Two-dimensional Acoustic Black Hole Research Articles

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

Many rooms struggle with the absorption of low-frequency sound due to its long wavelengths. The integration of existing solutions into these spaces is often challenging due to their intricate installations and large depths. To address this problem, a new type of resonance absorber has been developed: the Distributed Mode Absorber (DMA). It consists of a thin vibrating front panel and a volume of enclosed air behind it. This straightforward structure can be utilized to create acoustically functional furniture that can be seamlessly incorporated into rooms. This article is devoted to the structural optimization of the DMA front panel, using the Acoustic Black Hole (ABH) effect known within structural dynamics. A numerical model is constructed using a Finite Element Analysis (FEA) and examined numerically. Several geometric parameters of the ABH are studied with regard to their influence on the vibrations of the front panel. Prototypes are developed and manufactured based on these insights. The quality of the numerical model is verified during the subsequent validation. Finally, the sound absorption of the improved DMA is compared with that of the reference DMA.

Surrogate model-based multi-objective design optimization of vibration suppression effect of acoustic black holes and damping materials on a rectangular plate

The acoustic black hole (ABH) is a ground-breaking passive technology for vibration reduction and noise attenuation, characterized by its ability to manipulate flexural waves. When multiple two-dimensional ABHs are embedded in an irregular shaped complex plate structure used in engineering, such as the support plate of a refrigerator compressor, its vibration characteristics often cannot be solved through analytical or semi-analytical methods, resulting in the inability to carry out subsequent ABH optimization design. To address this issue, we propose a high-precision modelling method that combines surrogate models with finite element methods to construct a vibration characteristic database of the compressor support plate embedded with multiple ABHs in all design spaces of the ABH and damping materials geometric parameters using limited sample data. A high-precision surrogate model was constructed based on the vibration response data of the ABH plate under 50 parameter combinations of ABH and damping layer, and the fitting accuracy of the surrogate model was verified through vibration response data under another 25 parameter combinations. Based on the constructed surrogate model, the Multi-objective Genetic Algorithm (MOGA) was employed to optimize the five parameters of ABH and damping layer simultaneously, aiming to maximize the vibration reduction effect of the ABHs. Our investigation reveals that the optimized ABH and damping materials significantly improve the vibration suppression effect in a wide frequency range compared to the unoptimized structures. Finally, experimental verification was conducted to solidify the accuracy and efficacy of our approach in enhancing vibration reduction effect for irregular shaped complex plate structures using acoustic black holes.

The Modeling of Disc-shaped Acoustic Black Hole Plate and Vibration Characteristics

The Acoustic Black Hole (ABH) structure has great potential in vibration and noise control due to the characteristics of high damping and energy accumulation. A dish-shaped two-dimensional acoustic black hole plate is proposed in order to reduce the possibility of the structural damage happened in conventional embedded ABH in the centre of the plate. The dish-shaped acoustic black hole plate only cuts ABH on the edge. The finite element method is often used to establish the model of acoustic black hole plates. However, it is high cost and low efficiency in computation. A semi-analytical theoretical model of the disc-shaped acoustic black hole plate based on Gaussian expansion method is established in order to improve computation efficiency. Meanwhile, the shape function filtering method is proposed to solve the problem of non-convergence when Gaussian expansion method is used to model a non-rectangular plate. A finite element model of the disc-shaped acoustic black hole plate is established and used to verify the accuracy of the proposed semi-analytical theoretical model. The results show that the dish-shaped acoustic black hole plate has excellent energy accumulation effect and can be used further as Dynamic Vibration Absorber (DVA) to reduce the vibration of host structure.

Higgs phonon: conformal phonon and Hawking temperature in a two-dimensional acoustic black hole model

Higgs phonon: conformal phonon and Hawking temperature in a two-dimensional acoustic black hole model

Two-Dimensional Eulerian-Exponential-Law Acoustic Black Hole Structure for Energy Harvesting

Thin plates are widely used in engineering, so it is of great value to explore energy harvester based on this type of structure. Acoustic black hole (ABH) is helpful for the energy harvesting of thin plate. However, the traditional power-law ABH needs to be improved in the low-frequency energy harvesting. Thereupon, a new Eulerian-exponential-law for ABH is proposed, and a two-dimensional ABH structure based on the Eulerian-exponential-law is designed for harvesting low-frequency energy. This paper constructs a simple electromechanical coupling dynamic model for the Eulerian-exponential-law ABH energy harvester (EAEH). This model has low computation complexity as the dimension of thin plate is reduced by the Kronecker product of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> -direction and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> -direction beams’ modes. Combining the element division and modal analysis of beam, a new method with high computational efficiency is proposed for calculating the base functions of thin plate with two-dimensional ABH, and its effectiveness and accuracy are validated by the result of finite element analysis. Under different excitation frequencies, the voltage and power responses of EAEH are simulated, and their validity is verified by the experimental results. Moreover, EAEH is compared with the power-law ABH energy harvester through the simulation and experiment. The comparative results show EAEH has lower resonant frequencies and higher output of voltage and power.

Novel vibration control method of acoustic black hole plates using active–passive piezoelectric networks

In recent decades, many methods have been applied to vibration system damping and control, including acoustic black hole (ABH) structures and active–passive hybrid piezoelectric network(APPN) structures. This paper takes a two-dimensional ABH plate based on Kirchhoff plate theory as the research object, systematically researching the structure of the integration of APPN and ABH. Firstly, the vibration modes of the ABH plate are obtained by the finite element method. Then, Hamilton’s principle and the Rayleigh–Ritz method are used to derive the dynamic models. The open-loop and closed-loop control characteristics are analyzed, respectively. The results show that the ABH plates with active–passive piezoelectric networks perform better than those with active vibration control. Finally, the parameters (resistance and inductance) in APPN are optimized to obtain the best vibration control performance. The results show that the new system combined APPN and ABH firmly controls vibration and noise reduction.

Low-frequency sound radiation characteristics of imperfect acoustic black hole in thin plate

The unique dynamic characteristics and energy focalisation of the acoustic black hole (ABH) have been confirmed. Meanwhile, an ABH composite structure covered with a damping layer exhibits excellent performance in vibration control. However, limited by machining accuracy and conditions, imperfect ABH is easier to obtain than ideal ABH. This study focuses on the sound radiation characteristics of an imperfect ABH thin plate without a damping layer in the low-frequency range. The imperfect ABH in this paper replaces the traditional curve with an oblique line near the centre of two-dimensional ABH. The vibration and acoustic changes of imperfect ABH plate are investigated based on three key variables: ABH diameter, residual thickness and centre position of imperfect ABH indentation. The finite element method (FEM) is used to calculate the radiation efficiency of various imperfect ABH plates at eigenfrequencies. The acoustic radiation efficiency is measured and estimated via a sound-intensity experiment. Both the simulation and experimental results show that the acoustic radiation efficiency of thin plates can be controlled by an imperfect ABH in the low-frequency band, which is associated closely with the geometric parameters and position of imperfect ABH.

Research on Vibration Energy Harvester Based on Two-Dimensional Acoustic Black Hole

The wave energy focus effect of an acoustic black hole (ABH) is used for broadband vibration energy harvesting and boosts the harvested power. A vibration energy harvester based on two-dimensional ABH is proposed in this study, which consists of a rectangle plate with 2-D ABH and PZT film attached. The structure of ABH was designed and analyzed based on numerical simulation. The optimal parameters of the ABH were obtained, such as the power index, truncation thickness, cross-sectional length, and round table diameter, which were 3, 0.4 mm, 40 mm, and 24 mm, respectively. The quadratic velocity of the plate surface with ABH is up to 22.33 times that of a flat plate, and PZT film adheres to the corresponding positions of the ABH structure and plate structure, respectively. In the same condition, the average output power of a PZT with an ABH structure is higher than that of a flat plate under the same excitation-vibration condition.

Influence of Structural Form on the Acoustic Black Hole Array Coupled with Damping Layers

Because of the characteristics of manipulating bending wave, acoustic black hole (ABH) structures can efficiently concentrate vibration energy in the center. Other than single ABH structures, the ABH array or damping layers can be used to have a better performance in vibration reduction and noise control, which have great engineering application prospects of plate parts. In order to explore the influences of ABH array on vibration and noise reduction, finite element models of two-dimensional ABH array coupled with damping layers were established in this paper to study the effects of arrangements and number of ABH cells on dynamic characteristics. Firstly, this paper analyses the influences of array embedded with three ABH cells on the modal loss factor and vibration characteristics of the structures as well as the effects of different arrangements. Secondly, the array with different number of ABH cells were established to study the effects of the number of elements on the vibration response of the plate. Finally, the structure-sound coupling models were established to study the acoustic radiation characteristics and explain the noise response of the array plate. This study provides a reference for the design and application of the plates embedded with ABH array.

A method for improving wave suppression ability of acoustic black hole plate in low-frequency range

The acoustic black holes (ABH) with the power-law profile are applied in many fields, such as vibration control, energy collection, etc. It is widely known that the ABH only works above the cut-on frequency. However, few studies improve the vibration suppression performance of acoustic black hole structures below the cut-on frequency. This paper proposes shunt damping to improve the wave suppression ability of an ABH plate in the low-frequency range. The ABH plate with shunt damping obeys the Kirchhoff–Love plate theory. Based on the Hamiltonian principle, the modified Fourier series is selected as the shape function, and the natural frequency of the ABH plate is calculated by the energy method. Compared with the finite element method results, the correctness of this method is verified. Further, comparing the vibration characteristics of the ABH plate with those of the uniform thickness plate, it can be obtained that the ABH plate has excellent vibration damping performance in high frequency but a poor effect in low frequency. Therefore, a shunt damping with blocking circuits is pasted on one side of the central area of the ABH and successfully suppresses four resonate formants in the low-frequency band. Finally, the high-frequency vibration characteristics of the ABH plate with shunt damping are improved by increasing the thickness of the ordinary damping layer. This paper proposes a shunt damping ABH plate composite structure with excellent vibration suppression performance in both the high-frequency and low-frequency range, providing a new idea for the application of two-dimensional ABH plate structures in vibration control.

Attenuation band splitting in a finite plate strip with two-dimensional acoustic black holes

Acoustic black holes (ABH) lattice is an effective way to realize the bandgaps (BGs) through lightweight design. The predicted BGs using infinitely large periodic structures are commonly believed to enable corresponding attenuation bands (ABs) even the structure only contains a limited number of unit cells. This paper reports an unusual splitting phenomenon in the ABs of a finite plate strip with two-dimensional (2D) ABHs. A wide AB predicted by BG is split into two ABs in the finite strip separated by a high resonance peak, which challenges the aforementioned common belief. Results show that the increasing number of periodic unit cells has a negligible effect on the frequency and amplitude of the resonance peak. Its underlying mechanism is clarified by investigating the relationship between the BGs and ABs, obtained from infinite and finite periodic plate strips with the same 2D ABHs respectively. Complex wavenumber analysis results show the existence of two flexural wave modes in the considered frequency range due to the finite width of the strip. Two types of BGs, in which one satisfies the Bragg condition, are found when both wave modes fail to propagate. Analysis of structural modes further uncover the physical reason for the emerging AB splitting: a certain natural frequency of the boundary portion of the 2D ABHs strip falling into the theoretical BG. Due to the boundary reflection and energy concentration, this structural portion can loosely be regarded as a clamped-free plate strip. It is demonstrated that the resonance peak splitting the AB becomes tunable via disrupting the structural details of finite ABH strips. In particular, extending the terminal end of a finite ABH strip allows the change in boundary portion, which is conducive to eliminating the splitting peak. The reported study is helpful for the design of finite periodic structures with broadband attenuation bandgap.

Influence of Acoustic Black Hole Array Embedded in a Plate on Its Energy Propagation and Sound Radiation

The plate embedded with acoustic black hole (ABH) indentations is potential for structural vibration and noise control. This work focuses on the mid- and low-frequency performance of plates embedded with the array of ABH for energy focalization and vibration and noise suppression. Plates embedded with two-dimensional ABHs are modelled with detailed Finite Element models, and the power flow method is introduced to analyze the energy propagation characteristics arising from the ABH effect. Then, the distribution of average vibration power density along the ABH radius is studied. Next, the energy dissipation effects of the plate model embedded with the ABH array with two types of damping layers are investigated. Finally, the sound pressure levels of the ABH structure are calculated and discussed. This work is helpful to understand the characteristics of plates embedded with the ABH array in reducing vibration and noise radiation. Results show that the ABH array can realize more than 100 times energy focalization effect at some frequencies, which indicates a potential in vibration and noise control when coupled with damping materials.

Optimization of Damping Configurations in a Plate Embedded with ABH Array

Owing to its broadband and lightweight features, the Acoustic Black Hole (ABH) effect has attracted increasing interests in the structural dynamics and vibration-acoustic communities in recent years. And damping material is essential to achieve effective ABH phenomena. To explore effective vibration and noise control in thin-walled structures such as vehicle body panel using ABH effect, aiming at the plate embedded with two-dimensional ABH array, this paper investigates the coupling between ABH structure and damping material. First, the energy dissipation mechanism of viscoelastic damping material is analyzed to obtain the deformation characteristic that leads to effective energy dissipation. Next, the bending deflection of a plate with a single ABH under harmonic excitation is investigated, and the damping material configuration is optimized to obtain an optimal vibration suppression. Finally, the above-mentioned configuration is applied to a plate embedded with the ABH array and compared with the conventional damping arranging method. And the advantages of this damping material configuration scheme in vibration and noise control are investigated and summarized. This paper provides a reference for the damping material configuration and optimization of the thin plates embedded with ABHs.

The phonon mass and the Hawking temperature in the two-dimensional acoustic black hole model

In this paper, the acoustic metric and effective action are derived by using the shift transformation and functional integrals method, this metric can describe the fluctuation of the phonon fields in the quantum fluid. When the phonon fields are coupled with different types of 2-D gravity, i.e., Jackiw-Teitelboim model and Almheiri-Polchinski model, then the effective mass of the phonon fields and the Hawking temperature can be calculated in the analytical form. In addition, the influence of fluctuation intensity and deformation parameter to the phonon mass and the Hawking temperature are also analyzed and discussed.

A vibration absorber based on two-dimensional acoustic black holes

As a passive damping technique for vibration and noise mitigation, acoustic black hole (ABH) structures have been drawing an increasing attention because of their easy-to-realize and broadband wave focusing and energy dissipation characteristics. Structures with embedded ABHs, however, inevitably compromise the overall structural stiffness and strength, which hampers their use as critical structural components. As an alternative, this paper proposes a new type of device, i.e. a two-dimensional circular ABH-based dynamic vibration absorber (2D ABH-DVA), as an auxiliary component to be added to an existing structure for vibration suppressions. Using a plate as benchmark structure, finite element (FE) simulation results show a systematic reduction of its resonant peaks over a broad frequency range upon the deployment of the ABH-DVA. Analyses uncover two underlying mechanisms which dominate the physical process: dynamic interaction with the host structure and damping enhancement as a result of ABH-specific energy trapping. This is warranted by an effective dynamic coupling between the primary structure and the add-on ABH-DVA, which can be quantified by a mode-specific and location-dependent coupling coefficient defined in the paper. It is further demonstrated that, despite the rich modal contents of the ABH-DVA, strong coupling with the primary structure only takes place through a few DVA modes. Analyses also lead to a simple linear relationship relating the overall system damping with the properties of the damping material over the ABH-DVA. Finally, the broadband vibration suppression ability of the proposed 2D ABH-DVA is verified through experiments. The study demonstrates the unique coupling features between the DVA and the host structure, which provides design guidelines for unsymmetrical 2D or other ABH-DVA designs in the future.

Enhancement of Wave Energy Dissipation in Two-Dimensional Acoustic Black Hole by Simultaneous Optimization of Profile and Damping Layer

Acoustic black hole (ABH) effect in thin-walled structures provides drastic wave focalization. In a practical ABH structure with a tapering thickness profile, the concentrated wave energy can be efficiently dissipated by introducing a damping layer to the local high energy density area. In this paper, simultaneous optimization of the geometric parameters of the ABH profile and the topology of the damping layer covering the ABH area is investigated based on the former study of wave focalization. To optimize the ABH structure for achieving maximum energy dissipation, parametric modelling is implemented, and the dissipated energy is computed by the commercial finite element software Abaqus. The optimal geometric parameters of the ABH thickness profile are obtained by the method of moving asymptotes (MMA). The topological optimization problem of the damping layer is solved by using optimality criteria (OC). These two algorithms are nested alternatively in the main optimization procedure. The influence of mesh size and direction of wave incidence on the optimization is discussed. Numerical results show that the proposed approach is efficient in finding the optimal design for the ABH structure to achieve maximum wave energy dissipation. In addition, the influence of coupling between the host ABH plate and the layer on the optimization is investigated. Superior performance of energy dissipation is achieved by the proposed method comparing to the results before the optimization.

Effects of Acoustic Black Hole Parameters and Damping Layer on Sound Insulation Performance of ABH Circular Plate

The acoustic black hole (ABH) can be utilized to achieve aggregation of flexural wave in structures with the feature that the thickness gradually reduced to zero with a power exponent no less than 2. The above characteristics could be applied in vibration reduction, noise attenuation or improving sound insulation. Previous literatures on vibration and acoustic characteristics of ABH structures mainly focus on the structural response under mechanical force excitation, while the transmission loss (TL) of circular plates embedded with two-dimensional ABHs investigated in this paper is a vibro-acoustic coupling procedure under excitation of diffuse sound field. Series of vibro-acoustic coupling finite element models (FEM) for TL analysis of ABH circular plates were established by automatic matched layer (AML) method in this paper and an experimental platform for measuring TLs of ABH circular plates and uniform plates was constructed. The accuracy of the FEM analysis was verified by experimental measurements. To systematically analyze the influence mechanism of parameters of the ABH on TLs of ABH circular plates, the effects of diameter, orientation, number, and truncation thickness of ABHs on TLs of ABH circular plates were further studied. The effect of the damping layer on TLs of circular plates embedded with 1 and 19 ABHs was also analyzed and it reveals that the influence of damping layer mainly concentrates on the first-order resonance frequency and damping-controlled region of the plate, and at some frequencies, the greater the damping layer thickness, the worse the sound insulation performance, despite that the modal damping loss factor has been increased in the whole frequency domain.

Overview of localised flexural waves in wedges of power-law profile and comments on their relationship with the acoustic black hole effect

In the present paper, the relationship between localised flexural waves in wedges of power-law profile and flexural wave reflection from acoustic black holes is examined. The geometrical acoustics theory of localised flexural waves in wedges of power-law profile is briefly discussed. It is noted that, for wedge profiles with power-law exponents equal or larger than two, the velocities of all localised modes take zero values, unless there is a wedge truncation. It is demonstrated that this effect of zero velocities of localised flexural waves in ideal wedges is closely related to the phenomenon of zero reflection of flexural waves from ideally sharp one-dimensional acoustic black holes. A possible influence of localised wedge modes on flexural wave reflection from one-dimensional acoustic black holes having rough edges is discussed. With regard to two-dimensional acoustic black holes, the role of localised flexural waves propagating along wedge edges that are curved in their middle plane is considered. Such waves can propagate along edges of inner holes in two-dimensional acoustic black holes formed by circular indentations in plates of constant thickness. A possible impact of such localised waves on the processes of scattering of flexural waves by edge imperfections of inner holes in two-dimensional acoustic black holes is discussed, including their influence on the efficiency of two-dimensional acoustic black holes as vibration dampers.

Parametric study on shape of two-dimensional acoustic black holes

With the deployment of the passive damping in Acoustic Black Holes (ABH), the effectiveness of ABH in absorbing vibration are improved, as demonstrated in beam-plate structures. Apart from previous studies on the one dimensional ABH (by changing parameters such as the length, power-index of ABH thickness profile, and distribution of damping layer), this paper presents the study of the influence of the shape of a two-dimensional ABH on its absorptive performance. Keeping the area and amount of damping constant over the ABH region, different shapes of ABH embedded in the semi-infinitely long plate were simulated and studied using a finite element model. Dissipated power ratio (DPR) and root-mean-square velocity (RMSV) of the ABH region were measured to evaluate the ABH dissipative behaviors. Structural intensity was also used to visualize and analyze the flow of vibration energy in the system. These analyses of SI propose the correlation between the energy flow and the absorptive performances of ABH. This link between the energy flow and the shape of ABH provides a way to design an ABH for better absorption and dissipation of vibroacoustic energy in the system.With the deployment of the passive damping in Acoustic Black Holes (ABH), the effectiveness of ABH in absorbing vibration are improved, as demonstrated in beam-plate structures. Apart from previous studies on the one dimensional ABH (by changing parameters such as the length, power-index of ABH thickness profile, and distribution of damping layer), this paper presents the study of the influence of the shape of a two-dimensional ABH on its absorptive performance. Keeping the area and amount of damping constant over the ABH region, different shapes of ABH embedded in the semi-infinitely long plate were simulated and studied using a finite element model. Dissipated power ratio (DPR) and root-mean-square velocity (RMSV) of the ABH region were measured to evaluate the ABH dissipative behaviors. Structural intensity was also used to visualize and analyze the flow of vibration energy in the system. These analyses of SI propose the correlation between the energy flow and the absorptive performances of ABH. This l...

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

This paper presents a method for wide-field vibrometry based on high-speed digital holographic interferometry. We demonstrate the possibility of measuring transient vibrations of structures at 100 kHz frame rate when providing 46600 quantitative data on 380 cm2 rectangular spot at the object surface. Investigation of travelling acoustic waves propagating in alloy plate equipped with a two-dimensional acoustic black hole (ABH) is considered. Such a structure leads to localized vibrations of high amplitude and constitutes a good candidate for methodology testing. The wave front is generated by a short shock with duration about 50 μs? The time sequence of the vibration field obtained after the shock is depicted and exhibits the propagation of the wave front in the plate and inside the ABH. It follows that the observation of the modification of the wave propagation can be observed at very short time scale. The modification of the wave front due to the gradient in elastic properties related to the ABH area is also highlighted.