Viscous damper optimization considering practical design issues

Abstract

This research discusses the optimal height-wise distribution of viscous dampers in multistory structures considering practical design issues, all quantified with respect to the implementation cost. Seismic excitation is modeled as a stochastic process (filtered white noise), and response statistics of linear structural systems are obtained through state-space analysis. For applications involving nonlinear dampers, statistical linearization principles are employed to approximate damper and structural response. Emphasis is placed on three practical design issues: (i) realistic quantification of damper upfront cost, based on damper force capacity rather than merely on damping coefficients; (ii) explicit incorporation (into the optimization procedure) of the cost of column strengthening that might be required to accommodate the additional forces (with respect to those on the bare structure) due to the action of the supplemental dampers; and (iii) the maximum feasible force capacity of the dampers. Five different objective functions are defined to address these issues, all of them incorporating cost characteristics (for dampers and strengthening) at different fidelity levels. The impact of the statistical linearization when the objective function is defined in terms of peak response quantities (instead of RMS quantities) is discussed. The optimal design problem considers primarily the structural performance as a constraint, requiring that a specific level of vibration suppression be achieved (with respect to the structural response without dampers) through the damper implementation. The proposed framework is illustrated through the design of a supplemental viscous damping system for an actual Chilean 26-story building, considering an excitation that is compatible with the regional seismic hazard. Results demonstrate that explicitly optimizing for cost functions that consider practical design issues leads to substantial economic benefits with respect to optimization for simplified cost metrics.