Acoustic Black Hole Research Articles

Peculiarities of flexural wave propagation in a notched bar

The results of numerical modeling and experimental studies of the propagation of flexural elastic waves in a metal notched bar approximates the effect of an acoustic black hole are presented. The sample is a bar with notches, the depth of which increases according to the power law with an exponent equal to (4/3). It has been confirmed experimentally and with the simulation results, that such bars slow down the propagation of an elastic wave to the end of the bar. It is shown in such structures flexural waves have dispersion and their localization at the end of the bar is higher for some natural frequencies than that of a solid rod. The natural oscillations of the whole and notched bars are compared, i.e. the shape of the amplitude of the flexural wave along the rods. The dependence of the flexural wave length in a notched bar on the frequency is investigated as a wave propagates to the end of the bar.

Design of a lightweight broadband vibration reduction structure with embedded acoustic black holes in viscoelastic damping materials

Viscoelastic damping materials (VDMs) are valued for their high damping characteristics in vibration and noise control. However, they typically underperform at lower frequencies and add substantial mass to structures. This study introduces an innovative approach by embedding an acoustic black hole (ABH) structure within VDMs (ABH-VDM) to achieve lightweight and broadband vibration damping. Firstly, a finite element method-based vibration model is developed to analyse the propagation and attenuation characteristics of vibrations in a plate strip embedded with ABH-VDM. This analysis provides insights into the dynamic behaviour and damping effectiveness of the proposed structure. Secondly, the study investigates the vibration reduction capabilities and mass implications of ABH-VDM on large-scale plate structures. The influence of ABH structural parameters, including the power exponent, cutoff thickness, and array configuration, is systematically investigated to optimize damping performance. Finally, experimental validation confirms that ABH-VDM achieves an additional 1.4 dB reduction in vibration across the entire frequency spectrum, with a bandwidth extension of 900 Hz. Moreover, ABH-VDM reduces mass by 8.6 %, demonstrating its potential for lightweight vibration control in structural applications. This research contributes valuable insights into advancing lightweight and broadband damping solutions for enhanced vibration management in engineering systems.

Acoustic black hole effect enhanced micro-manipulator

Microparticle manipulation is a critical concern across various fields including microfabrication, flexible electronics and tissue engineering. Acoustic-activated sharp structures have been designed as simple and flexible tools to manipulate microparticles with their good compatibility, fast response, and broad tunability. However, there still lacks rational acoustic-structure design for effective energy concentration at the acoustic-activated sharp structures for microparticle manipulation. Here, we present the acoustic black hole (ABH) effect as enhancement for the acoustic micro-manipulator. It provides great reliability, simplicity and ease of use, supporting custom design of high-throughput patterning modes. Moreover, compared to commonly used configurations, such as cylindrical or conical microneedles, those microneedles with ABH profile exhibit superior acoustic energy focusing at the tip and induce stronger acoustofluidic effects. The average acoustic flow velocity induced by the ABH microneedle is 154 times greater than that of the conical one and 45 times greater than that of the cylindrical microneedle. Besides, the average acoustic radiation force (ARF) produced by the ABH microneedle against acrylic microparticles is about 319 times greater than that of the cylindrical one and 16 times greater than that of the conical one. These results indicate that ABH design significantly enhances microparticle manipulation. We demonstrate this concept with ABH effect enhanced microparticle manipulation and study the parameters influencing its performance including operating frequency, operating voltage and particle diameter. Furthermore, considering the flexibility of this system, we employ it for various patterning and high-throughput microparticle manipulation. This work paves the way for controllable microparticle manipulation, holding great potential for applications in microfabrication and biomedicine.

Enhancing wave retarding and sound absorption performances in perforation-modulated sonic black hole structures

Sonic black hole (SBH) effects in a retarding duct can be exploited for sound wave manipulation and absorption. The phenomenon relies on two fundamental physical mechanisms: wave speed reduction and energy dissipation. In this study, we demonstrate that these two physical processes can be meticulously balanced through adjusting the perforation parameters in a perforation-modulated SBH (PMSBH). To elucidate the mechanism of slow wave generation and the effect of perforation parameters, an analytic model based on the Wentzel-Kramers-Brillouin (WKB) solutions to the linear acoustic wave equation is established. Alongside transient finite element simulations, the study unveils the roles that major physical parameters play in terms of regulating sound speed and sound absorption. The perforation ratio of the PMSBH is identified as the dominant factor affecting the slow-sound effect, with an optimal range of above 10 % for a PMSBH with densely segmented internal rings. Owing to the inclusion of the perforated boundary, prominent slow wave effects can still be maintained even with a reduced number of rings, provided that the perforation ratio is properly chosen within a reduced variation range. In both cases, the identified perforation ratio largely exceeds the conventional range widely adopted in the micro-perforation community when the slow wave effects are absent. On top of this, tuning the hole size can further enhance air friction for better sound absorption. Theoretical and numerical findings are experimentally validated, and the performance of the PMSBH is demonstrated. While bringing forward the concept of tunable design, this study offers physical insights and guidance for realizing effective sound absorbers embracing slow wave principles and perforation-induced sound absorption.

A parametric study of dynamic stress in acoustic black holes

Acoustic Black Holes (ABHs) make modifications to a structure that act to reduce the speed of a wave travelling through the ABH region. The reduced wavespeed has a corresponding reduced wavelength which increases the effectiveness of damping treatment applied to the ABH. A common way in which the reduction of wavespeed can be achieved is by gradually reducing the thickness of a structure. This is commonly implemented as a beam termination, which results in a thin tip. In this case, the energy focusing effect of the ABH causes high amplitude vibrations to occur in the thin section of the structure, raising concerns about high levels of dynamic stress that could result in fatigue failure. This paper presents an investigation into the effect of changing the ABH taper length, tip height and power law on the dynamic stress in an ABH terminated beam. This is achieved via numerical model of the structure, which enables a full parametric analysis to be carried out. For each ABH parameterisation, the performance is also quantified in terms of reflection coefficient so that trade-offs between performance and stress can be observed.

The modeling of acoustic black hole beam by spectral element method

A technique developed in recent decades for the passive control of vibrations and noise is the Acoustic Black Hole (ABH). The structural ABH effect is achieved by incorporating a local modification in the thickness of a thin structure, typically a beam or a plate, with a variation in thickness according to a spatial power law. The combination of the variation in the thickness power law and a local increase in damping, provided by the concomitant application of layers of viscoelastic material, produces a significant reduction in the wave propagation speed and an increase of attenuation properties. As an elastic wave propagates within an ABH, its propagation speed decreases smoothly and continuously, in theoretical case, when the structure's thickness disappears at the end of the ABH, the wave speed drops to zero. For practical applications, ABH is typically combined with dissipative materials to obtain significantly higher structural loss factors. This work aims to establish a numerical approach for modeling and designing a beam-type structural one-dimensional ABH device for vibration control device using the Spectral Element Method (SEM) and verified by the Finite Element Method (FEM). Examples are performed, and the results are compared with those found in the literature.

Acoustic black hole combined with microperforated plate for a rectangular waveguide

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.

Sound transmission loss of constrained layer damping composites featuring elastic plates embedded with acoustic black hole

This paper preliminarily investigates the influence of an elastic layer with an acoustic black hole (ABH) on the airborne sound insulation of a constrained layer damping (CLD) composite plate. ABHs represent a continuous impedance reduction in a local area of the structure, achieved by reducing material thickness. They efficiently dampen structure-borne sound in plate-like structures, resulting in excellent airborne sound attenuation performance. In the CLD composite structure, a damping layer is inserted between the elastic layers. This configuration achieves noise reduction and provides excellent airborne sound attenuation performance. By incorporating an ABH on one side of the elastic layer within the constrained damping composite structure and utilizing the damping layer as the terminal damping material for ABH, we achieve a lightweight structure with outstanding airborne sound insulation performance. Using finite element numerical calculations, we assess the airborne sound transmission loss of ABHs embedded within the CLD plate. Our analysis compares their transmission losses within the frequency range of 10 to 4000 Hz under normal-incidence and random incidence acoustic field excitations. While the ABH does not enhance the overall sound isolation performance of the CLD plate, it significantly improves the sound isolation dip at the resonance frequency.

Acoustic Black Hole silencers for broadband dissipation in ducted geometries

The design of novel absorbers avoiding the use of porous or fibrous materials for ventilation and air-conditioning systems constitutes a challenging issue. Recently, the development of metamaterials has provided new noise control perspectives for this problem. Traditional Acoustic Black Holes (ABHs) have been derived with close-ended configurations to achieve broadband absorption. These solutions are suitable as anechoic termination but they cannot be used as silencer as they require a mean flow going through the axis of the acoustic treatment. In this study different configurations of opened ABHs will be considered. Nominal ABHs build on straight cavities of increasing depth along the axial direction. To extend the bandwidth of acoustic performance towards the low frequencies, two different types of ABH silencers will be studied. Cavities with coiled geometries will be considered as a first instance, while the entrance of these cavities will be covered by micro-perforated consequently. The transfer matrix formulation will be adapted to these configurations and used to provide the ABH acoustical performance in terms of reflection and transmission of the silencer to find out the best configuration. These results will be validated against a Finite Element method and experiments will be carried out for the nominal configuration.

Numerical investigation of simply supported periodic rectangular plates with acoustic black hole wedge

In this paper, we propose the periodic rectangle plate with one-dimensional acoustic black hole (ABH) wedge under the simply supported condition. The vibration performances have been investigated by the semi-analytic method based on the levy solution method combined with WKB approximation, which is also validated by finite element method (FEM) simulation. For the rectangle ABH wedge, we derive the flexural wave dispersive relationship in plate, which also revealed the cut-on frequency. It can also be found that with the increase of periodic number, the vibration of plate structure can be reduced not only in the high frequency range where traditional ABH effect takes effect, but in low and middle frequency range the periodic ABH wedge can also show its advantage. Meanwhile, the damping coupling performance between the periodic ABH wedge and attached damping layers has also been investigated to enhance the vibration reduction. This novel kind ABH structure shows its potential in engineering applications.

Design of a multi-material acoustic black hole using geometric profile mapping

Since their inception, acoustic black holes (ABHs) have taken on many forms. A wide range of profiles has been investigated for beam termination applications, including power laws and cosine profiles. However, all of these configurations have a common issue - the profiles have an inherent thin section at the end of the beam. This makes the profile susceptible to damage towards the tip, particularly through fatigue. Multi-material ABHs have been proposed as an alternative solution, maintaining a constant external geometry whilst varying the material properties along the length of the ABH termination. Previous work on multi-material ABHs has focused on optimising section lengths of each material based on a cost function, namely kinetic energy in the host beam. This work investigates the performance of multi-material ABH designs with section lengths chosen to approximate the effective impedance change of a range of geometric ABH terminations. The relative performance of each discretised gradient is compared through simulation in addition to comparison to an equivalent continuous gradient.

Analysis of the physical mechanisms responsible for the Acoustic Black Hole effect

An acoustic black hole (ABH) inserted into a mechanical structure provides effective vibration damping without making the structure heavier. This property is particularly interesting in contexts where mass reduction is important. In practice, the ABH effect embedded in a beam or in a plate results from the combination of a local reduction in thickness and the addition of a thin viscoelastic damping layer. Consequently, an ABH is a weak point in the structure, which leads to the existence of local modes. An ABH can be seen as a penetrable resonant scatterer, with a high density of modes, all critically coupled. These properties intrinsically define the conditions required to obtain a true ABH effect. This definition will be presented and illustrated on examples of increasing complexity.

Optimizing acoustic black hole structures for vibration control in beams: a comprehensive analysis

Acoustic black holes (ABH) have caught the attention of researchers because of their potential to absorb sound and control vibrations. This study presents an analytical framework that determines reflection coefficients in ABH structures. It focuses on implementing an acoustic black hole with a power-law tapered profile on beams. Moreover, this research investigates how various geometric shapes affect Damping Loss Factor (DLF) coefficients. This helps identify optimal approaches to optimize ABH structures based on specific requirements. The finite element method and a topology optimization solver were used to optimize various parameters systematically. The aim is to reduce weight and response, thereby improving the efficiency of ABH designs, especially in low-frequency insulation applications. The results demonstrate that ABH exhibits excellent performance in suppressing vibrations.

Topological interface states in deep-subwavelength phononic beams with acoustic black hole configurations

We present deep-subwavelength phononic beams engineered with unit cells incorporating acoustic black hole (ABH) configurations. The ABH design enables the realization of topological interface states (TISs) within the first band gap at low frequencies, where the lattice constant (a) is far smaller than the wavelength (λ) of the controlled wave. Manipulating the ABH configuration and breaking the unit-cell symmetry allow us to control Zak phases for the topological beams. Two topologically distinct phononic beams are interconnected to produce the TIS within their low-frequency band gaps. Through numerical and experimental demonstrations, we confirm the existence of TISs at frequencies ranging from 4.3 to 8.5 Hz using the designed topological beams of which a/λ is less than 1/20. We also offer the potential to further reduce the value of a/λ by rearranging the ABH unit cells.

Virtual acoustic black holes as a means to achieve low-frequency vibration reduction

Acoustic black holes (ABH) offer exceptional broadband vibration capabilities but have the inherent drawback of being only effective beyond a specific cut-off frequency. The most straightforward approach to set this threshold to a low value is to increase the ABH length. However, such a strategy leads to a very thin tip of the ABH, making it very complicated if not impossible to manufacture. Improving this ABH property has been for the past decade an active field of research. Recently, the concept of a virtual acoustic black (VABH) has been proposed by the authors. The key idea of this approach is to implement digitally the mechanical impedance of the ABH. The virtual feature of this strategy enables the implementation of any kind of ABH (any dimensions, material). Setting the cut-off frequency to low values thus becomes possible. The VABH is implemented through the use of piezoelectric patches, making it very compact and autonomous. Experimental demonstration shows that the proposed idea is able to mitigate vibration below 100 Hz.

Geometrically nonlinear vibrations of plate embedding a large circular acoustic black hole

The concept of acoustic black hole (ABH) designates a decrease in bending stiffness and a localized added damping within a thin structure aiming to localize and efficiently dissipate vibrations. The small thickness results in large amplitude vibrations, which suggests to take into account geometrical nonlinearities. The subject has been previously studied on a beam with a one dimensional ABH. Previous research studied a geometrically nonlinear plate embedding a one dimensional ABH. This study aims at solving the Von Karman equations for a variable thickness plate, via a modal projection using the eigenmodes obtained with a finite element model. The use of a finite element model in this context allows to take into consideration more complex geometries. The methodology is then applied to a rectangular plate embedding a large circular ABH with added damping. The convergence of the nonlinear coefficients is studied and time domain computations show the relative importance of the geometrical nonlinearity.

Vibration damping of sandwich panels using the Acoustic Black Hole effect

Among the existing passive vibration control techniques, the use of the acoustic black hole (ABH) is a solution that has the advantage of not increasing the mass of the structure in which it is integrated. In this paper, the benefits of inserting an ABH into a three-layer sandwich panel (fibreglass skins and honeycomb core) are investigated. It is known that an ABH effect can be achieved in a panel by locally reducing its stiffness (using a reduction in plate thickness according to a power law profile) and increasing local damping (using a coating of viscoelastic material). A sandwich panel induces a shear effect that strongly affect the wave propagation and lead to specific properties to the ABH effect. The equations of motion of a thick, symmetrical sandwich panel with non-uniform characteristics are obtained within the framework of zig-zag theory by applying Hamilton's principle. These equations lead to a semi-analytical model of order 6, from which an effective bending stiffness, dependent on both frequency and space can be derived. Using this model, it is demonstrated that the sandwich effective bending stiffness favours the ABH effect. This interesting property is also validated by experimental tests on sandwich panels using laser vibrometry.

Vibroacoustic behaviour of a sound cavity enclosed by an acoustic black hole beam

In this paper, we propose a numerical approach to characterize the vibroacoustic coupling between a two-dimensional air cavity and an acoustic black hole (ABH) beam. Displacement variables expanded in terms of Gaussian basis functions are used for both the fluid and the solid, and the coupling condition at the interface between the beam and the cavity is imposed following the null space method (NSM). The approach turns out to be free of numerical instabilities. Concerning the simulations, it is shown that the noise inside the cavity is significantly reduced when the excitation is exerted on the ABH beam as compared to a uniform one. However, if a sound source is placed inside the cavity, no significant noise reduction is achieved by coupling the cavity to an ABH beam instead of a uniform one.

A piezoelectric acoustic black hole absorber for rail vibration reduction and energy harvesting: Semi-analytical model

Theoretically, vibration energy can be converted and harvested during the process of vibration reduction, thus enabling a self-powered supply for sensor nodes. However, little research was reported on rail absorbers that combine vibration reduction and energy harvesting. Accordingly, this study aims to design an absorber based on the acoustic black hole (ABH) effect, termed the P-ABH absorber, that can simultaneously achieve broadband vibration reduction and energy harvesting. Firstly, the P-ABH absorber was preliminarily designed, and the semi-analytical model of the track with the P-ABH absorber was established by the Rayleigh-Ritz method. Secondly, the semi-analytical model was verified by the 3D finite element method, and the vibration reduction and energy harvesting performance were initially evaluated. The dimensions of the ABH structure, along with the sizes of the piezoelectric patches, were then determined. Finally, the vibration reduction and energy harvesting performances of the P-ABH absorbers fully deployed between each fastener were evaluated. The results demonstrated that the P-ABH absorber exhibited a wider vibration reduction bandwidth than the uniform piezoelectric absorber and the piezoelectric patches, with an increase in energy harvesting power by 27.47 % and 115.26 %, respectively. The vibration reduction and energy harvesting performance were significantly affected by the number of piezoelectric patches but little affected by the thickness and total length. When the P-ABH absorbers were fully attached to the rail, the overall mean square velocities at the three resonant frequencies, which required emphatic control, were reduced by 36.77 %, 98.37 %, and 3.52 %, respectively. Meanwhile, the energy harvesting performance was excellent. The P-ABH absorber presents a promising solution for improving the sustainability and cost-effectiveness of track systems.

Acoustic Black Holes ceiling for noise control on board cruise ships

Entertainment is one of the principal noise sources on board cruise ships. To ensure high comfort standards in cabins located above public areas, ceilings made by rockwool and honeycomb panels are used as acoustic insulation. Engineers are searching for new solutions to substitute the traditional system, as the rockwool presents health concerns. Acoustic metamaterials are among the candidates for new products in this field. This paper aims to verify the feasibility of an innovative ceiling design with enhanced Acoustic Black Holes (ABH). The proposed solution is compared with the traditional ones, using the Sound Reduction (R) as Key Performance Index (KPI). Traditional solutions are experimentally tested, and the data are used to assess an acoustic Finite Element Method (FEM) model, which is then used to simulate the acoustic properties of the proposed ceiling.