Análise transiente de sistemas tratados com materiais viscoelásticos através de um modelo de derivadas fracionárias melhorado e uma técnica de redução

Abstract

Vibration control is an important field in the study of structures, and one of the ways often used to mitigate structural oscillations is passive control using viscoelastic materials. The properties of these materials are strongly dependent on environmental factors, mainly on the temperature and frequency of excitation, so that the models for the characterization of their dynamic behavior must be able to represent this dependence. In this sense, this work presents the application of an improved fractional derivative model in the time domain analysis of some structures treated with viscoelastic material, and the application of a model reduction technique. To this purpose, finite element modeling of two types of structures: a beam and a frame is carried out. The viscoelastic effects were incorporated through the FDM, capable of eliminating self-dependence in the stress field by including a recurrence term, which reduces the computational cost. Through this procedure it was possible to represent the transient behavior of the structure and analyze the influence of several parametric variations. The numerical simulations presented in this work demonstrate the effectiveness of the model and the reduction technique, which was able to reduce the computational analysis time in about 95%. It is worth mentioning that this reduction may be even greater in more complex structures of industrial interest. In addition, the model reduction method presented can be used in other dynamic systems that do not have viscoelastic damping