The crucial point in the field of seismic engineering is to diminish the induced vibration energy as much as possible in a fast and almost irreversible manner. Recently the concept of Nonlinear Energy Sink (NES) has been developed such that the imposed energy to a linear single Degree of Freedom (DoF) substructure is transferred to one or series of strongly nonlinear light attachments; the mechanism is based on a 1:1 resonance capture. Nonlinear attachments can be designed to passively vibrate with any frequency; hence the system is efficient for both of transient and periodic excitations. Some drawbacks of these systems are as follows: they cannot kill the first peak of oscillation in the free time response that is linked to the energy activation of NES; moreover, the transformation of energy vanishes in time due to decrease of the strength of energy pumping. Using NES in series even cannot accelerate the phenomenon of energy pumping and some strange behavior due to the delay in the cooperation of NES in series is noticed. In this study, the transient dynamic behavior of multiple DoF systems with trees of parallel NES at each DoF is investigated, then experimental and numerical results of a four DoF structure with two parallel NES at the top floor are demonstrated and commented upon.

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