Response regimes in forced system with non-linear energy sink: Quasi-periodic and random forcing

The system under investigation comprises a linear oscillator coupled to a non-linear energy sink (NES) under quasi-periodic forcing in the regime of 1:1:1 resonance. Interaction of the quasi-periodic excitation with the strongly modulated response (SMR) regime is studied in detail both analytically and numerically. Theoretical study developed in the paper allows establishing the threshold value for the amplitude of modulation beyond which SMR regime is excited. This phenomenon is of great practical use since applying the quasi-periodic excitation beyond the threshold results in elimination of possible undesired regimes causing high-amplitude oscillations of the main structure. Bifurcations of the SMR caused by quasi-periodic excitation were analyzed with the help of semi-analytical procedure based on two-dimensional maps. Numerical evidences for exciting the strongly modulated bursts in the response by a random, quasi-periodic narrow-band excitation are also provided. Fairly good correspondence was observed between analytical model and numerical simulations.