Resonant Modes of One-Dimensional Metamaterial Containing Helmholtz Resonators with Point Defect

Abstract

The metamaterial constructed by Helmholtz resonators (HR) has low-frequency acoustic forbidden bands and possesses negative mass density and effective bulk modulus at particular frequencies. The resonant modes in one-dimensional HR structure with point defect were studied using finite element method (FEM). The results show that the acoustic energy is localized between the resonant HR and the opening in the local-resonant-type gap. There is a high pressure area around the defect resonator at the frequency of defect mode. In the Bragg type gap, the energy mainly distributes in the waveguide with harmonic attenuation due to the multi-scattering. Phase opposition demonstrates the existence of negative dynamic mass density. Local negative parameter is observed in the pass band due to the defect mode. Based on further investigation of the acoustic intensity and phase distributions in the resonators corresponding to two different forbidden bands, only one local resonant mode is verified, which is different from the three-component local resonant phononics. This work will be useful for understanding the mechanisms of acoustic forbidden bands and negative parameters in the HR metamaterial, and of help for designing new functional acoustic devices.