Effective damping and frequencies of viscous damper braced structures considering the supports flexibility

This paper presents a study on the optimal sizing of damping braces of MDOF systems equipped with viscous dampers where, unlike well-established computer-based optimisation methods, the deformability of the elastic supports is integrated by means of a novel non-iterative design tool. Mainstream optimisation methods usually focus on sizing supplemental damping devices neglecting the damper supports' flexibility and therefore their effect on the overall structural damping and frequencies of vibration. In this work, the damping braces are modelled by way of viscous-elastic assemblies using the Maxwell representation. The equations of motion are formulated in the state-space representation to facilitate the assessment of the viscous-elastic assemblies' effects. The system solution presented in form of contour plots is then used as a prime tool to select the design parameters for both dampers and supporting braces, while preserving a desired level of added damping. In addition, it is shown how this approach also gives the engineer the flexibility of either fixing a damper size to then determine the required supporting brace stiffness or fixing the supporting brace stiffness to then determine the maximum achievable damping. A case study taken from the literature is presented to illustrate the advantages of the proposed approach.