<p>To prevent excessive vibrations in the rotor system at critical rotational speeds caused by unbalanced excitation, a nonlinear vibration absorber is proposed in this paper. The absorber consists of a rigid mass ring and four circumferentially distributed variable thickness circular arches. It is mounted in the grooves of the disk and rotates with it. The variable thickness circular arches in the absorber is used to provide linear positive and nonlinear stiffness. The absorber achieves rotor vibration reductions by absorbing vibrational energy. When the attachment does not contain linear positive stiffness, the absorber becomes a nonlinear energy sink. The motion equations of the rotor system with the absorber are derived using Lagrange’s equation. The differential evolution algorithm has the advantages of being easy to implement and high optimization efficiency, and it also can avoid getting trapped in local optima during the optimization process. In this study, the DE algorithm is employed to investigate the vibration reduction capability of the designed nonlinear vibration absorber. The present results indicate that with the equivalent stiffness to a composite of linear positive and cubic nonlinear stiffness, the absorber demonstrates a pronounced suppression effect on the vibration of the rotor system. This study offers a novel approach to the vibration reduction of rotors.</p>