Seismic analysis and design with Maxwell dampers

The paper presents a convenient formulation for the optimal design of viscous dampers, represented by a Maxwell model. The Maxwell model captures the frequency dependence of the damping and stiffness coefficients observed in the fluid orifice dampers, especially at higher frequencies of deformation. A gradient-based optimization scheme is used to obtain the optimal distribution and the parameters of the dampers in a structure subjected to seismic motions. Since the objective of using supplemental damping is to reduce the dynamic response, the optimal solution aims to minimize a response-based performance index. Different forms of the performance indices are considered to obtain the numerical results. The effectiveness of supplemental damping is evaluated in terms of the reduction of the response quantities such as base shear, story drifts, story accelerations, and floor, response spectra. The effect of spring in the Maxwell model as well as that of the brace flexibility is also examined. Both tend to reduce the effectiveness of the viscous dampers.