Development of optimal design formula for bi-tuned mass dampers using multi-objective optimization

In this paper the development of a closed-form, easy-to-use design formula for optimal control performance of bi-tuned mass dampers is described. First, optimal parameters of bi-tuned mass dampers are investigated by a multi-objective optimization technique for which two performance measures, termed as nominal and robust performance indices, are defined in terms of the maximum value of the frequency response function of the damped structure in its original design condition and that in perturbed conditions, respectively. Since the ratio of the mass of the bi-tuned mass dampers to that of the structure affects the control performance significantly, the multi-objective optimization process is repeated for various mass ratios. For each configuration, the plot of Pareto-optimal solutions in the objective function space exhibited a bifurcation point which could be used to improve the nominal or robust performances. Since the robust performance can be greatly improved up to the bifurcation point without a significant loss of the nominal performance, these bifurcation points are selected for the development of an optimal design formula. Simple closed-form expressions for such optimal tuning frequencies and damping ratios of bi-tuned mass dampers are then derived using a nonlinear curve-fitting technique. To verify the performance of the bi-tuned mass dampers system obtained by the proposed optimal design formula, illustrative examples are presented for a single- and bi-tuned mass dampers systems using the full-order model of the building structure. The nominal and robust performances of the optimal designs are examined through a parametric study on characteristics of ground motions. The results of a stochastic dynamic analysis demonstrate that the proposed design formula guarantees both nominal and robust performances of bi-tuned mass dampers systems in controlling the responses of the building structures under seismic excitations.