BIFURCATIONS OF SELF-EXCITATION REGIMES IN OSCILLATORY SYSTEMS WITH NONLINEAR ENERGY SINK

. The paper investigates regimes of self – excitation in oscillatory systems with attached nonlinear energy sink (NES). For the simple example of primary Van der Pol oscillator, the initial equations are reduced by averaging to 3D system. Small relative mass of the NES justifies analysis of this averaged system as singularly perturbed with two "slow" and one "super – slow" variable. Such approach, in turn, provides complete analytic description of possible response regimes. In addition to almost unperturbed limit cycle oscillations (LCOs), the system can exhibit complete elimination of the self – excitation, small – amplitude LCOs as well as excitation of quasiperiodic strongly modulated response (SMR). In the space of parameters, the latter can be approached by three distinct bifurcation mechanisms: canard explosion, Shil'nikov bifurcation and heteroclinic bifurcation. Some of the above oscillatory regimes can co – exist for the same values of the system parameters. In this case, it is possible to establish the basins of attraction for the co-existing regimes. Direct numeric simulations demonstrate good coincidence with the analytic predictions. More complicated primary systems with internal resonance can give rise to more complicated self – excited responses, including chaotic modulation of the primary frequency.