Vibration characteristics of linear and nonlinear dissipative elastic metamaterials rotor with geometrical nonlinearity

Theoretical researches on the vibration characteristics of a dissipative elastic metamaterials rotor with geometrical nonlinearity are presented in this work. Both linear and nonlinear damping cases are implemented in parallel to the spring of the unit. The dynamic model of the dissipative metamaterials rotor is built and discretized by the assumed mode method. Then the solutions of the nonlinear equations are obtained using the harmonic balance method, and the numerical integration method is applied to validate the solutions obtained by the analytical method. The comparisons of the dynamic behaviors for the rotor with different types of geometrical nonlinearities and dissipations are presented, and the effect of the distribution position of the absorber unit on the dynamic behaviors is investigated. The results show that the linear damping has a better capacity to reduce the amplitude compared to the nonlinear damping due to the energy dissipation near the resonance region. On the other hand, compared to the linear dissipation, the nonlinear dissipation has a better performance around the bandgap that forbids the propagation of the vibration. Moreover, these properties can be further improved by adjusting the position of the unit on the rotor. The results presented in this paper provide a theoretical basis for enhancing the properties of metamaterials rotors.