Caracterização de modelos fenomenológicos de amortecimento viscoelástico em sistemas vibratórios: uma abordagem Bayesiana

Abstract

Advanced damping materials, due to their ability to dissipate energy, have been increasingly employed on the vibration control of mechanical vibrations.The conception, design and real-time operation of such sort of strategy heavily relies upon modeling and computational simulation. Computer models, typically, result from the combination of physical principles (e.g momentum balance) with closure phenomenological equations (e.g.constitutive equations).In this work the attention has been devoted to limitations in computer model predictions due to potential discrepancies related to such closure equations.We propose here two different approaches aiming at evaluating the ability of constitutive models employing internal variables to reproduce viscoelastic and damping response of vibrating systems undergoing small deformations.Both approaches are built within Bayesian settings, and they differ in the way model discrepancy is introduced and modeled. In the first one employ a hypothesis of stochastic model error embedded in the damping parameters, while in the second we use a more conventional formulation based on additive model error hypothesis included in the observation equation relating state variables to observables. We present preliminary results obtained with numerical examples show that the proposed formulations establish a formal and rigorous basis for performing the study, although they also point to the need of a more comprehensive analysis, especially regarding the flexibility of embedded model error approach to accommodate more sophisticated stochastic modeling for the discrepancy modeling.