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Frequency dependence of the sound reflection coefficients from QABH (blue line), QABH (Sponge covers the hole of Rib1) (dashed green line) and QABH (Sponge covers the holes of the first four ribs) (dashed red line).
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In the present paper, the results of the first experimental investigation of the acoustic black hole for sound absorption in air are described. To achieve the required power-law de-crease in sound velocity with propagation distance the inhomogeneous acoustic waveguides earlier proposed by Mironov and Pislyakov (2002) and made of quasi-periodic ribb...
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Context 1
... the LABH (with sponge covering the cavity of the first four ribs) is more efficient than the LABH (without sponge inserted), this increase in efficiency is not as large as could be expected. The measured sound reflection coefficients from QABH (with small pieces of sponge inserted at the end) and from QABH (without sponge) also do not show much difference (see Figure 6). ...
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Citations
... In subsequent theoretical works [2,3], the behavior of ABHs with quadratic radius profile has been modeled employing the transfer matrix method (TMM), the application of fractional calculus has been also explored [4]. Acoustic black holes have also been studied experimentally [5,6]. The authors of these works constructed ABHs with linear and quadratic radius profiles and demonstrated a reduction of the reflection coefficient when the ABH was used as an absorbing duct termination. ...
... Mi et al. [8] studied the performance of an ABH with a quadratic profile and closed or open end. They performed experimental measurements on a rather fine (compared to the previous works [5][6][7]) 3D-printed structure. Various modifications and applications of ABHs have also been explored, such as open mufflers inspired by ABHs [9], mufflers based on ABHs combined with micro-perforated plates [10,11], a duct with embedded periodic ABHs [12], or thin ABH-inspired metamaterials [13]. ...
This article presents a systematic numerical study of the absorbing properties of acoustic black holes (ABHs) serving as an anechoic termination of waveguides. The study focuses on the sensitivity of ABHs’ absorbing performance to their profile and internal-structure parameters. The article compares numerical predictions from 1D model based on the Riccati equation with a detailed 2D model based on the linearized Navier-Stokes equations and the finite element method, finding good agreement among all results, especially for ABHs with fine internal structures. The mean value of the reflection coefficient modulus is used to quantify the ABH’s absorbing performance, and the article introduces the use of power-law functions and cubic splines to define the ABH’s shape function. An evolutionary algorithm is employed to optimize the ABH’s profile, resulting in improved absorbing performance. The numerical results suggest that the optimum shape is simple and more-or-less insensitive to other geometrical and internal-structure parameters.
... The retarding mechanism progressively reduces to zero the effective velocity of the incoming perturbation until it reaches the structure edge, where a non-reflecting condition takes place. This slow-sound generation phenomenon has also been considered for the design of metamufflers in order to trap and dissipate the energy of acoustic waves propagating in a waveguide [18][19][20]. Such metamufflers are composed of a set of ring sections separated by air cavities of variable depths distributed along the whole axial length. ...
Acoustic detection of machinery defaults from in-duct measurements is of practical importance in many areas, such as the health assessment of turbines in ventilation systems or engine testing in the surface and air transport sectors. This approach is, however, impeded by the low signal-to-noise ratio (SNR) observed in such environments. In this study, it is proposed to exploit the slow sound effect of Sonic Black Hole (SBH) ducted silencers to enhance the sensing of incident pulse acoustic signals with low SNR. It is found from transfer matrix and finite element modelling that fully opened SBH silencers with perforated skin interfaces are able to substantially enhance an incident pulse amplitude while channeling an air flow. We demonstrate that the graded depths of the SBH cavities provide rainbow spectral decomposition and amplification of the incident pulse frequency components, provided that impedance matching, slow sound, and critically coupled conditions are met. In-duct experiments showed the ability of a 3D printed SBH silencer to simultaneously enhance acoustic sensing and fully trap the pulse spectral components in the SBH cavities in the presence of a low-speed flow. This study opens up new avenues for the development of dual-purpose silencers designed for acoustic monitoring and noise control in duct systems without obstructing the air flow.
... Due to its satisfactory bending wave attenuation ability, ABH structures have great potential for mechanical vibration and acoustic radiation control [6][7][8][9][10][11]. Acoustic black hole structures can be integrated into the existing L. Yan and Q. Ding structures, such as fuselages and vehicles, as effective energy dissipation components [12][13][14]. ...
This paper introduces a structural design which has superior energy harvesting ability. The proposed structure is based on the ability of most periodic structures to prohibit elastic waves from propagating in a specific frequency range of the phonon band gap. By leading into acoustic black hole (ABH) units and utilizing the energy concentration characteristics of the ABH structure, the filtering effect can be made more significant. These two characteristics can produce significant strain and energy localization, which is conducive to energy harvesting. In this paper, we obtained ABH unit capable of producing broadband gaps by adjusting the geometric parameters of the ABH structure, and chose a cantilever as the research object for energy harvesting, by applying a piezoelectric patch on the unit located near the fixed end to gain a broader application in the actual situation. The results show that the beam combining the energy concentration characteristics of band gap and ABH structure has a significant improvement in energy harvesting efficiency. Optimization on the parameters of ABH unit shows that the band gap characteristic of the periodic ABH structure can further optimize the energy harvesting efficiency of practical energy harvesters, and opens up a new possibility of energy harvesting of ABH structure.
... When the number of rings in a SBH is small, the TMM is not accurate enough to describe its performance. Earlier experiments in [18,19] for linear and quadratic SBHs left some open questions regarding the efficiency of the absorption material in SBHs at high frequencies. These discrepancies have recently been investigated by means of finite element method (FEM) simulations. ...
... These discrepancies have recently been investigated by means of finite element method (FEM) simulations. The latter were initially carried out for SBHs in [20], revealing the importance of cavity resonances for practical realizations, but it has not been until the simulations in [21,22] that the role of different types of damping and cavity resonances have helped to understand the results in [18,19]. Moreover, in [23] a semi-analytical equivalent fluid model was developed, which improves the TMM description and showed, for the considered example, that at low frequencies the resonances along the duct axis determined the SBH performance according to the theory in [1], while at higher frequencies the resonances of the cavities took the leading role, as in the rainbow-trapping absorber of [24] (see also the recent SBH inspired muffler design in [25]). ...
The standard configuration of a sonic black hole (SBH) is a discrete set of rings with back cavities at a duct termination, whose inner radii decrease according to a power-law. Although several practical realizations of this type of slow-sound waveguide have been investigated, the continuous problem in which the number of ring/cavity sets goes to infinity has not been analyzed in depth. Understanding its performance is interesting in itself and could provide clues for new designs. For this purpose, we transform the generalized Webster equation for the acoustic pressure inside the ideal SBH into a spatially varying wavenumber Helmholtz equation for a new locally scaled pressure. We eliminate the singularity of the original problem at the SBH termination by considering a rigid residual surface that will be shown to play a role analogous to that of the acoustic black hole (ABH) residual thickness in beams and plates. The variational formulation of the Helmholtz equation is presented and solved by expanding the unknown scaled pressure in terms of a basis of Gaussian functions. The same framework is used to set up an eigenvalue problem that provides the SBH modes and thereby a modal decomposition for the pressure within the SBH. Once the theoretical foundations are established, the variation of the speed of sound and wavenumber in the SBH is presented. The dependence of the shape and distribution of the modes on the residual surface and damping helps to clarify the occurrence and disappearance of oscillations in the input admittance and reflection coefficient of the SBH at different frequencies. For the latter, a detailed parametric study is carried out. Alternative profiles to the power law are also investigated, some showing reflection coefficient values similar to those of the classical SBH.
... The TMM can partially take them into account, but for a more realistic description showing, for example, the inhomogeneous acoustic pressure distribution inside the cavities or the interaction between them, the finite element method (FEM) is required. The first FEM simulations for the wave equation in SBHs were reported in [15] and recently, a very thorough analysis studying the effects of different types of damping inside a SBH has been presented in [16], using FEM simulations for the Helmholtz equation to try to explain the discrepancies between predictions and experiments in [17,18]. FEM simulations have been carried out for the linearized Euler equations in [19] showing also the influence of cavity resonances and in [20] a semi-analytical fluid model is developed demonstrating how at low frequencies on-axis resonances dominate (associated with the SBH effect), while at higher frequencies cavity resonances prevail (depending on the particular SBH design). ...
... As can be seen in all the figures, filling some cavities with absorption produces a substantial G. Serra et al. improvement, since the reflection coefficient decreases significantly at all frequencies (see [6] for the influence of damping without optimization processes). It is observed that this is the case except for the highest frequencies in the linear and redesigned cases, a problem already noticed in experimental work in the literature [4,17,18], for which a plausible explanation has recently been proposed [16,19,20]. It should be noted that this high-frequency problem is small in our case but more pronounced for large radius SBHs, where the SBH effect is not the main sound dissipation mechanism and cavity resonances can play a major role. ...
Sonic black holes (SBH) at duct ends constitute a particular type of anechoic termination. Acoustic waves get slowed down by means of a set of rings separated by cavities, whose inner radii diminish following a power law. Ideally, such design produces no wave reflection. In practice, however, this is not possible though the reflection coefficient remains low for a broadband frequency range. In this work, an evolutionary strategy (ES) is used to optimize the shape of SBH profiles and to try to improve the results of the standard power-law design. We test several cost functions for the reflection coefficient and impose constraints on the radii to fasten convergence. Different optimization problems are addressed. The first one is to determine the optimum exponent for the classical power-law profile. In the second one, the inner ring radii are only imposed to be monotonically decreasing from the SBH entrance. This results in new designs that overcome the performance of the optimum power-law profile at almost all frequencies. To perform the computations, we use a transfer matrix method for the SBH and resort to a derandomized ES with covariance matrix adaptation, which can easily deal with multiobjective optimization at a very reasonable computational cost.
... The TMM can partially take them into account, but for a more realistic description showing, for example, the inhomogeneous acoustic pressure distribution inside the cavities or the interaction between them, the finite element method (FEM) is required. The first FEM simulations for the wave equation in SBHs were reported in [15] and recently, a very thorough analysis studying the effects of different types of damping inside a SBH has been presented in [16], using FEM simulations for the Helmholtz equation to try to explain the discrepancies between predictions and experiments in [17,18]. FEM simulations have been carried out for the linearized Euler equations in [19] showing also the influence of cavity resonances and in [20] a semi-analytical fluid model is developed demonstrating how at low frequencies on-axis resonances dominate (associated with the SBH effect), while at higher frequencies cavity resonances prevail (depending on the particular SBH design). ...
... As can be seen in all the figures, filling some cavities with absorption produces a substantial improvement, since the reflection coefficient decreases significantly at all frequencies (see [6] for the influence of damping without optimization processes). It is observed that this is the case except for the highest frequencies in the linear and redesigned cases, a problem already noticed in experimental work in the literature [17,18,4], for which a plausible explanation has recently been proposed [16,19,20]. It should be noted that this high-frequency problem is small in our case but more pronounced for large radius SBHs, where the SBH effect is not the main sound dissipation mechanism, but cavity resonances play a major role. ...
Sonic black holes (SBH) in duct terminations consist of a set of inner rings separated by cavities whose inner radii typically decrease according to a power-law profile. The combination of profile shape and wall impedance is such that, in an ideal situation, waves entering the SBH would slow down without reaching the end of the duct, resulting in a perfect anechoic termination. However, in practice this is not possible and the reflection coefficient, although small for a broadband frequency range, characterizes the performance of the SBH. In this paper, we pose several optimization problems in an attempt to improve the efficiency of conventional SBHs. First, we present a general cost function with constraints for the weighted reflection coefficient of a SBH, to be minimized for each particular problem to be addressed. We start by optimizing the order of conventional SBHs and then take a step forward by allowing a free design for the SBH profile with a monotonic condition, but not restricted to the standard power-law decay. These two optimization problems are solved by a derandomized evolutionary strategy (ES) with covariance matrix adaptation, which can deal with multi-objective optimization problems very efficiently. On the other hand, the performance of the SBH can be improved by filling its cavities with absorption material. Therefore, for a limiting number of filled cavities that must not be exceeded, we find what is the best absorption distribution for the linear and quadratic power-law SBHs, as well as for the SBH with optimal profile found in the previous optimization problem. Each individual cavity can be either empty or filled with absorption material. Since the derandomized ES strategy is not suitable for problems with binary solutions, genetic algorithms are used instead. Finally, we perform a simultaneous optimization of the SBH profile and the absorption distribution with a loop combination of the derandomized ES and genetic algorithms. An important aspect of this paper is that the cost function is not viewed as an immutable quantity that always provides the best result for the physical problem at hand. Although the latter is true from a mathematical perspective, we show the effects of varying the weights and constraints of the cost function on the solutions and how these can give clues to improve existing designs and find new ones.
... They are often comprised of a series of rings with different radii positioned along the inner wall of a rigid cylindrical tube, forming a conical shape. At the tip, there is an extremely small diameter, causing the sound waves to be reflected back and forth multiple times, resulting in a substantial reduction of sound energy and effective sound absorption [8]. ...
Noise pollution from transportation vehicles is a growing
problem in densely populated areas. Among various sources
of noise pollution, helicopters are known for their disruptive
and intrusive sounds, which can have harmful effects on the
health and well-being of nearby residents. The continuous exposure to high levels of noise in urban environments can lead
to annoyance, sleep disturbance, and even more severe longterm health problems, including hypertension, stroke, and
heart attacks [1].
Conventional porous materials such as foams exhibit favorable sound absorption characteristics. However, very
thick layers of such materials are required for absorbing lowfrequency sounds, thus making them unpractical in most applications. Moreover, they have limited design tailorability,
and they cannot be effectively employed in complex structures [2].
Acoustic metamaterials are innovative materials engineered to manipulate and control the propagation of sound
waves in ways that are not possible with traditional materials.
These structures typically consist of periodic arrangements of
subwavelength unit cells, which interact with sound waves at
specific frequencies to achieve desired acoustic effects [3].
The aim of this review is (i) to contribute valuable insights to the field of noise control and its practical implementation in the aviation industry and (ii) to propose a metamaterial design suitable for large-scale manufacturing and capable
to address low-frequency noise reduction in helicopters.
... In subsequent theoretical works [2,3], the behavior of ABHs with quadratic radius profile has been modeled employing the transfer matrix method (TMM), the application of fractional calculus has been explored in [4]. The effect of ABH has also been studied experimentally [5,6]. The authors constructed ABHs with linear and quadratic radius profiles and demonstrated a reduction of the reflection coefficient when the ABH was used as an absorbing duct termination. ...
... Mi et al. [8] studied the performance of an ABH with a quadratic profile and closed or open end. They performed experimental measurements on a rather fine (compared to the previous works [5][6][7]) 3D-printed structure. ...
... In contrast to ABH, the sonic counterpart of the structural ABH concept, referred to as Sonic Black Hole (SBH), has rarely been applied and researched [9][10][11][12][13][14][15][16][17]. SBH is constructed by fitting a series of rings with a power-law decreasing inner radius inside a duct. ...
... SBH is constructed by fitting a series of rings with a power-law decreasing inner radius inside a duct. The experimental results of Mironov and Krylov verify that SBH can reduce the reflection of sound waves [9][10][11]. Zhang's work has advanced the application of SBH in sound absorption due to the reduction in sound velocity caused by SBH which allows lower frequency sound waves to be absorbed [17]. ...
In order to improve and broaden the absorption performance of Sonic Black Hole (SBH), we propose a modified SBH structure with micro-perforated panels which is embedded the multiple resonator cavities, and investigate the sound absorption effect of the structure. Characteristics of acoustic streaming effects are embodied in sound pressure and flow velocity distribution. Further, proposed SBH structure can achieve high sound absorption under 6.0 kHz. Based on the symmetry of the structure, the Two-dimensional axisymmetric Finite Element Method (FEM) model is proposed to study the sound absorption mechanism, which shows that the change of flow velocity gradient of acoustic medium leads to the loss of acoustic energy inside the structure. By discussion on acoustic streaming effects of different frequencies , the resonator cavity and micro-perforated panels contributes more to the sound absorption performance at low frequencies, and SBH produces a sound absorption advantage at high frequencies. The theoretical calculation and simulation result match and prove the correctness of the sound streaming effect. Sound absorption tests by acoustic impedance tube confirm that the proposed structure can maintain a sound absorption coefficient of over 0.5 in the range of 0.05-6.0 kHz. The combination of micro-perforated panels and SBH structure is widely applicable to muffler design and has good application prospects.
... The predictions were verified experimentally using a serial distribution of cavities whose rigid walls were made up of discs with parabolic increase of their diameters and decrease of their interspacing [13]. Other practical realisations of in-duct ABHs have been achieved through a distribution of quasi-periodic ribbed structures with linear or quadratic variations of the ribs inner radii [14]. It led to appreciable reduction of the reflection coefficient that stayed below 20% above 650 Hz, e.g. ...
... A "lock-on" state will then arise if the nth aeroacoustic mode coincides with the mth acoustic depth mode of the ith cavity, e.g. when Str U,n = Str cav,i,m = f i,m,cav d /U. Fig. 17(d) shows the predicted "lock-on" frequencies at the intersection between the two first aeroacoustic modes (n = 1, 2) and the first depth mode (m = 1) of the cavities (i = 1, 7,11,14). They occur over the Mach number range 0.02 -0.04 (resp. ...
