Supporting brace sizing in structures with added linear viscous fluid dampers: A filter design solution

Viscous fluid dampers have proved to be effective in suppressing unwanted vibrations in a range of engineering structures. When dampers are fitted in a structure, a brace is typically used to attach them to the main structure. The stiffness of this brace can significantly alter the effectiveness of the damper, and in structures with multiple dampers, this can be a complex scenario to model. In this paper, we demonstrate that the effects of the brace compliance on the damper performance can be modelled by way of a first-order filter. We use this result to formulate a procedure that calculates the stiffness required by the supporting brace to provide a specified effectiveness of the damping action. The proposed procedure assumes that viscous dampers have been sized in a previous design step based on any optimal methodology in which, as is usually the case, the presence of supporting braces and their dynamic effects were neglected. Firstly considering a one degree-of-freedom system, we show that the proposed method ensures a desired level of damper efficiency for all frequencies within a selected bandwidth. Then the analysis is extended to the case of multi-degree-of-freedom systems to show that the design criteria can be applied in a straightforward and successful manner to more complex structures.