Modern technological advances allow for the study of systems with additional synthetic dimensions. Higher-order topological insulators in topological states of matters have been pursued in lower physical dimensions by exploiting synthetic dimensions with phase transitions. While synthetic dimensions can be rendered in the photonics and cold atomic gases, little to no work has been succeeded in acoustics because acoustic wave-guides cannot be weakly coupled in a continuous fashion. Here, we formulate the theoretical principles and manufacture acoustic crystals composed of arrays of acoustic cavities strongly coupled through modulated channels to evidence one-dimensional (1D) and two-dimensional (2D) dynamic topological pumpings. In particular, the higher-order topological edge-bulk-edge and corner-bulk-corner transport are physically illustrated in finite-sized acoustic structures. We delineate the generated 2D and four-dimensional (4D) quantum Hall effects by calculating first and second Chern numbers and physically demonstrate robustness against the geometrical imperfections. Synthetic dimensions could provide a powerful way for acoustic topological wave steering and open up a platform to explore any continuous orbit in higher-order topological matter in dimensions four and higher.

Recently, sound attenuation with ventilation is highly needed in many practical applications. In this study, we report on a subwavelength acoustic silencer, named double-layer acoustic silencer (DAS), based on compactly assembled slit-type Helmholtz resonators (SHRs) for low-frequency broadband sound insulation while preserving ventilation. A simple yet insightful theoretical model is first established to characterize the sound insulation performance in terms of transmission loss (TL) and used for microstructure designs of the DAS. The fluctuating TL of the DAS, inevitably produced by the SHR resonances, is then mitigated and optimized via the introduction of viscosity and proper SHR frequency detuning. The overall TL is numerically investigated and experimentally observed to reach beyond 30 dB over the target working band of 0.48–0.95 kHz, with a maximum exceeding 50 dB. In addition, the proposed design also provides perfect ventilation when deployed in a duct environment, due to the straight and conserved airflow cross section. We believe that the proposed acoustic silencer design and its associated theoretical model pave the way for designing and optimizing highly efficient low-frequency subwavelength acoustic liners and silencers.

Membrane-type acoustic metamaterials (MAMs) have demonstrated unusual capacity in controlling low-frequency sound transmission, reflection, and absorption. In this paper, an analytical vibroacoustic-electromagnetic coupling model is developed to study MAM harvester sound absorption, energy conversion, and energy harvesting behavior under a normal sound incidence. The MAM harvester is composed of a prestressed membrane with an attached rigid mass, a magnet coil, and a permanent magnet coin. To accurately capture finite-dimension rigid mass effects on the membrane deformation under the variable magnet force, a theoretical model based on the deviating acoustic surface Green's function approach is developed by considering the acoustic near field and distributed effective shear force along the interfacial boundary between the mass and the membrane. The accuracy and capability of the theoretical model is verified through comparison with the finite element method. In particular, sound absorption, acoustic-electric energy conversion, and harvesting coefficient are quantitatively investigated by varying the weight and size of the attached mass, prestress and thickness of the membrane. It is found that the highest achievable conversion and harvesting coefficients can reach up to 48%, and 36%, respectively. The developed model can serve as an efficient tool for designing MAM harvesters.

Low-frequency noise is a growing problem in large structures of modern transportation technologies. In this study, we report a large-scale acoustic panel made of double-layer membrane-type metamaterials (DMAMs) for broadband noise reduction. A complete theoretical model based on the unit cell is fully developed and extended for finite multi-celled membrane-type acoustic metamaterial (MAMs) array. A large-scale acoustic panel constructed from 8 × 8 DMAM unit cells is proposed. To deal with the global compliance of the large-scale support structure, the double-layer panel frame structure with large bending stiffness is designed to shift the global resonances to higher frequencies and provide an efficient way to well maintain the MAM's performance. Moreover, the double-layer configuration further guarantees ultra high transmission loss within the frequency range of interest. Experiments are carried out to validate the analytical and numerical predictions. Excellent transmission loss ranging from 20 to 59 dB within ten third octave bands (0.32–2.5 kHz) is observed, deeply breaking the mass density law. We believe the proposed design and the associated theoretical model could serve as an efficient tool for designing acoustic metamaterial-based panels and soundproof walls with high noise reduction in low/middle frequency regions.

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