The paper proposes and studies a nonlinear mass damper that uses frict
ion dampers acting transversely to the direction of the motion of the
mass damper as a means for energy dissipation. The resistant scheme of
this mass damper shows a hysteretic damping mechanism in which the di
ssipation of energy is quadratic in the amplitude of deformation. The
effectiveness of the mass damper in reducing vibrations of the main st
ructural system to which it is attached is investigated. The statistic
al linearization technique is used to estimate the mean square respons
e of the system subjected to random excitation. The optimum parameters
of this mass damper are defined as those that minimize the mean squar
e deformation of the main structural system subjected to random excita
tion. The study confirms that the efficacy of this nonlinear tuned mas
s damper (TMD) system is comparable to that of a linear TMD system for
a wide range of excitation intensity.