Estudo do cálculo fracionário aplicado à modelagem de sistemas vibratórios com amortecimento viscoelástico

Abstract

Fractional Calculus is a mathematical tool that has been applied to various problems of Science and Engineering, such Rheology, Heat Transfer and Active Control. Essentially, fraction integration and derivation can be regarded as extensions of the traditional concepts of integration and derivation of integer orders. Their application is justified mainly by the fact that their properties can provide more accurate modeling of certain physical phenomena. The present dissertation addresses the use of Fractional Calculus for the modeling of viscoelastic behavior in the realm of Structural Dynamics. First, it is presented the fundamental concepts and main properties of fraction integrators and derivatives, followed by the description of some methods intended for the resolution of systems of fractional differential equations. Then, a review of linear viscoelasticity is presented, including classical rheological models and fractional models. Aiming at simulating the dynamic behavior of structural systems containing viscoelastic dampers in the time domain, two strategies, considered as being some of the most modern ones, are used for the incorporation of fractional viscoelastic models into finite element models. Numerical simulations are performed aiming at the validation of the modeling procedures.