Improving Low-Frequency Panel Absorbers with Two-Dimensional Acoustic Black Hole

Acoustic black hole (ABH) structures, known for their unique wave-focusing capabilities, have found wide application in the fields of acoustics and vibration. Leveraging this property, this study proposes a novel high-sensitivity hydrophone design incorporating a two-dimensional (2D) ABH structure. Drawing on principles of geometrical acoustics, the wave-converging behavior of bending waves in ABH structures is analogized to acoustic ray bending in underwater acoustics. A simplified theoretical model describing the relationship between the bending wave trajectory and the wave speed gradient in polar coordinates is established for 2D ABH configurations and verified through numerical simulations. Based on this mechanism, a 2D ABH hydrophone is developed by integrating the ABH structure into bending-plate hydrophone, enabling vibration energy concentration and significantly enhancing sensitivity. Comparative studies with hydrophones using uniform-thickness plates and linearly tapered thickness plates as receiving surfaces confirm the superior performance of the ABH hydrophone in the 1.7–5.8 kHz frequency range. To address the pronounced undulations observed in the sensitivity response—attributed to vibration superposition—a liquid cavity of specific length is introduced. This leads to the development of an ABH-Helmholtz-coupled hydrophone (ABHH hydrophone), wherein the first two bending modes of the ABH structure are coupled with the resonant modes of a single-ended open liquid cavity, resulting in broadband reception capability. Prototypes of both hydrophone designs were fabricated and experimentally tested in an anechoic water tank. Results show that both devices achieve peak receiving sensitivities exceeding –169 dB. Notably, the ABHH hydrophone maintains sensitivity fluctuations within 8 dB across the 2.6–5.3 kHz frequency band. This study confirms that 2D ABH structures can effectively enhance hydrophone sensitivity via bending wave convergence and, when coupled with liquid cavity resonators, enable broadband acoustic detection. These findings establish a solid foundation for the application of ABH structures in underwater acoustic transducer design.

Noise mitigation by means of the acoustic black hole (ABH) effect is a well-known engineering solution. However, the conventional method of applying ABH effect which requires modification of the structure geometry has various limitations which encourage the research of virtual ABH concept. In this study, the effect of ABH was applied through introducing virtual stiffness by a shunt circuit. According to the force-voltage electric analogy, stiffness has an inverse relationship with capacitance. So that the ABH effect can be virtually realized by following a power law profile using an array of independent capacitive shunts. The concept is studied through finite element simulation developing a macro code in ANSYS Parametric Design Language (APDL). To evaluate the influence of capacitance profile on the acoustic radiated power, parametric studies are conducted. Based on the results of the parametric studies, the capacitance profile is tuned for minimum radiated power. It is revealed that the virtual acoustic black hole (ABH) effect can offer 10.29%, 6.37%, and 7.47% reduction in the radiated power from the first to the last targeted mode, respectively. The virtual ABH effect introduced in this study can be used for semi-active structural noise isolation without any weight or manufacturing penalty.

Visualization of travelling waves propagating in a plate equipped with 2D ABH using wide-field holographic vibrometry

In the recent decade, there are increasing numbers of reported studies on the use of acoustic black hole (ABH) effects for the damping of flexural vibrations in engineering structures. This effect can be obtained by the use of a high-order power-law profile change in the thickness of the structure to induce a gradual decrease in incident wave velocity, to almost zero, along the propagation distance. ABHs have great potential for mitigating vibrations and noise. This paper covers the review of one- and two-dimensional ABHs and the experimental and numerical study of 3D printed beams with embedded ABH features. Specimens fabricated with the 3D additive manufacturing process were studied due to its expanding applications towards aerospace and automotive industries. However, limitations to the smoothness of the end product may affect the ABH effect, since the printing is typically via bottom-up layering where geometric accuracy is only up to the layer thickness. The vibration response of the 3D printed ABH beams, which has not been reported previously, is analyzed using the mean quadratic velocity and structural intensity parameters.

The propagation of laser-generated Lamb waves in a two-dimensional acoustic black-hole structure was studied numerically and experimentally. The geometrical acoustic theory has been applied to calculate the beam trajectories in the region of the acoustic black hole. The finite element method was also used to study the time evolution of propagating waves. An optical system based on the laser-Doppler vibration method was assembled. The effect of the focusing wave and the reduction in wave speed of the acoustic black hole has been validated.

The Acoustic Black Hole (ABH) structure has been developed as a promising approach for passive vibration attenuation and noise control. The basic theory of ABH effect hinges on the geometry thickness gradual decreasing according to the power law. This feature of structure reduces flexural wave speed, resulting in "trapping" flexural wave into ABH indentation to achieve energy focalizing. In this work, the FE model of a plate embedded with ABH indentation and damp structure is established and excited by a series of harmonic forces respectively. The characteristics of energy distribution in this plate in full frequency band are investigated by the power flow method and wavenumber domain analysis. By transforming the spatial vibratory energy into wavenumber domain, the ABH effect is analyzed and compared with a uniform panel. Meanwhile, the dissipation effect of vibration and sound radiation energy has been studied with addition of damping material. Furthermore, the energy harvesting and dissipation performances of a plate embedded with heterogeneous ABH array are investigated in order to demonstrate the influence of ABH structure parameters and configuration. The research will be beneficial for the vibration energy control in full frequency band.

The acoustic black hole (ABH) has been developed in recent years as an effective, passive, and lightweight method for attenuating bending wave vibrations in beams and plates and reducing the sound radiation and structural-acoustic response of structures. The ABH effect utilizes a local change in the plate or beam thickness to reduce the bending wave speed and increase the transverse vibration amplitude. Attaching a viscoelastic damping layer to the ABH results in effective energy dissipation and vibration reduction. Surface-averaged mobility and radiated sound power measurements were performed on an aluminum plate containing an array of 20 two-dimensional ABHs with damping layers and compared to a similar uniform plate. Detailed laser vibrometer scans of an ABH cell (including the ABH and surrounding homogeneous plate) were also performed to analyze the vibratory characteristics of individual ABH cells and compared with mode shapes calculated using finite elements. The results showed that the surface-averaged mobility was reduced by up to 14 dB for the fully damped ABH plate compared to a uniform reference plate while also reducing the mass of the plate. The results demonstrated that the dynamics of plates with embedded ABHs can be characterized by low, mid, and high frequency ranges, with low-order local ABH modes contributing significantly to low frequency ABH performance. The effects of damping layer thickness and diameter were also investigated to assess ABH performance optimization. It was shown that the damping layer can have the added benefit of mass loading the ABH and enhancing low frequency performance. The results will be useful for designing the low frequency performance of future ABH systems and describing ABH performance in terms of design parameters.

Interpretation of the Acoustic Black Hole effect based on the concept of critical coupling

Two-dimensional traditional acoustic black hole (ABH) embedded in the plate has been recognized as a highly effective tool for wave energy harvesting, which enables wave trajectories to converge into a confined area. Traditional ABH is a rotational symmetrical circular indentation, and the residual thickness platform is always located in the center. This type of ABH has been widely investigated in previous study. However, the discussion on the structure configuration and layout of the residual thickness platform is rare. In this paper, two types of unconventional ABHs embedded in the plate are proposed and studied, namely “Heteromorphic ABH” and “Eccentric ABH,” which represent that the shape of indentation is no longer a circle and the inner platform is not located in the center, respectively. These unconventional ABHs can also converge the flexural wave, but the focalization phenomenon is obviously distinct from that of the traditional ABH. The converging performances are characterized through the ray-tracing method based on the geometrical acoustic method. The validation of calculated results is conducted using the finite element simulation. Moreover, the effects of ABH geometric parameters are investigated in detail. The unconventional ABH demonstrates the multiplicity in structure and shows the potential of the flexible manipulation for flexural waves.

Vibrational acoustic black holes (ABHs) have shown great promise for reducing structural vibrations and sound radiation in light fluids. However, it is still unknown whether the acoustic black hole (ABH) effect can be materialized in heavy fluids. This paper discusses this issue by developing a semi-analytical model on a simply supported ABH plate that vibrates and radiates sound into water. The proposed model is validated by finite element models and used to investigate the vibration and sound radiation properties of the ABH plate in different frequency ranges. The results show that the ABH effect can be systematically manifested in heavy fluids, as reflected by a significant increase in structural damping and a decrease in vibration and sound radiation. Numerical analysis of the radiation damping and mass loading effects shows that the radiation damping has little effect on the vibration reduction of the water-loaded plate. However, the mass loading effect mitigates the low-frequency drawback of conventional ABH structures in air, resulting in a broadband reduction in structural vibration and sound radiation from the water-loaded ABH plate.

A 2D Daubechies wavelet model on the vibration of rectangular plates containing strip indentations with a parabolic thickness profile

This presentation explores the acoustic black hole (ABH) effect achieved through variation of duct wall impedance. Unlike the method of Mironov and Pislyakov, which utilizes tapered annular rings within the duct to achieve the ABH effect, this approach leverages mechanical impedance variation to create the desired acoustic behavior. By engineering the impedance profile along the duct wall, an axially decreasing local phase speed results that mimics the event horizon of a black hole, causing sound waves to be significantly attenuated and trapped. Governing equations are derived and solved using both the WKB approximation and numerical methods. The solutions reveal that specific impedance profiles can effectively decelerate and absorb acoustic waves, resulting in substantial reduction in sound transmission. Verification is performed using the fully coupled structural acoustic finite element algorithm Sierra/SD. This research further paves the way for the development of innovative acoustic materials and devices which utilize ABH principles to achieve enhanced noise control and acoustic wave manipulation. [Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under Contract DE-NA-0003525.]

An Acoustic Black Hole (ABH) is a scatterer, embedded in a panel, allowing passive vibration control without adding mass. In practice, it is achieved by means of a local reduction in thickness (axisymmetric pit with a parabolic profile) and the addition of a thin viscoelastic coating in a central region of uniform thickness (plateau). The vibration absorption induced by the ABH, allows the design of stiff, light and non-resonant panels. In this paper, we propose to study this effect for a three-layer sandwich panel (glass fiber skin/honeycomb core/glass fiber skin), which gives rise to both bending and shear effects. The equations of motion of the thick, symmetrical sandwich panel with variable characteristics is obtained within the framework of the zig-zag theory by applying Hamilton’s principle. These equations lead to a sixth-order analytical model, allowing the dispersion curves to be obtained, and then an analytical model of the scatterer inserted in an infinite panel. The analysis of the local modes of the scatterer allows the evaluation of its absorption; the interpretation of the ABH effect is carried out using its scattering matrix. The model allows in particular the analysis of the effect of shear on the ABH effect. Experimental tests, based on vibrational maps obtained by vibrometry, are used to discuss and validate the predictions.

The concept of an acoustic black hole (ABH) for anechoic termination of waveguides has been well-established and extensively studied. The fundamental principle underlying an ABH is the deceleration of acoustic waves, leading to the accumulation and subsequent absorption of acoustic energy within the thermoviscous boundary layer formed along the ribs forming its internal structure. The primary advantage of ABHs, in contrast to classical solutions, lies in their avoidance of porous or fibrous materials, rendering them suitable for deployment in challenging environments. While the majority of published works have focused on ABHs with circular cross-sections, recent advancements have demonstrated the effectiveness of the ABH effect also in waveguides with rectangular cross-sections. However, it has been revealed that these ABHs require very fine internal structure for optimal performance, posing challenges in manufacturing. This study addresses this issue by utilizing a microperforated plate to provide the necessary resistance. To model these ABHs, a simple mathematical model is proposed, enabling the optimization of their parameters. Subsequently, their performance is investigated through numerical experiments. The validity of the results is confirmed by comparing them with a detailed mathematical model, ensuring the accuracy and reliability of the proposed approach.

The acoustic black hole (ABH) effect in waveguides is studied using frequency-domain finite element simulations of a cylindrical waveguide with an embedded ABH termination composed of retarding rings. This design is adopted from an experimental study in the literature, which surprisingly showed, contrary to the structural counterpart, that the addition of damping material to the end of the waveguide does not significantly reduce the reflection coefficient any further. To investigate this unexpected behavior, we model different damping mechanisms involved in the attenuation of sound waves in this setup. A sequence of computed pressure distributions indicates occurrences of frequency-dependent resonances in the device. The axial position of the cavity where the resonance occurs can be predicted by a more elaborate wall admittance model than the one that was initially used to study and design ABHs. The results of our simulations show that at higher frequencies, the visco-thermal losses and the damping material added to the end of the setup do not contribute significantly to the performance of the device. Our results suggest that the primary source of damping, responsible for the low reflection coefficients at higher frequencies, is local absorption effects at the outer surface of the cylinder.