelsofthefluidconsideredasa1INTRODUCTIONsubsystem,byconsideringtheresponseofthefluidtoapre-scribednormaldisplacementofthefluid-structureinterface.Fluid-structurevibrationsoccurinvarioussituations,inTwodistinctsituationsareanalyzed.Ononehand,weaerospace,automotive,civilengineeringar
5、easaswellasinconsiderlinearvibrationsofanelasticstructurecompletelybiomechanics.Forageneraloverviewofaerospaceinteriorfilledwithacompressiblegasorliquidand,ontheotherfluid-structureproblems,wereferforinstancethereadertohand,weconsiderthecaseofanelasticstructurecontain-Abramson(1966).inganincompress
6、ibleliquidwithfree-surfaceeffectsdueThecomputationalaspectsconcerningthelinearvibra-togravity.toryresponseoffluid-structuresystemstoprescribedloadsThefirstcaseisastructural-acousticproblem.Inthemaylead,forcomplexstructures,toaprohibitivenumbercaseofastructurecontainingagas,weconsideramodalofdegrees
7、offreedom.Inordertoquantifytheweakorinteractionbetweenstructuralmodesinvacuoandacousticstronginteractionsofthecoupledfluid-structuresystem,modesinrigidmotionlesscavity.Forastructurecontain-inordertocarryoutsensitivityan
