Interaction of nonlinear energy sink with a two degrees of freedom linear system: Internal resonance

We investigate the dynamics of 2DOF linear subsystem with close frequencies with attached nonlinear energy sink (NES). In this system, simultaneous targeted energy transfer from both linear oscillators to the NES is possible. It was demonstrated that the process of the TET can be analytically described as transient beats of relaxation—like motion arising due to the internal resonance. Contrary to previously studied models, the approach based on Hamiltonian structure of the system (study of the periodic orbits in the absence of the damping) fails to provide insight into the TET process. The reason of that is large number of secondary resonances activated through interaction between two primary 1:1 resonances. In the damped system these resonances are eliminated and then averaging—based approach is applicable. It was shown by the Hilbert Vibration Decomposition (HVD) that in the damped case there is a single significant component of the response regarded to the 1:1:1 resonance. Analytical model was verified numerically and a fairly good correspondence was observed.