Startingfromnonlinearequationsonthef-planecontainingfrictionaldissipationundertheBoussinesqapproximation,anewkindofgeneralizedenergyisproposedastheLyapunovfunction,andaveragesaretakenasanyfunctionsof(x,z)insteadofthecommonly-usedmeansofbilinearfunctionsof(x,z),therebyresultinginanewcriterionofgeneralizednonlinearsymmetricstability.Itshowsthatnotonlymustthedissipativecoefficientbegreaterthanacertaincriticalvaluebuttheinitialdisturbanceamplitudemustbesynchronouslysmallerthananothermarginalvalueaswell.Itfollowsthatthelatterimposesacrucialconstraintontheformer,thusleadingtothefactthatwhentheamplitudeisbiggercomparedtoanothercriticalvalue,generalizednonlinearsubcriticalsymmetricalinstabilitymayoccur.Thenewcriterioncontributesgreatlytotheimprovementofthepreviousresultsofitskind.
