简介：ThenonlinearvibrationsofviscoelasticEuler–BernoullinanobeamsarestudiedusingthefractionalcalculusandtheGurtin–Murdochtheory.EmployingHamilton'sprinciple,thegoverningequationconsideringsurfaceeffectsisderived.Thefractionalintegro-partialdifferentialgoverningequationisfirstconvertedintoafractional–ordinarydifferentialequationinthetimedomainusingtheGalerkinscheme.Thereafter,thesetofnonlinearfractionaltime-dependentequationsexpressedinastate-spaceformissolvedusingthepredictor–correctormethod.Finally,theeffectsofinitialdisplacement,fractionalderivativeorder,viscoelasticitycoefficient,surfaceparametersandthickness-to-lengthratioonthenonlineartimeresponseofsimply-supportedandclamped-freesiliconviscoelasticnanobeamsareinvestigated.