This paper investigates the mechanism referred to as clamping by branching (DBB), and its ability to attenuate the response of an oscillating structure, in the range of large amplitudes. More specifically, we give an experimental proof of this mechanism and we show that it is very robust against variations of the physical parameters and constituents: nature of the damping mechanism, geometrical structure. These results motivated the design of the Tuned Mass Branched Damper (TMBD) which is shown to be a little more efficient than the classical Tuned Mass Damper (TMD) in some domains of the parameter space.