Optimal design of a beam-based dynamic vibration absorber using fixed-points theory

Abstract

The addition of a dynamic vibration absorber (DVA) to a vibrating structure could provide an economic solution for vibration suppressions if the absorber is properly designed and located onto the structure. A common design of the DVA is a sprung mass because of its simple structure and low cost. However, the vibration suppression performance of this kind of DVA is limited by the ratio between the absorber mass and the mass of the primary structure. In this paper, a beam-based DVA (beam DVA) is proposed and optimized for minimizing the resonant vibration of a general structure. The vibration suppression performance of the proposed beam DVA depends on the mass ratio, the flexural rigidity and length of the beam. In comparison with the traditional sprung mass DVA, the proposed beam DVA shows more flexibility in vibration control design because it has more design parameters. With proper design, the beam DVA's vibration suppression capability can outperform that of the traditional DVA under the same mass constraint. The general approach is illustrated using a benchmark cantilever beam as an example. The receptance theory is introduced to model the compound system consisting of the host beam and the attached beam-based DVA. The model is validated through comparisons with the results from Abaqus as well as the Transfer Matrix method (TMM) method. Fixed-points theory is then employed to derive the analytical expressions for the optimum tuning ratio and damping ratio of the proposed beam absorber. A design guideline is then presented to choose the parameters of the beam absorber. Comparisons are finally presented between the beam absorber and the traditional DVA in terms of the vibration suppression effect. It is shown that the proposed beam absorber can outperform the traditional DVA by following this proposed guideline.