Modelagem numérico-computacional de sistema multicorpos flexíveis contendo materiais viscoelásticos

Abstract

This dissertation deals with the dynamic modeling of flexible multibody systems subjected to viscoelastic damping for the purpose of passive vibration control. Accounting for the fact that the large majority of previous research work has been focused on viscoelastic vibration control of fixed-geometry structures, the main goals of this essay are: i) to integrate, sistematically, the formulation pertaining to the various aspects addressed in the derivation of the numerical models of viscoelastic flexible multibody systems, namely: Lagrangean approach as applied to flexible multibody systems, finite element discretization, viscoelastic constitutive models, algorithms for numerical solution of differential-algebraic systems of equations; ii) to implement and validate computer codes intended for the dynamics simulation of flexible multibody systems containing viscoelastic elements; iii) to appraise, through numerical simulations, the effectiveness of viscoelastic treatments in terms of vibration mitigation of two types of mechanical systems, namely: closed-chain plane mechanisms and spacecraft containing flexible appendages. A constitutive law based of fractional derivatives is considered for the modeling of the viscoelastic behavior. Both the Finite Element Method, associated to floating reference frames, and the Assumed Modes Method are used to perform spatial discretization of the equations of motion. Numerical simulations are accomplished for two different multibody systems: a plane flexible four bar linkage, and an artifitial satellite containing flexible appendages and attitude control based on a reaction wheel. The results obtained from numerical integration of the nonlinear dynamic equations of motion enabled to evaluate the influence of the components compliance on the dynamic responses. They also prove that viscoelastic treatments can be effectively implemented.