Dynamic analysisofframeswithviscoelasticdampersmodelledby rheologicalmodelswithfractionalderivatives

摘要

Frame structureswithviscoelasticdampersmountedonthemareconsideredinthispaper. Viscoelastic(VE)dampersaremodelledusingtwo,three-parameter,fractionalrheological models.Thestructuresaretreatedaselasticlinearsystems.Theequationofmotionofthe whole system(structurewithdampers)iswrittenintermsofstate-spacevariables.The resultingmatrixequationofmotionisthefractionaldifferentialequation.Theproposed state spaceformulationisnewanddoesnotrequirematriceswithhugedimensions.The paper isdevotedtodeterminethedynamicpropertiesoftheconsideredstructures. The nonlineareigenvalueproblemisformulatedfromwhichthedynamicparametersof the systemcanbedetermined.Thecontinuationmethodisusedtosolvethenonlinear eigenvalueproblem.Moreover,resultsoftypicalcalculationsarepresented.