Design of optimum systems of viscoelastic vibration absorbers for a given material based on the fractional calculus model

So-called vibration absorbers, which might more appropriately be called vibration neutralizers, are mechanical devices designed to be attached to another mechanical system, or structure, called the primary system, for the purpose of controlling, or reducing, the vibration ( and consequent sound production) of machines, structural surfaces and panels. The cheapest and easiest way to construct a vibration absorber is by incorporating a viscoelastic material, functioning as both the resilient and the energy dissipating component. The viscoelastic material acts as a damped spring. This article sets out to describe how to design an optimal system of viscoelastic absorbers for a known material, through a model using four fractional parameters. A real example, of the design of a system of six viscoelastic vibration absorbers for mitigation of the response to fluid-structure instability in a hydroelectric generator system, is presented and discussed.