Absorbent acoustic metamaterial

Abstract

Some embodiments are directed to an elementary acoustic metamaterial cell, including a body made of solid material and at least one resonator defining a groove of width l and depth p, the groove being open on the surface of the body, wherein the depth p is set by a resonant frequency (f) of the cell according to a relationship x, c being the speed of sound in air and the width l is set by an energy density confined in the cell according to a logarithmic relationship E.sub.max αlog (l) determined experimentally, the groove having an acoustic absorption controlled by a ratio between the depth p and the width l of the groove. Some embodiments are also directed to an acoustic screen including such an elementary cell.

Claims

1. An elementary cell of acoustic metamaterial, comprising: a body made of solid material; and at least one resonator defining a groove of width l and of depth p, the groove opening only onto one surface of the body, wherein: the groove is cylindrical, polygonal or rectilinear; wherein the one or more grooves are folded, in a section orthogonal to said surface, so as to have only one aperture and a plurality of folds in the interior of the cell; the depth p is determined by a resonant frequency (f) of the cell using a relationship $f=\frac{c}{4p},$ c being the speed of sound in air; and the width l is determined by an energy density confined in the cell using an experimentally determined logarithmic relationship E.sub.max∝log (l), the groove having a sound absorption controlled by a ratio between the depth p and the width l of the groove.

2. The cell as claimed in claim 1, wherein the groove is discontinuous and takes the form of sectors that are separated by the solid material from which the body is made.

3. The cell as claimed in claim 1, wherein the cell body includes a plurality of grooves.

4. The cell as claimed in claim 3, wherein the grooves are concentric.

5. The cell as claimed in claim 1, wherein the one or more grooves have a constant width l over the entire depth p of the groove.

6. The cell as claimed in claim 3, wherein at least two grooves have different widths l and/or different depths p.

7. The cell as claimed in claim 1, wherein the body includes at least one through-notch.

8. The cell as claimed in claim 1, wherein at least one groove contains a fluid or polymer.

9. The cell as claimed in claim 1, wherein the cell body is cylindrical, parallelepipedal or pyramidal.

10. An acoustic screen taking the form of a panel, comprising: the elementary cell as claimed in claim 1.

11. The acoustic screen as claimed in claim 10, further comprising a multitude of elementary cells that are arranged so that each cell is able to act on another neighboring cell so as to modify the resonant frequencies.

12. The acoustic screen as claimed in claim 11, wherein the elementary cells are arranged in the panel periodically.

13. The cell as claimed in claim 1, wherein the groove is discontinuous and takes the form of sectors that are separated by the solid material from which the body is made.

14. The cell as claimed in claim 1, wherein the cell body includes a plurality of grooves.

15. The cell as claimed in claim 2, wherein the cell body includes a plurality of grooves.

16. The cell as claimed in claim 1, wherein the one or more grooves have a constant width l over the entire depth p of the groove.

17. The cell as claimed in claim 2, wherein the one or more grooves have a constant width l over the entire depth p of the groove.

18. The cell as claimed in claim 3, wherein the one or more grooves have a constant width l over the entire depth p of the groove.

19. A method for determining the depth p and the width l of a cell according to claim 1, wherein: the depth p is determined by a resonant frequency (f) of the cell according to a relation: $f=\frac{c}{4p},$ c being the speed of sound in air, and in that the width l is determined by an energy density confined in said cell according to an experimentally determined logarithmic relation:
E.sub.max∝log (l).

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) Some embodiments will be better understood on reading the following description of advantageous or preferred nonlimiting embodiments, which are given by way of illustrative example, with reference to the drawings, in which:

(2) FIGS. 1a to 1c show a first example embodiment of an elementary cell according to some embodiments, including a single cylindrical groove;

(3) FIGS. 2a to 2c show a second example embodiment, in which the elementary cell is parallelepipedal and includes a linear groove;

(4) FIGS. 3a to 3d show an example embodiment, in which the elementary cell is cylindrical and includes three concentric cylindrical grooves;

(5) FIGS. 4a to 4c show an example embodiment, in which the cell is parallelepipedal and includes three linear grooves;

(6) FIGS. 5a to 5c show an example embodiment, in which the cell is cylindrical and includes a folded cylindrical groove;

(7) FIGS. 6a to 6c show an example embodiment, in which the cell is parallelepipedal and includes a folded linear groove;

(8) FIG. 7 shows the sound-wave absorption response of an elementary cell according to some embodiments;

(9) FIG. 8 shows a comparison of absorption curves obtained with elementary cells according to some embodiments the grooves of which have different widths; and

(10) FIG. 9 shows a variation in confined energy density as a function of the width of a groove the effective length of which defines a resonant frequency of 1 kHz, according to some embodiments.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

(11) FIG. 1a shows an isometric view of an elementary cell 1 of an acoustic metamaterial according to some embodiments. FIGS. 1b and 1c show a top view and a view of a longitudinal cross section cut along the axis AA of the cell 1, respectively.

(12) The cell 1 includes a cylindrical solid body 2 including a groove 3 that is also cylindrical. The groove 3 is characterized by a depth p and a width l, as shown in FIG. 1c. The width l is the distance between the sidewalls of the groove 3.

(13) The presence of the groove, which forms a reasoning cavity, allows a high degree of spatial confinement of acoustic energy to be obtained, this therefore allowing sound waves to be absorbed and reflection and transmission to be decreased.

(14) The depth p defines the resonant frequency and the width l determines the effectiveness of the cell. It is therefore possible to use these two parameters to adjust the frequency at which and how effectively the sound waves are absorbed by the elementary cell 1.

(15) FIG. 2a shows an isometric view of a parallelepipedal elementary cell 1′. FIGS. 2b and 2c show a top view and a view of a longitudinal cross section cut along the axis A′A′, of the cell 1′, respectively.

(16) The cell 1′ includes a parallelepipedal solid body 2′ including a linear groove 3′. The groove 3′ is characterized by a depth p′ and a width l′, as in the case of the example of FIG. 1c.

(17) FIG. 3a shows an isometric view of an elementary cell 10 including a cylindrical solid body 20 and three concentric cylindrical grooves 30, 31, 32. FIGS. 3b and 3c show a top view and a view of a longitudinal cross section cut along the axis BB, of the cell 10, respectively.

(18) In this example embodiment, the three grooves 30, 31, 32 have the same depth and the same width as FIG. 3c shows.

(19) FIG. 3d illustrates a view of a cross section that is similar to the view illustrated in FIG. 3c, of a cell 10′ that includes a cylindrical solid body 20′ and three concentric cylindrical grooves 30′, 31′, 32′. The cell 10′ is identical to the cell 10 illustrated in FIGS. 3a to 3c, except as regards the depths and widths of the grooves 30′, 31′, 32′ which are different for each of the three grooves 31′, 32,′, 33′. This allows the resonant frequency at which and how effectively each groove absorbs to be made different.

(20) FIG. 4a shows an isometric view of a parallelepipedal elementary cell 10″. FIGS. 4b and 4c show a top view and a view of a longitudinal cross section cut along the axis B″B″, of the cell 10″, respectively.

(21) The cell 10″ includes a parallelepipedal solid body 20″ including three grooves 30″, 31″, 32″ that have the same depth and the same width as the cross-sectional view of FIG. 4c shows.

(22) FIG. 5a shows an isometric view of an elementary cell 100 according to one example embodiment, in which the cell 100 includes a cylindrical solid body 200 and a folded cylindrical groove 300. FIGS. 5b and 5c show a top view and a view of a longitudinal cross section cut along the axis CC, of the cell 100, respectively.

(23) FIG. 5c illustrates the folds of the groove 300. The folding of the groove 300 allows the thickness of the cell 100 to be considerably decreased, while keeping the effectiveness of absorption of a groove with a depth corresponding to the length of the walls of the groove 300.

(24) FIG. 6a shows an isometric view of a parallelepipedal elementary cell 100′ including a parallelepipedal solid body 200′ and a folded linear groove 300′. FIGS. 6b and 6c show a top view and a view of a longitudinal cross section cut along the axis C′C′ of the cell 100′, respectively.

(25) The parallelepipedal shape has the advantage of allowing the area of an acoustic panel to be better filled.

(26) In FIGS. 2a, 4a and 6a the cells appear to open onto the sides. In fact, the grooves only open onto the surface: such apertures opening onto the sides do not exist and are shown only to allow the shape of the grooves in the interior of the solid body to be better understood.

(27) FIG. 7 illustrates the absorption response of an elementary cell according to the example embodiment illustrated in the schematics of FIGS. 3a to 3c, but with a different depth for each groove. This elementary cell has an overall height of 196.5 mm and includes 3 resonant cavities taking the form of concentric cylindrical grooves of a fixed width of 2.7 mm, and of different depths of 160.5 mm, 177 mm and 193.5 mm, respectively.

(28) The cell was manufactured using a Projet SD3500 3D printer, and the properties of the Visijet Crystal resin used were: Density (g/cm): 1.02 (liquid, at 80°) Young's modulus: 1463 MPa Flexural strength: 49 MPa

(29) The presented characterization, which allowed the acoustic properties of the cell to be studied in the audible-frequency range, was obtained by virtue of a standing wave tube equipped with 4 microphones. A Brüel & Kjær 4206-T transmission-loss tube kit was employed.

(30) The diameter of the transmission-loss tube used was 100 mm, this allowing measurements to be carried out in the frequency interval 50-1600 Hz.

(31) A loudspeaker, placed at one end of the tube, generated white noise in the frequency band of interest.

(32) The pressure measurements were carried out using two terminations of different impedance.

(33) FIG. 7 in particular shows the three first resonant frequencies at which an intense absorption occurred, with absorption coefficients reaching as high as 0.97.

(34) For example, the absorption values obtained were: 0.97 at 315 Hz; 0.95 at 353 Hz; 0.96 at 364 Hz; 0.95 at 1031 Hz; 0.96 at 1150 Hz; 0.93 at 1294 Hz.

(35) Thus, with this structure, two bands of intense absorption were obtained: 1st band: centered on 360 Hz, and reaching 0.87 with a relative bandwidth of 44:7%; 2nd band: centered on 1159 Hz, and reaching 0.49 with a relative bandwidth of 44:6%.

(36) FIG. 8 is a comparison of the absorption curves obtained for different groove widths with four cells according to the example embodiment shown in FIGS. 1a to 1c.

(37) The cells each had a cylindrical groove of a depth of 100 mm and groove widths of 15 mm, 10 mm, 5 mm and 2 mm, respectively. The radius of each cell was 25 mm.

(38) FIG. 8 shows an increase in absorption as the width of the grooves decreases. The absorption passed respectively from 0.05 to 0.08 to 0.26 then to 0.37 simply by decreasing the dimensional parameter 1.