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Sound reflection coefficients as functions of frequency obtained by the SWR method for a rigid board, for an empty wooden box, for a box with a sponge, and for the full QFAA.
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In this paper, the design of a new quasi-flat acoustic absorber (QFAA) enhanced by the presence of a graded metamaterial layer is described, and the results of the experimental investigation into the reflection of sound from such an absorber are reported. The matching metamaterial layer is formed by a quasi-periodic array of brass cylindrical tubes...
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Context 1
... white noise generator was used to drive the loudspeaker. Two microphones have been used to measure sound pressure, and a program compiled in Matlab was used to compute the transfer function between two microphone positions and then calculate the reflection coefficient from the sample. The distance from the sample face to the first microphone was 155 mm, and the distance between the microphones was 35 mm. The microphones were connected to a PC via a five-channel dynamic signal acquisition module NI-USB-4431 card. Schematic views of the experimental setups using SWR method and TFM method are shown in Fig. 5, (a) and (b) respectively. The choice of porous materials for the absorbing zone was based on values of their acoustic impedance in comparison with the effective impedance at the internal row of the metamaterial quasi-periodic structure described in the previous sections. Two types of absorbing porous materials, sponge and fiberglass, have been used in the absorbing material zone. Impedance measurements have been carried out using the Transfer Function Method. The normalized acoustic impedances of sponge and fiberglass (relative to the acoustic impedance of air Z 0 ) calculated from the measured reflection coefficients are shown in Fig. 6 as functions of frequency. In the first step of the detailed measurements of the reflection coefficients for the full QFAA and for its different components, the SWR method has been employed to measure the sound pressure as a function of distance from the empty wooden box, from the rigid board, from the box with sponge inserted, and from the full QFAA containing both the sponge and the array of brass tubes at the frequency range of 500 -3000 Hz. Figure 7 shows the sound pressure as a function of distance from the full QFAA at the frequencies 500, 1000, 1500 and 3000 Hz. As it can be seen from Fig. 7, the sound pressure measured along the x-axis in front of the full QFAA shows distinctive standing wave patterns. Therefore, it is easy to determine the sound reflection coefficients by measuring the maximum and minimum values of the sound pressure, using equation (5). Plots of the sound reflection coefficients as functions of frequency obtained by SWR method for the full QFAA with inserted sponge and for some of its components are shown in Fig. 8. Note that the plots in Fig. 8 show that the full QFAA produces lower reflection coefficient in comparison with the reflection from the rigid board and from the empty wooden box. However, it shows higher reflection coefficient than the box with sponge only. These observations illustrate the fact that in this case there is no impedance matching between the sponge and the internal row (row 12) of the metamaterial layer (compare Fig. 3 and Fig. 6). The same measurements of the reflection coefficients have been repeated with the TFM method for frequencies from 500 Hz to 3000 Hz. The results are shown in Fig. 9. A comparison between reflection coefficient behaviour measured using the SWR method (Fig. 8) and the TFM method (Fig. 9) shows that the results are quite similar. The TFM method exhibits the same features as the SWR method does. In particular, the box with sponge inserted still produces a lower reflection coefficient than the full QFAA. In order to achieve lower reflection from the full QFAA described above, one has to insert a suitable porous absorbing material with a matching impedance. In what follows, only the TFM method will be employed to measure the reflection coefficients. The reason for that is that it gives the reflection coefficient from a sample for all frequencies (within limits) using only a couple of quick measurements. In contrast, the SWR method only gives the result at one frequency at a time, and the procedure for locating minima and maxima in the standing wave, which is needed to get the phase information, is rather slow, so that measuring at a large number of frequencies is very time consuming. The same tests as above were repeated for fiberglass as an absorbing porous material. Its acoustic impedance is greater than that for the sponge, see Fig. 6, so that one would expect its better matching to the effective impedance at the last row of the metamaterial layer. The results of the measurements of the reflection coefficients, at frequencies from 500 Hz to 3000 Hz, for the box with inserted fiberglass and for the full QFAA (the quasi- periodic array of cylinders with fiberglass inserted) are shown in Fig. 10. It can be seen that at the frequency range of 500 - 1581 Hz and of 2434 - 2745 Hz, the QFAA with fiberglass inserted provides lower reflection coefficient than the box with fiberglass inserted. In addition, it also provides lower reflection coefficient than the QFAA with sponge inserted (see Fig. 9)), except for the frequency range of 1920 - 2432 Hz. Although the measured reflection coefficients in Fig. 10 clearly demonstrate the benefit of using a matching metamaterial layer to reduce reflection, further improvement can be made. In order to achieve better results, one needs to adjust the effective acoustic impedance at the exit of the metamaterial layer to make it even closer to the acoustic impedance of the inserted fiberglass. Therefore, it has been decided to remove a few last rows of brass cylinders to reduce the effective impedance at the exit of the metamaterial layer and to get an adequate matching of the impedances. Two last rows have been removed, thus reducing the relative effective impedance at the exit of the matching metamaterial layer down to 2.4. Measurement of the reflection coefficient have been carried out for the full QFAA containing only 10 rows of brass cylinders, with fiberglass inserted. The results are shown in Fig. 11 in comparison with the results for the box with fiberglass inserted, but in the absence of the metamaterial layer. It can be seen that at all frequencies the reflection coefficient for the box with fiberglass inserted is strongly reduced when the QFAA (with 10 rows of brass cylinders and with fiberglass inserted) has been added. This demonstrates the functionality of matching the impedances using metamaterial layers. The device with 10 rows strongly outperforms the device with 12 rows in terms of the values of reflection coefficient at frequencies above 750 Hz. However, it provides higher reflection coefficient for frequencies below 750 Hz. Note that at frequencies above 750 Hz the values of reflection coefficient do not exceed 26 %. This means that at these frequencies the full QFAA with 10 rows of solid cylinders acts as an efficient acoustic absorber, with more than 93% of the impinging acoustic energy being absorbed. A quasi-flat acoustic absorber (QFAA) enhanced by the presence of a gradient metamaterial layer has been designed, manufactured and tested over a wide range of frequencies. The QFAA consists of a quasi-periodic system of solid cylinders with varying filling fraction and an absorbing layer made of a porous material. The impedance matching metamaterial layer was formed by up to twelve rows of brass cylinders of equal length and with diameters gradually increasing from the external row facing the open air towards the internal row facing the absorbing layer. It has been demonstrated experimentally that the values of sound reflection coefficient for the QFAA depend strongly on the impedance matching between the porous absorbing material and the exit of the gradient metamaterial layer. In particular, it has been shown that the full QFAA with 10 rows of cylinders and with fiberglass as inserted absorbing material is more efficient than the full QFAA with 12 rows of cylinders (also with fiberglass inserted). This can be explained by a nearly perfect impedance matching achieved in this case. The obtained results show that, for the quasi-flat geometrical configuration considered, the presence of the impedance matching metamaterial layer in front of the porous absorbing material can bring a substantial reduction in sound reflection coefficient in comparison with the case of reflection from the porous material ...
Context 2
... white noise generator was used to drive the loudspeaker. Two microphones have been used to measure sound pressure, and a program compiled in Matlab was used to compute the transfer function between two microphone positions and then calculate the reflection coefficient from the sample. The distance from the sample face to the first microphone was 155 mm, and the distance between the microphones was 35 mm. The microphones were connected to a PC via a five-channel dynamic signal acquisition module NI-USB-4431 card. Schematic views of the experimental setups using SWR method and TFM method are shown in Fig. 5, (a) and (b) respectively. The choice of porous materials for the absorbing zone was based on values of their acoustic impedance in comparison with the effective impedance at the internal row of the metamaterial quasi-periodic structure described in the previous sections. Two types of absorbing porous materials, sponge and fiberglass, have been used in the absorbing material zone. Impedance measurements have been carried out using the Transfer Function Method. The normalized acoustic impedances of sponge and fiberglass (relative to the acoustic impedance of air Z 0 ) calculated from the measured reflection coefficients are shown in Fig. 6 as functions of frequency. In the first step of the detailed measurements of the reflection coefficients for the full QFAA and for its different components, the SWR method has been employed to measure the sound pressure as a function of distance from the empty wooden box, from the rigid board, from the box with sponge inserted, and from the full QFAA containing both the sponge and the array of brass tubes at the frequency range of 500 -3000 Hz. Figure 7 shows the sound pressure as a function of distance from the full QFAA at the frequencies 500, 1000, 1500 and 3000 Hz. As it can be seen from Fig. 7, the sound pressure measured along the x-axis in front of the full QFAA shows distinctive standing wave patterns. Therefore, it is easy to determine the sound reflection coefficients by measuring the maximum and minimum values of the sound pressure, using equation (5). Plots of the sound reflection coefficients as functions of frequency obtained by SWR method for the full QFAA with inserted sponge and for some of its components are shown in Fig. 8. Note that the plots in Fig. 8 show that the full QFAA produces lower reflection coefficient in comparison with the reflection from the rigid board and from the empty wooden box. However, it shows higher reflection coefficient than the box with sponge only. These observations illustrate the fact that in this case there is no impedance matching between the sponge and the internal row (row 12) of the metamaterial layer (compare Fig. 3 and Fig. 6). The same measurements of the reflection coefficients have been repeated with the TFM method for frequencies from 500 Hz to 3000 Hz. The results are shown in Fig. 9. A comparison between reflection coefficient behaviour measured using the SWR method (Fig. 8) and the TFM method (Fig. 9) shows that the results are quite similar. The TFM method exhibits the same features as the SWR method does. In particular, the box with sponge inserted still produces a lower reflection coefficient than the full QFAA. In order to achieve lower reflection from the full QFAA described above, one has to insert a suitable porous absorbing material with a matching impedance. In what follows, only the TFM method will be employed to measure the reflection coefficients. The reason for that is that it gives the reflection coefficient from a sample for all frequencies (within limits) using only a couple of quick measurements. In contrast, the SWR method only gives the result at one frequency at a time, and the procedure for locating minima and maxima in the standing wave, which is needed to get the phase information, is rather slow, so that measuring at a large number of frequencies is very time consuming. The same tests as above were repeated for fiberglass as an absorbing porous material. Its acoustic impedance is greater than that for the sponge, see Fig. 6, so that one would expect its better matching to the effective impedance at the last row of the metamaterial layer. The results of the measurements of the reflection coefficients, at frequencies from 500 Hz to 3000 Hz, for the box with inserted fiberglass and for the full QFAA (the quasi- periodic array of cylinders with fiberglass inserted) are shown in Fig. 10. It can be seen that at the frequency range of 500 - 1581 Hz and of 2434 - 2745 Hz, the QFAA with fiberglass inserted provides lower reflection coefficient than the box with fiberglass inserted. In addition, it also provides lower reflection coefficient than the QFAA with sponge inserted (see Fig. 9)), except for the frequency range of 1920 - 2432 Hz. Although the measured reflection coefficients in Fig. 10 clearly demonstrate the benefit of using a matching metamaterial layer to reduce reflection, further improvement can be made. In order to achieve better results, one needs to adjust the effective acoustic impedance at the exit of the metamaterial layer to make it even closer to the acoustic impedance of the inserted fiberglass. Therefore, it has been decided to remove a few last rows of brass cylinders to reduce the effective impedance at the exit of the metamaterial layer and to get an adequate matching of the impedances. Two last rows have been removed, thus reducing the relative effective impedance at the exit of the matching metamaterial layer down to 2.4. Measurement of the reflection coefficient have been carried out for the full QFAA containing only 10 rows of brass cylinders, with fiberglass inserted. The results are shown in Fig. 11 in comparison with the results for the box with fiberglass inserted, but in the absence of the metamaterial layer. It can be seen that at all frequencies the reflection coefficient for the box with fiberglass inserted is strongly reduced when the QFAA (with 10 rows of brass cylinders and with fiberglass inserted) has been added. This demonstrates the functionality of matching the impedances using metamaterial layers. The device with 10 rows strongly outperforms the device with 12 rows in terms of the values of reflection coefficient at frequencies above 750 Hz. However, it provides higher reflection coefficient for frequencies below 750 Hz. Note that at frequencies above 750 Hz the values of reflection coefficient do not exceed 26 %. This means that at these frequencies the full QFAA with 10 rows of solid cylinders acts as an efficient acoustic absorber, with more than 93% of the impinging acoustic energy being absorbed. A quasi-flat acoustic absorber (QFAA) enhanced by the presence of a gradient metamaterial layer has been designed, manufactured and tested over a wide range of frequencies. The QFAA consists of a quasi-periodic system of solid cylinders with varying filling fraction and an absorbing layer made of a porous material. The impedance matching metamaterial layer was formed by up to twelve rows of brass cylinders of equal length and with diameters gradually increasing from the external row facing the open air towards the internal row facing the absorbing layer. It has been demonstrated experimentally that the values of sound reflection coefficient for the QFAA depend strongly on the impedance matching between the porous absorbing material and the exit of the gradient metamaterial layer. In particular, it has been shown that the full QFAA with 10 rows of cylinders and with fiberglass as inserted absorbing material is more efficient than the full QFAA with 12 rows of cylinders (also with fiberglass inserted). This can be explained by a nearly perfect impedance matching achieved in this case. The obtained results show that, for the quasi-flat geometrical configuration considered, the presence of the impedance matching metamaterial layer in front of the porous absorbing material can bring a substantial reduction in sound reflection coefficient in comparison with the case of reflection from the porous material ...
Context 3
... white noise generator was used to drive the loudspeaker. Two microphones have been used to measure sound pressure, and a program compiled in Matlab was used to compute the transfer function between two microphone positions and then calculate the reflection coefficient from the sample. The distance from the sample face to the first microphone was 155 mm, and the distance between the microphones was 35 mm. The microphones were connected to a PC via a five-channel dynamic signal acquisition module NI-USB-4431 card. Schematic views of the experimental setups using SWR method and TFM method are shown in Fig. 5, (a) and (b) respectively. The choice of porous materials for the absorbing zone was based on values of their acoustic impedance in comparison with the effective impedance at the internal row of the metamaterial quasi-periodic structure described in the previous sections. Two types of absorbing porous materials, sponge and fiberglass, have been used in the absorbing material zone. Impedance measurements have been carried out using the Transfer Function Method. The normalized acoustic impedances of sponge and fiberglass (relative to the acoustic impedance of air Z 0 ) calculated from the measured reflection coefficients are shown in Fig. 6 as functions of frequency. In the first step of the detailed measurements of the reflection coefficients for the full QFAA and for its different components, the SWR method has been employed to measure the sound pressure as a function of distance from the empty wooden box, from the rigid board, from the box with sponge inserted, and from the full QFAA containing both the sponge and the array of brass tubes at the frequency range of 500 -3000 Hz. Figure 7 shows the sound pressure as a function of distance from the full QFAA at the frequencies 500, 1000, 1500 and 3000 Hz. As it can be seen from Fig. 7, the sound pressure measured along the x-axis in front of the full QFAA shows distinctive standing wave patterns. Therefore, it is easy to determine the sound reflection coefficients by measuring the maximum and minimum values of the sound pressure, using equation (5). Plots of the sound reflection coefficients as functions of frequency obtained by SWR method for the full QFAA with inserted sponge and for some of its components are shown in Fig. 8. Note that the plots in Fig. 8 show that the full QFAA produces lower reflection coefficient in comparison with the reflection from the rigid board and from the empty wooden box. However, it shows higher reflection coefficient than the box with sponge only. These observations illustrate the fact that in this case there is no impedance matching between the sponge and the internal row (row 12) of the metamaterial layer (compare Fig. 3 and Fig. 6). The same measurements of the reflection coefficients have been repeated with the TFM method for frequencies from 500 Hz to 3000 Hz. The results are shown in Fig. 9. A comparison between reflection coefficient behaviour measured using the SWR method (Fig. 8) and the TFM method (Fig. 9) shows that the results are quite similar. The TFM method exhibits the same features as the SWR method does. In particular, the box with sponge inserted still produces a lower reflection coefficient than the full QFAA. In order to achieve lower reflection from the full QFAA described above, one has to insert a suitable porous absorbing material with a matching impedance. In what follows, only the TFM method will be employed to measure the reflection coefficients. The reason for that is that it gives the reflection coefficient from a sample for all frequencies (within limits) using only a couple of quick measurements. In contrast, the SWR method only gives the result at one frequency at a time, and the procedure for locating minima and maxima in the standing wave, which is needed to get the phase information, is rather slow, so that measuring at a large number of frequencies is very time consuming. The same tests as above were repeated for fiberglass as an absorbing porous material. Its acoustic impedance is greater than that for the sponge, see Fig. 6, so that one would expect its better matching to the effective impedance at the last row of the metamaterial layer. The results of the measurements of the reflection coefficients, at frequencies from 500 Hz to 3000 Hz, for the box with inserted fiberglass and for the full QFAA (the quasi- periodic array of cylinders with fiberglass inserted) are shown in Fig. 10. It can be seen that at the frequency range of 500 - 1581 Hz and of 2434 - 2745 Hz, the QFAA with fiberglass inserted provides lower reflection coefficient than the box with fiberglass inserted. In addition, it also provides lower reflection coefficient than the QFAA with sponge inserted (see Fig. 9)), except for the frequency range of 1920 - 2432 Hz. Although the measured reflection coefficients in Fig. 10 clearly demonstrate the benefit of using a matching metamaterial layer to reduce reflection, further improvement can be made. In order to achieve better results, one needs to adjust the effective acoustic impedance at the exit of the metamaterial layer to make it even closer to the acoustic impedance of the inserted fiberglass. Therefore, it has been decided to remove a few last rows of brass cylinders to reduce the effective impedance at the exit of the metamaterial layer and to get an adequate matching of the impedances. Two last rows have been removed, thus reducing the relative effective impedance at the exit of the matching metamaterial layer down to 2.4. Measurement of the reflection coefficient have been carried out for the full QFAA containing only 10 rows of brass cylinders, with fiberglass inserted. The results are shown in Fig. 11 in comparison with the results for the box with fiberglass inserted, but in the absence of the metamaterial layer. It can be seen that at all frequencies the reflection coefficient for the box with fiberglass inserted is strongly reduced when the QFAA (with 10 rows of brass cylinders and with fiberglass inserted) has been added. This demonstrates the functionality of matching the impedances using metamaterial layers. The device with 10 rows strongly outperforms the device with 12 rows in terms of the values of reflection coefficient at frequencies above 750 Hz. However, it provides higher reflection coefficient for frequencies below 750 Hz. Note that at frequencies above 750 Hz the values of reflection coefficient do not exceed 26 %. This means that at these frequencies the full QFAA with 10 rows of solid cylinders acts as an efficient acoustic absorber, with more than 93% of the impinging acoustic energy being absorbed. A quasi-flat acoustic absorber (QFAA) enhanced by the presence of a gradient metamaterial layer has been designed, manufactured and tested over a wide range of frequencies. The QFAA consists of a quasi-periodic system of solid cylinders with varying filling fraction and an absorbing layer made of a porous material. The impedance matching metamaterial layer was formed by up to twelve rows of brass cylinders of equal length and with diameters gradually increasing from the external row facing the open air towards the internal row facing the absorbing layer. It has been demonstrated experimentally that the values of sound reflection coefficient for the QFAA depend strongly on the impedance matching between the porous absorbing material and the exit of the gradient metamaterial layer. In particular, it has been shown that the full QFAA with 10 rows of cylinders and with fiberglass as inserted absorbing material is more efficient than the full QFAA with 12 rows of cylinders (also with fiberglass inserted). This can be explained by a nearly perfect impedance matching achieved in this case. The obtained results show that, for the quasi-flat geometrical configuration considered, the presence of the impedance matching metamaterial layer in front of the porous absorbing material can bring a substantial reduction in sound reflection coefficient in comparison with the case of reflection from the porous material ...
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Citations
... The authors of Ref. [10] develop a semianalytical model and test it experimentally. A somewhat similar design but for the flat case (the box) is proposed in Ref. [11]. There bras rods with increasing radii served as the impedance matching layer. ...
... Solution given by Eqs. (11) and (15) is quite similar to the solution for the SBH in sect. 2.1, Eqs. ...
... Thus, there is a strengthening of the connection between the acoustic design and a constructive development of the material. With the advent 50 of high-performance computing, micro-structural approach has become feasible and important in the development of sound absorbing materials, periodic structures and metamaterials [17,18,19]. ...
Porous materials present many important characteristics for the field of acoustics like thermal insulation, acoustic absorption, impact insulation and lightweight. There are many situations where one can find applications, such as aeronautics, automotive industries, heat and air conditioning systems, buildings, industry in general and others. Nowadays, with advances in the material fabrication process, it's possible to create complex structures according to the final objective. In this study, the greater interest is to increase sound wave absorption for industrial or residential applications. For a complete understanding of the needed characteristics to have a good absorber, it is recommended to model the structure through geometric pore reconstruction. This is a better way to later define which direction to take in order to increase the absorption curve, as well as which modifications and geometric restrictions must be performed to manufacture the best material for a given application. Simple macroscopic or empiric analytical models can be used to describe the visco-thermal dissipation inside the material. However, this approach does not present a clear link between micro and macro properties. This study proposes the reconstruction of cellular porous media using microscopic technique images. The proposed model basically is a 2D duct network made of simple uni-dimensional acoustical cylinders or pores. The theory based on acoustic transfer matrix method and mobility matrix model has been merged with analytical visco-thermal dissipation to implement the model proposed. Two cellular materials have been experimentally validated against the surface impedance and absorption for normal incidence: melamine foam and the porous aluminum. Valid agreements have been found between the experimental and numerical data. Future experiments will investigate geometry optimization methods to increase the absorption curve in frequency bands of interest.
... A wide range of measurements of sound reflection coefficients at normal and oblique incidence from different absorbing materials combined with matching metamaterial layers formed by the arrays of brass tubes have been carried out. Part of the material described in this paper was presented at the conferences [10,11]. The results show that the presence of matching metamaterial layers brings substantial reduction in the sound reflection coefficients, thus increasing the efficiency of sound absorption. ...
... Let us now consider the effect of matching metamaterial layers on sound reflection from fibreglass as an absorbing material. A fibreglass as a porous absorbing material for QFAA has been earlier investigated at normal incidence [10,11]. In what follows, the results of further experimental investigations of QFAA containing 10 rows and with fibreglass inserted are reported, both at normal incidence and at oblique incidence. ...
The efficiency of acoustic absorbers used for noise control can be improved by providing a smooth transition from the impedance of air to the impedance of the absorbing material in question. In the present work, such a smooth transition is materialised via application of gradient index metamaterial layers formed by quasi-periodic arrays of solid cylinders (tubes) with their external diameters gradually increasing from the external row of tubes facing the open air towards the internal row facing an absorbing porous layer. If acoustic wavelengths are much larger than the periodicity of the array, such a structure provides a gradual increase in the acoustic impedance towards the internal row of cylinders. This allows the developer to achieve an almost perfect impedance matching between the air and porous absorbing materials, such as sponges, fibreglass, etc. In the present work, a wide range of measurements of sound reflection coefficients from different absorbing materials combined with matching metamaterial layers formed by the arrays of brass tubes have been carried out at the frequency range of 500-3000 Hz. Both normal and oblique incidence of sound have been considered. The results show that the presence of matching metamaterial layers brings substantial reduction in sound reflection coefficients, thus increasing the efficiency of acoustic absorbers.
... In this section, we describe the results of the recent investigations of the acoustic absorbing structure, the "Quasi-Flat Acoustic Absorber" (QFAA), enhanced by the presence of gradient metamaterial layers [9,10]. A typical example of such a device consists of an absorbing layer and a quasi-periodic array of solid cylinders (brass cylindrical tubes) with their filling fractions varying from the external row facing the open air towards the internal row facing the absorbing layer made of a porous material. ...
... The main difficulty here is to materialise a linear or higher order power-law decrease in velocity of the incident sound wave down to zero. Note in this connection that the recently developed acoustic absorbers based on gradient index metamaterials [6][7][8][9][10], in which no zero values of sound velocity were achieved, represent not acoustic black holes, but impedance matching absorbing devices (also see the previous section). ...
In the present work, an overview of experimental investigations of the two types of periodicity-enhanced acoustic absorbing structures is given. In the first type of structures, the performance of acoustic absorbing materials is improved by providing a smooth transition from the impedance of air to the impedance of the absorbing material in question. This smooth change in the impedance is materialised using gradient index metamaterial layers formed by quasi-periodic arrays of solid cylinders. In the second type of performance improving devices, the principle of acoustic black holes has been implemented. To achieve the required power-law decrease in sound velocity with propagation distance the cylindrical inhomogeneous acoustic waveguides enhanced by quasi-periodic systems of concentric rings have been used. Measurements of the reflection coefficients for both types of structures have been carried out. The results show the possibility of substantial reduction of the acoustic reflections in both cases.
... The main difficulty here is to materialise a linear or higher order power-law decrease in velocity of the incident sound wave down to zero. For that reason, the recently developed acoustic absorbers based on gradient index metamaterials [13][14][15] , in which zero values of sound velocity were not achieved, represent not acoustic black holes, but impedance matching absorbing devices. ...
So far, acoustic black holes have been investigated mainly for flexural waves in thin plates for which the required linear or higher order reduction in wave velocity with distance can be easily achieved by changing the plate’s local thickness. In the present paper, the results of the experimental investigations of the acoustic black hole for sound absorption in air are described. To achieve the required power-law decrease in sound velocity with propagation distance the inhomogeneous acoustic waveguides earlier proposed by Mironov and Pislyakov (2002) and made of quasi-periodic ribbed structures have been used. Two samples of acoustic black hole terminations formed by these ribbed structures have been manufactured to provide linear and quadratic decreases in acoustic wave velocity with distance. Measurements of the reflection coefficients for guided acoustic modes incident on the black holes have been carried out in the frequency range of 100-1000 Hz. Initial measurements were conducted without insertion of any absorbing materials. The results show the possibility of significant reduction of the acoustic reflection in this case. Addition of small pieces of absorbing porous materials caused further reduction in the reflection coefficients, albeit not as significant as it could be expected.
... No inserted absorbing materials were considered in that work. A number of theoretical and experimental works considered the specially designed gradient metamaterial layers (arrays of quasi-periodic solid cylinders) to increase efficiency of acoustic absorbers in air [12][13][14][15][16]. However, in all these works the useful effect was achieved via using metamaterials as impedance matching devices, rather than as acoustic black holes. ...
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 ribbed struc-tures materialising walls of variable impedance have been used. Two different samples of acoustic black holes formed by these ribbed structures have been manufactured to provide linear and quadratic decreases in acoustic wave velocity with distance. Small pieces of ab-sorbing porous material have been inserted at the end. Measurements of the reflection coef-ficients for guided acoustic modes incident on the black holes have been carried out in the frequency range of 100-1000 Hz. The results show the possibility of significant reduction in the acoustic reflection without using additional absorbing materials. However, contrary to the expectations, the introduction of absorbing materials did not cause further noticeable re-duction in the sound reflection coefficients.
... The designed structure was manufactured and experimentally tested in an anechoic chamber at the frequency range of 500 ± 3000 Hz. Part of the material described in this paper was presented at the ASA meeting in October 2014 [10]. ...
The performance of acoustic absorbers can be improved by providing a smooth transition from the impedance of air to the impedance of the absorbing material in question. In the present work, such a smooth transition is materialised via application of gradient index metamaterial layers formed by quasi-periodic arrays of solid cylinders (tubes) with their external diameters gradually increasing from the external row of tubes facing the open air towards the internal row facing an absorbing porous layer. If acoustic wavelengths are much larger than the periodicity of the array, such a structure provides a gradual increase in the acoustic impedance towards the internal row of cylinders. This allows the developer to achieve an almost perfect impedance matching between the air and porous absorbing materials, such as foams, sponges, etc. Measurements of sound reflection coefficients from different absorbing materials combined with matching metamaterial layers formed by the arrays of brass tubes have been carried out in an anechoic chamber at the frequency range of 500-3000 Hz. The results show that the presence of matching metamaterial layers brings substantial reduction in the sound reflection coefficients, thus increasing the efficiency of sound absorption.
