Flexural vibration band gaps in Bragg acoustical hyperstructure beam with local-resonance system

Abstract

Bragg acoustical hyperstructure can scatter elastic wave, local resonance system can fight against vibration by the reaction force with reversed phase in low-frequency range, for improving the scattering performance of Bragg hyperstructure, a novel composite beam of Bragg beam with local resonator is investigated theoretically. Its dispersion relations and bang gaps are calculated by the established theoretical model. In order to confirm the veritable existence of band gaps, the transmission spectrum of flexural vibration waves are also studied by finite-element method, and comparing the relationship of vibration transmission spectrum and band gaps, the results indicate that the proposed theoretical model can accurately predict the band gaps of the proposed composite beam. For probing the dispersion mechanics, comparing the band gaps and modes shapes of the proposed composite beam with an unalloyed Bragg beam, the results denoted that local resonator can add two band gaps at the base of Bragg beam. Further, the changes of the band gaps that depend on the local resonator and on Bragg beam are studied. It is indicated that the total band gaps can be narrowed when the resonance frequency of the local resonators located at the band gaps of the Bragg beam and the branches will become approximately flat. The band gaps will broaden if the branch that depends on the local resonator gets closer to the branch on Bragg beam.