Acoustic characteristics of Helmholtz mufflers enhanced by acoustic black holes

Acoustic Black Hole (ABH) is an acoustic wave manipulation technology with broad development prospects. It addresses the limitation of insufficient noise reduction at non-resonant frequencies in traditional Helmholtz resonator (HR) mufflers. In this paper, a coupled HR muffler enhanced by an ABH is proposed. By applying the Wentzel–Kramers–Brillouin (WKB) method, two fundamental functions are assumed—respectively describing the acoustic field and the structural (solid) field—and these functions are determined using the boundary conditions and continuity requirements of the coupled system. The coupling relationship between these two fundamental functions is thereby established. Based on the principle of energy conservation, the energy-based transmission loss (TL) of the ABH-enhanced muffler is derived theoretically, yielding an analytical solution for the key performance metric under investigation. Results show that, within the critical frequency band of 200–600 Hz, significant bandwidth broadening is achieved, and the peak noise reduction reaches up to 110 dB. Furthermore, quantitative parametric analyses are conducted in the frequency domain to examine the influence of key design parameters—including the power-law index *m*, the cutoff thickness *h*₀, and the number of ABH arrays—on the muffler’s transmission loss. Finally, comparative analysis demonstrates the optimization effect of the ABH coupling system on the conventional HR muffler.