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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. © 2014 The Authors.

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Earthquake Engineering & Structural Dynamics published by John Wiley & Sons Ltd. 1 INTRODUCTION The idea of incorporating damping devices into a structure that can absorb a considerable portion of the vibration energy has been used for many decades. A popular solution is based on passive viscous fluid dampers deployed in a wide range of configurations. The typical aim is to protect structures from the damaging effects of destructive natural events, while offering reliable supplemental energy dissipation systems at relatively low installation and maintenance cost. This paper focuses on the design of supporting braces for structures provided with linear viscous fluid dampers.

A well‐designed system based on viscous fluid damper could effectively mitigate the hazard posed by strong dynamic forces like those generated by wind or seismic loads. Over many years, research efforts have been aimed at reliable and cost‐effective design practices.

Optimal design methodologies for passive dampers based on a number of theories have been proposed for determining both damper sizes as in - and damper locations as in - among others. They commonly differ on how the optimisation problem is addressed and in which cost function and constraints the optimisation problem are subjected to. Zolotie bukvi.

Nevertheless, most conventional approaches for designing energy dissipation devices do not take into account the presence of supporting braces, whose local compliance can significantly reduce the desired dissipative action of the dampers. This said, work that has acknowledged this problem includes that of Takewaki & Yoshitomi, where the authors proposed a damping optimisation procedure by considering the minimisation of the inter‐storey drifts evaluated at the undamped fundamental natural frequency. Other relevant studies include those of Park et al.

And Singh et al. Who describe the use of gradient‐based optimisation algorithms to obtain the optimal parameters of dampers and their supporting braces in structures subjected to seismic motions. More recently, Chen et al. Also proposed a gradient‐based numerical procedure for determining the minimum brace stiffness together with a set of optimal damper coefficients to meet a target response reduction. They used Maxwell model‐based brace–damper systems and concluded that a brace stiffness equal to the first storey stiffness would be adequate for the desirable levels of response reduction in typical applications. Although optimisation gives solutions, insight into how individual brace stiffnesses affect the overall dissipation is unclear. As an alternative to complex optimisation, our approach is to use one of the existing damper sizing strategies (where damper coefficients are typically optimised assuming infinitely stiff braces) and then use a filter method to select the stiffness of all braces in a way that the damper efficiency reaches a predetermined specification.