Local resonances-induced low-frequency band gaps in two-dimensional phononic crystal slabs with periodic stepped resonators

In this paper, the numerical investigation of Lamb wave propagation in two-dimensional phononic crystals composed of an array of stepped resonators on a thin slab is presented. The dispersion relations, power transmission spectra and spectra of resonances are studied using a finite-element method. Because of the simultaneous mechanisms of the local resonances and Bragg scattering, the structures exhibit low-frequency forbidden bands and Bragg band gaps, which can be effectively shifted by changing the resonator geometries as well as the lattice symmetries of the resonator array. As a result, a low-frequency gap within the audible regime can be demonstrated. Furthermore, for a finite phononic crystal slab, the calculated transmission and resonance spectra show an evident resonance nature which can be directly related to the formation of the low-frequency gaps. Based on the spectra of elastic waves through the single-layer stepped resonators, the resonances of the stepped resonators are found to either induce high reflection or intensify the transmission. The effects of different excitation conditions for generating specific slab modes with different polarization states on the acoustic energy transmission and attenuation are also studied. The results show that the polarization states of the incident slab modes influence the spectra of resonances, power transmission and attenuation.