Dynamical Analysis Of Viscoelastic Materials Using Prony Series And GHM Viscoelastic Models

The analysis of rheological models in engineering has definitely been a main focusof research in the last3decades. Since material modeling and mathematical analysishave become very sophisticated, the incursion of new techniques to improve theaccuracy of the simulation and prediction of the behavior of viscoelastic materials in adynamical environment.The use of viscoelastic materials in structures is justified in order to add damping tothese materials. Several models have been developed by many researchers throughoutthe world, but in this paper, we will concentrate on the application of the rheologicalmodel GHM (Golla-Hughes-McTavish) and the Maxwell viscoelastic model, whichintroduces the use of extra dissipation coordinates to allow the canonical forms of theMass and Stiffness matrices of the undamped motion equation are expanded toencompass viscoelastic damping.Two main sets detailing different cases of study will be presented here. The first setof cases will consist on analyzing in deep the viscoelastic properties of two materials byusing both the GHM and Maxwell models. The second set of studies will deal with theFinite Element Analysis formulation of three viscoelastic elements is the2Drepresentation of a rubber bushing that will simulate axial deformation. The effects ofthe viscoelastic properties of this model and its behavior under cyclic loads will beanalyzed. The second set of cases of study will consist on analyzing the dynamics of atire model using Maxwell viscoelastic model. The aim of this study is to simplydemonstrate the importance of choosing the adequate parameters and, the necessity fordeveloping a mathematical formulation combined with the development of robustMATLAB routines in order to approximate the results as close as possible to apply thisformulation in a real case of study. A set of real cases of application will consist on thefinite element analysis formulation of a3D tire model and a3D air spring model usingthe CAE interface of ABAQUS.