Inthiswork,sandwichbeamsarestudiedtorevealtheunderlyingsizeeffectsoftheperiodiccorecellsforthefirsttimewithintheframeworkoffreevibrationanalysisofsuchanadvancedlightweightstructure.Theenergyequivalencemethodisformulatedasatheoreticalapproachthattakesintoaccountthecellsizeeffect.Itiscomparedwiththeasymptotichomogenizationmethodanddirectfiniteelementmethodsystematicallytoshowtheirconsistenceandapplicability.Theaccuracyoffreevibrationresponsespredictedbythedetailedfiniteelementmodelisusedasthestandardofcomparison.Itisshownthatthecellsizeisanimportantparametercharacterizingthecellularcorerigiditiesthatinfluencevibrationresponses.Thehomogenizationmodelagreesexactlywiththeasymptoticsolutionoftheanalyticalexpressionofthebeammodelonlywheneverthecellsizetendstobeinfinitelysmall.
