DESIGN OF OPTIMUM VISCOELASTIC VIBRATION ABSORBERS BASED ON THE FRACTIONAL CALCULUS MODEL

Abstract. The so often called vibration absorbers, which more appropriately should be called vibration neutralizers, are mechanical devices to be attached to another mechanical system, or structure, called the primary system, with the purpose of controlling, or reducing vibration and sound radiation from machines, structural surfaces and panels. The cheapest and easiest way to construct a vibration neutralizer is by incorporating a viscoelastic material, both as the resilient and energy dissipating part. A major problem in the analysis and design of such neutralizers is that, when applied to a structure, they render equations with coefficients dependent on frequency. Such a difficult problem was first efficiently solved by Espíndola and Silva (1992), with the introduction of a new concept of generalized quantities for the neutralizer. Espíndola and Bavastri used such a concept for the design of optimum viscoelastic neutralizers systems, first using techniques of non-linear optimization (1997) and, subsequently, a hybrid technique combining both genetic algorithm and non-linear optimization (1998). A difficult question still remained after the computation of the optimum parameters: the selection of a proper viscoelastic material to match such parameters. This question has been solved recently by the authors of this paper with the help of the four parameter fractional model for the viscoelastic part of the neutralizers. This paper sets out to describe such a solution. In the output, one has th