Abstract: Aiming at eliminating the broadband line spectrum generated by the periodic rotation of submarine mechanical equipment, the vibration suppression effect was investigation and the structural parameter optimization of nonlinear energy sink (NES) were carried out under harmonic excitation. The dynamic model of mechanical equipment coupled with the nonlinear energy sink was established, and the periodic motion and stability of the coupled system were analyzed by incremental harmonic method, arc-length continuation method and Floquet theory. The influence of damping, mass ratio and stiffness on the vibration suppression effect of the nonlinear energy sink was discussed by taking the system vibration energy as evaluation criterion. Furthermore, the optimized damping and stiffness were obtained through local optimization algorithm, also the robustness of the vibration suppression effect was studied. The results show that the proposed method is in good agreement with Runge-Kutta numerical method, which can effectively construct the complete image of the coupled system periodic solution. Besides, weak damping is a prerequisite for a nonlinear energy sink to have good vibration suppression effect and robustness within a range of 20% of excitation frequency and of 50% amplitude after parameter optimization. A NES, parallel with vertical linear springs and constituted by flexible hinges under preloaded state, was proposed and related test research was also carried out to verify the theoretical findings.