This study develops a new class of Euler-buckled beam nonlinear energy sink (EBNES) with three configurations, which is expected to attenuate the disturbance effects and further enhance vibration suppression under launching and on-orbit loads simultaneously. The effects of arrangements on amplitude-frequency responses of the primary system are analyzed, and the approximate solutions are verified by numerical results. Comparisons with results exhibit that the EBNES-I is much more effective with significantly enhanced vibration reduction performance and stability in a broad frequency range. Furthermore, a two-degree-of-freedom dynamic model of the flywheel system, which integrates the EBNES-I and the satellite platform, is established. The vibration attenuation and bifurcation behaviors of the proposed EBNES-I is investigated, and the efficiency of the proposed EBNES-I in vibration reduction of the flywheel is compared to that of a cubic-stiffness NES. It is found that the EBNES-I exhibits a good vibration reduction performance on the dynamic responses of the flywheel system in launching and on-orbit stage simultaneously. Additionally, the bifurcations of the system are studied in order to find influences of gravity, excitation amplitudes and geometrical parameters on the stability of the EBNES. Calculation results provide suitable conditions for occurrence of the SN and Hopf bifurcations.