Vibrationofacircularmembraneincontactwithafluidhasextensiveapplicationsinindustry.Thenaturalvibrationfrequenciesfortheasymmetricfreevibrationofacircularmembraneincontactwithaboundedincompressiblefluidarederivedinthispaper.Consideringsmalloscillationsinducedbythemembranevibrationinanincompressibleandinviscidfluid,thevelocitypotentialfunctionisusedtodescribethefluidfield.Twoapproachesareusedtoderivethefreevibrationfrequenciesofthesystem,whichincludeavariationalformulationandanapproximatesolutionemployingtheRayleighquotientmethod.Agoodcorrelationisfoundbetweenfreevibrationfrequenciesevaluatedbythesemethods.Finally,theeffectsofthefluiddepth,themassdensity,andtheradialtensiononthefreevibrationfrequenciesofthecoupledsystemareinvestigated.
