简介：Thispaperdealswiththefreevibrationanalysisofcircularalumina(Al2O3)nanobeamsinthepresenceofsurfaceandthermaleffectsrestingonaPasternakfoundation.ThesystemofmotionequationsisderivedusingHamilton'sprincipleundertheassumptionsoftheclassicalTimoshenkobeamtheory.Theeffectsofthetransversesheardeformationandrotaryinertiaarealsoconsideredwithintheframeworkofthementionedtheory.Theseparationofvariablesapproachisemployedtodiscretizethegoverningequationswhicharethensolvedbyananalyticalmethodtoobtainthenaturalfrequenciesofthealuminananobeams.TheresultsshowthatthesurfaceeffectsleadtoanincreaseinthenaturalfrequencyofnanobeamsascomparedwiththeclassicalTimoshenkobeammodel.Inaddition,fornanobeamswithlargediameters,thesurfaceeffectsmayincreasethenaturalfrequenciesbyincreasingthethermaleffects.Moreover,withregardtothePasternakelasticfoundation,thenaturalfrequenciesareincreasedslightly.Theresultsofthepresentmodelarecomparedwiththeliterature,showingthatthepresentmodelcancapturecorrectlythesurfaceeffectsinthermalvibrationofnanobeams.

简介：Variousmesoporouschromiaaluminacatalystswerepreparedbyfivedifferentmethodsbasedonametal-organicframeworkMIL-101andtheircatalyticperformancesoverisobutanedehydrogenationwereinvestigated.ThehighlydispersedchromiumspecieswereproducedoncatalystKCrAl-I1withlargestspecificsurfaceareaof198m2g-1preparedwithaluminiumisopropoxide(Al(i-OC3H7)3)byultrasonicimpregnationmethod.However,thecatalystKCrAl-I2synthesizedbystirringimpregnationpossessedcrystallineα-Cr2O3phase,whichwaspoorlydispersed.TwotypesofCr-richandAl-richCrxAl2-xO3solidsolutions,designatedasCrAl-IandCrAl-IIphase,wereformedoverthecatalystsKCrAl-I3(preparedbyAl(i-OC3H7)3withnitricacidregulation),KCrAl-C4(preparedbyaluminiumchloridehexahydrate)andKCrAl-N5(preparedbyaluminiumnitratenonahydrate).CatalyticevaluationresultsrevealedthatKCrAl-I1exhibitedthehighisobutaneconversionduetoitshighlydispersedchromiumspecies.However,KCrAl-I3,KCrAl-C4andKCrAl-N5showedthehigherisobuteneselectivity(95.2%-96.4%)onaccountoftheformationofchromiaaluminasolidsolutionsinthecatalysts.Moreover,thesolidsolutionoverthechromiaaluminacatalystscouldgreatlysuppressthecokeformation.