A methodology for identifying optimum vibration absorbers with a reaction mass

Tuned mass dampers (TMDs), in which a reaction mass is attached to a structural system via a spring–parallel–damper connection, are commonly used in a wide range of applications to suppress deleterious vibrations. Recently, a mass-included absorber layout with an inerter element, termed the tuned mass damper inerter (TMDI), was introduced, showing significant performance benefits on vibration suppression. However, there are countless mass-included absorber layouts with springs, dampers and inerters, which could potentially provide more preferred dynamic properties. Currently, because there is no systematic methodology for accessing them, only an extremely limited number of mass-included absorber layouts have been investigated. This paper proposes an approach to identify optimum vibration absorbers with a reaction mass. Using this approach, a full class of absorber layouts with a reaction mass and a pre-determined number of inerters, dampers and springs connected in series and parallel, can be systematically investigated using generic Immittance-Function-Networks. The advantages of the proposed approach are demonstrated via a 3 d.f. structure example.