Earthquake protection of structures with nonlinear viscous dampers optimized through an energy-based stochastic approach

he earthquake protection of structures equipped with energy dissipation devices in the form of nonlinear fluid viscous dampers (FVDs) is investigated. Most of the optimal design strategies from the literature either address a simplified linear (Newtonian) idealization of the devices, or identify the characteristics of the nonlinear FVDs in a later stage, by invoking the concept of “energy-equivalent” dampers to compromise between the nonlinear power law force-velocity behavior and a simplified (equivalent, in terms of energy dissipation) linear modeling. In this paper, the nonlinear power law behavior of the devices is incorporated a priori in the optimal design process. The proposed strategy, based upon a numerical approach to a constrained optimization problem, invokes a performance criterion that is derived from the energy balance equation of the system, expressed in stochastic terms. To handle the nonlinear constitutive behavior of the FVDs, a novel equal-energy non-Gaussian stochastic linearization technique is integrated in the optimal design process. For a given power-spectral-density function of the seismic excitation, the most effective set of nonlinear FVDs that maximize the energy dissipation behavior can be identified. By stochastic dynamic analysis and by nonlinear response-history-analysis with an ensemble of ground motions, the proposed energy-based design philosophy is found to be better able to control the overall seismic response of the structure than alternative procedures that are not based on energy concepts and that minimize other performance indices.