STUDY ON ENERGY BAND STRUCTURES AND ITS DYNAMICS CHARACTERISTICS IN CYCLIC-PERIODIC SYMMETRIC STRUCTURES

In view of the problems of local damage and vibration localization in cyclic-periodic symmetric structures such as impellers in service, the energy band structure and dynamic characteristics of the whole cyclic periodic symmetric structure are obtained by analyzing the dynamic characteristics of elastic wave propagation in the ring cell based on the band theory of chain periodic structures, meanwhile, formation mechanism of vibration localization is revealed. First, Euler-Bernoulli beam model and Kirchhoff plate model are used to model the thin region of the impeller, and the bending wave equation is solved with the corresponding mechanical assumptions and boundary conditions. Further, the transfer matrix of the bending wave propagating around the waveguide is derived in detail and the finite space Lyapunov indexes are given. The results show that the Euler-Bernoulli beam model cannot accurately describe the propagation law of curved wave along the circumferential waveguide, and the Kirchhoff plate model could give the band gap around 5000Hz in a wide range. Finally, the finite element method is used to compute the energy band structure of the centrifugal impeller, and the results are analyzed and studied in detail. The results show that there is one energy band structure in the centrifugal impeller with 3 "standing wave" band gaps and 1 local resonance band gap. Among them, the existence of "local resonance" band gap is one of the reasons for vibration localization in the centrifugal impeller, that is, as the frequency of external excitation acting on the centrifugal impeller falls within the "local resonance" band gap, the circumferential transfer of bending wave is blocked, and the energy is collected on part of the blades, resulting in vibration localization, demonstrating “cyclic-periodic symmetry-breaking”. In summary, the results reveal the dynamic characteristics of cyclic symmetric structures, which can provide theoretical basis for further improving the design criteria and vibration suppression of centrifugal impellers in the future.