In this work, we develop a deep subwavelength metasurface which is capable of reflected wave manipulation arbitrarily. Each unit cell of the metasurface is constructed of a Helmholtz resonator with an extended neck. The possibility of creating a phase shift offered by different unit cells is analytically explored based on characteristic mode analysis and demonstrated by the finite element method. It is found that the phase shift of the reflected wave ranging from 0 to 2π in a supercell (consists of eight inhomogeneous unit cells) can be engineered by tuning the length of the extended neck. A periodical array of the supercell is used to construct the designed metasurface. The reflection performance of the proposed metasurface is investigated both numerically and experimentally, and good agreement is achieved. Anomalous phenomena such as converting an incident wave to a surface wave and negative reflection are demonstrated using the designed metasurface. The key features of the proposed metasurface are the thin thickness ≈λ/30 (λ is the operation wavelength), simple configuration, and easy fabrication, making it possess a promising potential in miniaturization and integration in acoustic devices.

This study presents a thin absorber for low-frequency noise mitigation based on a Helmholtz resonator with an extended neck (HREN). An analytical model is established based on the transfer matrix method and the equivalent medium model to predict the acoustic characteristics of the HREN-based absorber, and is validated by experiments and simulations. The acoustic properties of the HREN are characterized comprehensively, including the effects of the radius and length of the extended neck. It is demonstrated that a feature of the HREN is its thin thickness (around 1/30th wavelength of the operating frequency), and its resonance frequency can be flexibly tuned by adjusting the geometry of the extended neck. The HREN can achieve effective low-frequency absorption in a constricted space, but is only effective within a narrow bandwidth. To overcome the limitation, a checkerboard absorber consisting of alternately distributed inhomogeneous HRENs is investigated. Results show that the HRENs in a checkerboard absorber operate almost independently, resulting in a dual-band sound absorber, when the adjacent HREN units are largely dissimilar. In contrast, a bandwidth extension of effective absorption can be obtained if the adjacent HRENs in the checkerboard absorber are strongly coupled. The absorber with a broadened absorption bandwidth exhibits a quasi-perfect absorption (the absorption coefficient above 0.85) within the bandwidth between the two absorption peaks induced by two corresponding HRENs.

The noise attenuation properties of an acoustic liner consisting of Helmholtz resonators with extended necks (HRENs) are investigated. An optimal liner constructed by 16 inhomogeneous HRENs is designed to be effective in sound absorption in a prescribed frequency range from 700 to 1000 Hz. Its quasi-perfect absorption capability (average absorption coefficient above 0.9) is validated by measurements and simulations. The resonance frequencies of the individual resonators in the designed liner are just located within the effective absorption bandwidth, indicating the overlapping phenomenon of absorption peaks. In addition, the liner maintains a thin thickness, about 1/25th with respect to the longest operating wavelengths. To assess the acoustic performance of the designed liner in the presence of mean flow, experimental investigations are performed in a flow tube. Results show a near flat transmission loss is attained in the target frequency range by the designed liner. Additionally, the impedance of the uniform HREN-based liner is extracted at flow condition. In all, the inhomogeneous HREN-based liner is featured by the thin thickness and the excellent wide-band noise attenuation property. These features make the designed liner an promising solution for noise attenuation in both static and flow conditions.