The present study aims at developing optimal design formulae of nonlinear tuned mass damper(TMD) for damped main systems under the acceleration response quantity being minimized. Direct search technique is used to obtain the optimum damping coefficient and tuning frequency ratio of a nonlinear TMD system for which the response of a damped single degree-of-freedom main system subjected to white-noise random excitation is minimized. Optimal design formulae for these optimum parameters are then obtained by a sequence of curve-fitting techniques. The feasibility of the proposed optimal design formulae is illustrated numerically by using Taipei 101 structure implemented with TMD.
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