Analysis of the transient behavior in a two dof nonlinear system

Highlights: → We analyze the behavior of a two dof nonlinear system under impulse loadings. → The possibility of existence of chaos is revealed by Melnikov's integral. → During 1 : 1 resonance the system is guided to forced system of nonlinear modes. → Strongly nonlinear zone of the system and its stable area are enlightened. → Complicated basin of attractions of the system is traced. - Abstract: In this paper we analyze the behavior of a nonlinear system under impulse loadings. The system is composed of a master 'linear' degree of freedom (dof) substructure which is attached to a slave 'nonlinear' energy sink (NES) for the sake of the control. Melnikov integral is endowed in order to study the possibility of existence of chaos and transversal homoclinic orbits in the system. Then, the complexification method as an alternative to nonlinear normal modes is implemented to reveal the behavior of the system during the energy exchange between two oscillators. The non-smooth time transformation (NSTT) technique is implemented in order to enlighten the system behavior during its extremely nonlinear regime, meanwhile stable and unstable zones of the system during its quasi-linear regime are highlighted.