A semi-analytical model and synergistic mechanism for broadband sound radiation control in double-layer periodic acoustic black hole plates

Low-frequency vibration and noise control of lightweight structures remains a critical engineering challenge. While acoustic black hole (ABH) structures offer a promising lightweight passive solution, existing designs suffer from venerable structural stiffness and low-frequency deficiency. To address these issues, this study investigates a composite double-layer periodic ABH plate that integrates lightweight property, broadband performance, and high stiffness compared with conventional single-layer ABH plates. Through combining the Gaussian expansion method (GEM) and radiation impedance matrix, the vibroacoustic response of the system can be efficiently and accurately predicted by a semi-analytical sound radiation model, as demonstrated through comparisons with Finite Element simulations. Both numerical and experimental results confirm the structure's superior broadband sound suppression ability when compared with a uniform plate of equivalent mass, evidenced by a substantial reduction in radiated sound power within its flexural wave bandgap, and extension to frequencies far below the cut-on frequency of a single ABH unit with damping treatment. Analyses reveal the asymmetric vibration and sound radiation between the two plate facets when excitation is applied to the ABH region, a phenomenon stemming from the synergetic effects of the ABH, bandgaps and the double-layer design: within bandgaps, energy localization combined with ABH-induced wave retarding impairs the radiation efficiency of the excited plate; outside bandgaps, the ABH effect and double-layer configuration facilitates a sequential energy concentration-dissipation process, leading to strong suppression of the output plate's vibration and sound radiation. This work elucidates the underlying mechanisms of the composite periodic ABH structures, and provides an efficient analytical tool for designing lightweight, low-noise engineering structures.