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－Traditionally, the use of a tuned mass damper (TMD) is to improve the surviability of the primary structure under extraordinary loading environment while the design loading condition is described by either a harmonic function or a stationary random process that can be fully characterized by a power spectral density (PSD) function. Aiming at prolonging the fatigue life of an offshore platform, this study considers an optimal design of TMD for the platform under long-term nonstationary loading due to long-term random sea waves characterized by a probabilistic power spectral density (PPSD) function. In principle, a PPSD could be derived based on numerous ordinary PSD functions; and each of them is treated as realization of the corresponding PPSD. This study provides a theoretical development for the optimal TMD design by minimizing the cost function to be the mean square value of the expected long-term response. A numerical example is presented to illustrate the developed design procedure.