Optimal design theory for linear tuned mass dampers (TMD) has been thoroughly investigated, but is still under development for nonlinear TMDs. In this paper, optimization procedures in the time domain are proposed for design of a TMD with nonlinear viscous damping. A dynamic analysis of a structure implemented with a nonlinear TMD is conducted fi rst. Optimum design parameters for the nonlinear TMD are searched using an optimization method to minimize the performance index. The feasibility of the proposed optimization method is illustrated numerically by using the Taipei 101 structure implemented with TMD. The sensitivity analysis shows that the performance index is less sensitive to the damping coeffi cient than to the frequency ratio. Time history analysis is conducted using the Taipei 101 structure implemented with different TMDs under wind excitation. For both linear and nonlinear TMDs, the comfort requirements for building occupants are satisfi ed as long as the TMD is properly designed. It was found that as the damping exponent increases, the relative displacement of the TMD decreases but the damping force increases.

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SUMMARY Optimal design for tuned mass dampers (TMDs) with linear or nonlinear viscous damping is formulated in order for design practitioners to directly compute the optimal parameters of a TMD in a damped structure subjected to wind excitations. The optimal TMD tuning frequency ratio and damping coefficient for a viscous TMD system installed in a damped structure under 10 white noise excitations are determined by using the time‐domain optimization procedure, which minimizes the structural response. By applying a sequence of curve‐fitting schemes to the obtained optimal values, design formulas for optimal TMDs are then derived. These are expressed as a function of the mass ratio and damping power‐law exponent of the TMD as well as the damping ratio of the structure. The feasibility of the proposed optimal design formulas is verified in terms of formulary accuracy and of comparisons with existing formulas from previous research works. In addition, one numerical example of the Taipei 101 building with a nonlinear TMD, which is redesigned according to the proposed optimal formulas, is illustrated in effort to describe the use of the formulas in the TMD design procedure and to investigate the effectiveness of the optimal TMD. The results indicate that the proposed optimal design formulas provide a convenient and effective approach for designing a viscous TMD installed in a wind‐excited damped structure. Copyright © 2011 John Wiley & Sons, Ltd.

Tuned mass dampers with viscous damping and isolation systems with friction pendulums have been proposed and widely applied over the past several decades. By combining these two ideas, a friction pendulum tuned mass damper (FPTMD) is proposed in this study. Because the restoring and friction forces are provided by the spherical surface of the FPTMD, springs and dampers are not needed. Moreover, suspension is not necessary and the installation space is greatly reduced. The optimal design of the FPTMD with varying friction coefficients for wind-excited high-rise structures is investigated. The optimization procedures are demonstrated by the FPTMD implemented on Taipei 101 under white-noise wind force, and the optimization results are validated by threedimensional graphs. From the results of the sensitivity study, the effectiveness of the FPTMD with two different patterns of friction coefficients is sensitive to the tuning frequency ratio but not very sensitive to the friction parameters. Moreover, an FPTMD with a friction coefficient that linearly varies with displacement is even less sensitive to the friction parameters and the amplitude of excitation. The feasibility of the FPTMD with two different patterns of friction coefficient is illustrated by Taipei 101 subjected to the design wind force with a return period of 50 years. Following design optimization and numerical verification, the effect of vibration reduction for Taipei 101 is demonstrated.Viscous dampers are devices used to dissipate energy for the TMD. Optimal design formulae for the linear viscous TMD for undamped single degree-of-freedom (SDOF) structures were proposed in references 2-5. If damping is present in the primary structure, it is difficult to obtain closed-form solutions for the optimal TMD parameters 6-14. The effectiveness of the primary structure with a linear viscous TMD may be impaired because of its sensitivity to the tuning frequency; therefore, the multiple linear viscous TMD was further developed in references 15-21. Nonlinear viscous dampers may be cost effective in fabrication and maintenance. Chung et al. 22 proposed optimization procedures in the time domain for the design of a TMD with nonlinear viscous damping. Optimal design parameters for a nonlinear TMD were found using an optimization method to minimize structural responses. For TMDs with linear or nonlinear viscous damping, the comfort requirements for building occupants were satisfied as long as the TMD was properly designed. As the damping exponent was increased, it was found that the relative displacement of the TMD decreased but the damping force increased. Rudinger 23,24 proposed an optimal TMD with nonlinear viscous damping that is obtained by statistical linearization and further developed the optimal design procedure for a nonlinear viscous TMD.The energy-dissipating mechanism may be replaced with friction dampers. Inaudi and Kelly 25 proposed a friction-dissipating TMD where the restoring force was provided by linear springs and the dissipating force was provide...