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1 Introduction Totheauthors’knowledge ,therearerarelypapersconcerningthedynamicbehaviorofviscoelasticshells.Uptonowmostofworkwasconcernedwiththestabilityofviscoelasticshells.Potapov ( 1978) [1]studiedthestabilityofcompressedviscoelasticor thotropicshells.