Control of low-frequency noise for piping systems via the design of coupled band gap of acoustic metamaterials

• A metamaterial-type pipe system with Bragg and resonant acoustic gaps.
• A low-frequency acoustic coupled gap.
• Exact coupling condition for Bragg and resonant gaps.
• Effects of resonant parameters on coupled gaps.

Acoustic wave propagation and sound transmission in a metamaterial-based piping system with Helmholtz resonator (HR) attached periodically are studied. A transfer matrix method is developed to conduct the investigation. Calculational results show that the introduction of periodic HRs in the piping system could generate a band gap (BG) near the resonant frequency of the HR, such that the bandwidth and the attenuation effect of HR improved notably. Bragg type gaps are also exist in the system due to the systematic periodicity. By plotting the BG as functions of HR parameters, the effect of resonator parameters on the BG behavior, including bandwidth, location and attenuation performance, etc., is examined. It is found that Bragg-type gap would interplay with the resonant-type gap under some special situations, thereby giving rise to a super-wide coupled gap. Further, explicit formulation for BG exact coupling is extracted and some key parameters on modulating the width and the attenuation coefficient of coupled gaps are investigated. The coupled gap can be located to any frequency range as one concerned, thus rendering the low-frequency noise control feasible in a broad band range.