Nonlinear dynamics and stability of metamaterial rotor/seal system

Metamaterials are employed to modulate the propagation of forced vibrations. The periodic structure inherently influences self-excited vibrations. Theoretical researches on the nonlinear dynamics and stability of a metamaterial rotor/seal system are presented in this paper. The nonlinear model of the metamaterial rotor/seal system is established. The instability threshold speed is calculated by the eigenvalue theory. Then the nonlinear differential equations are solved using the numerical integration method, and the dynamic behaviors including bifurcations are obtained. Also, the instability threshold speed is validated by the nonlinear responses. The results show that the local resonance bandgap generated by the metamaterial cannot forbid the propagation of the fluid-induced vibration in the rotor/seal system. The metamaterial can forbid the propagation of the instability vibration as incorporating the damping. This research provides a theoretical basis for suppressing self-excited vibrations in metamaterials and has potential for engineering applications.