The present study aimed at developing optimal design formulae of nonlinear friction pendulum tuned mass damper(FPTMD) for damped main systems under the acceleration response quantity being minimized. The FPTMD has the following properties:(1) the mass slides on the spherical surface so that the space to accommodate the FPTMD is much less than the suspension type;(2) the restoring force is provided by the spherical surface so that no extra spring is needed; and(3) the vibration energy is dissipated by the friction mechanism of the interface between the mass and the spherical surface. Direct search technique was used to obtain the optimum friction coefficient and tuning frequency ratio of the FPTMD for which the response of a damped single degree-of-freedom(SDOF) main system subjected to white-noise random excitation is minimized. Optimal design formulae for FPTMD were then obtained by a sequence of curve-fitting techniques. The feasibility of the proposed optimal design formulae is illustrated numerically using Taipei 101 structure implemented with FPTMD as a reference.
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