Steady state dynamics and robustness of a harmonically excited essentially nonlinear oscillator coupled with a two-DOF nonlinear energy sink

•Steady state dynamics and robustness of a harmonically excited essentially nonlinear oscillator coupled with a two-DOF nonlinear energy sink are considered.•Results show that the system with one NES has low robustness to the changes of the parameters and external force.•Increasing the degrees of freedom of the NES would increase the robustness of the system to the changes in system parameters and amplitude of external force.•For the system with two-DOF NES, changes in control parameters cause fewer changes in the behavior of the main oscillator.

Steady state dynamical behavior of two degrees of freedom (DOF) system composed of a harmonically excited nonlinear oscillator coupled with a single DOF nonlinear energy sink (NES) is studied in comparison with the behavior of a system consisting of a nonlinear oscillator coupled with a two-DOF NES subjected to external harmonic excitation. First, an optimized set of parameters was obtained using optimization for the two-DOF system. Results show that the system with one NES has low robustness to the changes of the parameters and external force. By adding a degree of freedom to the first system, the steady state behavior of the resulting three-DOF system was investigated. Conclusions illustrated that increasing the degrees of freedom of the NES would increase the robustness of the system to the changes in system parameters and amplitude of external force.