Vibration characteristics of multi-acoustic metamaterials rotor with geometrical nonlinearity

A theoretical research on the vibration characteristics of the multi-acoustic metamaterials rotor with the weak and strong geometrical nonlinearities is presented in this paper. The acoustic metamaterials open a worthy avenue in the propagation of the vibration for the rotor. The multi-metamaterials consist of the rotor dynamic vibration absorbers. The dynamic model of the multi-metamaterials rotor is employed and discretized by the assumed mode method. The solutions of the nonlinear equations are obtained using the harmonic balance method. The finite element model based on the Bernoulli–Euler beam element and numerical integration method is utilized to validate the analytical method. The dispersion relation, bandgaps, and nonlinear characteristics are presented by the theoretical simulations. The influences of the geometrical nonlinearity on the vibration characteristics for the multi-acoustic metamaterials rotor are investigated. The results show that the dispersion curve shifts due to the geometrical nonlinearity. The multi-independent bandgaps are generated by the multi-metamaterials. The twice jumps of the hardening-type nonlinearity exist around every bandgap for the multi-metamaterials rotor. Furthermore, the capability of the localized and miniaturized metamaterials to affect the propagation of the rotor vibration is verified.