Low-Frequency Forbidden Bands in Phononic Crystal Plates with Helmholtz Resonators

A theoretical investigation of Lamb wave propagation in two-dimensional phononic crystals composed of an array of solid Helmholtz resonators (HRs) on a thin plate is presented. The dispersion relations, power transmission spectra, and spectra of resonances are calculated by finite-element analysis. Owing to the simultaneous mechanisms of local resonances and Bragg scattering, the structure exhibits low-frequency forbidden bands and Bragg band gaps that can be effectively shifted by changing the geometry of the HRs. As a result, low-frequency band gaps within the audible range can be achieved. Furthermore, the calculated power transmission and resonance spectra for a finite phononic crystal structure show an evident resonance nature and are directly related to the formation of low-frequency band gaps. The spectra of the monolayer HR structure show that the resonances can either induce high reflection or intensify transmission. The effects of different excitation conditions for generating different Lamb wave modes on the transmission of the wave energy are also studied. The calculated results show that the transmission varies with the incident Lamb waves of different modes. (C) 2011 The Japan Society of Applied Physics