Acoustic black hole sound absorber structure with Helmholtz silencer and design method

Abstract

The invention relates to an acoustic black hole sound absorber structure with a Helmholtz silencer and a design method. Comprising a cross-shaped partition plate, a cylindrical cavity with a stepped tail end, four groups of 1 / 4 annular thin plate arrays, two single-degree-of-freedom Helmholtz silencers and one double-degree-of-freedom Helmholtz silencer. The structure is simple, the cost is low, and stable broadband sound absorption can be achieved.

Description

Technical Field

[0001] The invention belongs to a broadband sound absorbing structure designed by optimizing the combination of acoustic black hole sound absorbers of different sizes and Helmholtz silencers of different sizes, and specifically relates to an acoustic black hole sound absorber structure with a Helmholtz silencer and a design method. Background Art

[0002] In recent years, acoustic black hole absorber structures with broadband sound absorption effect have attracted widespread attention from many scholars. Due to the imperfection of its structure during the processing, the acoustic black hole absorber structure requires a larger structure length to ensure low-frequency sound absorption in practical applications. In order to improve its sound absorption effect in a shorter structure size, many scholars have proposed a variety of methods, such as arranging micro-perforated plates, folded cavities, slits and trapezoidal cavities in the acoustic black hole structure ([1] Ou Y, Zhao Y. Design, analysis, and experimental validation of a sonic black hole structure for near-perfect broadband sound absorption[J]. Applied Acoustics, 2024, 225: 110196.). In previous work, we proposed a combined acoustic black hole absorber (patent application number: 202310893644.7). This structure has a lower cutoff frequency than traditional acoustic black hole absorber structures of the same size, but some space at the end of the structure is not fully utilized. The present invention arranges a Helmholtz silencer that is easy to use for low-frequency sound absorption in the unused space of the combined acoustic black hole absorber, and designs a combined acoustic black hole absorber with a Helmholtz silencer that has greater space utilization and a wider sound absorption band for broadband sound absorption. Summary of the invention

[0003] The present invention proposes an acoustic black hole sound absorber structure with a Helmholtz silencer, which has a wide-band sound absorption effect and a Helmholtz silencer that has a good sound absorption effect at low frequencies. The structure is not only simple in structure, but also has a stable wide-band sound absorption effect.

[0004] The present invention is achieved through the following technical solutions.

[0005] An acoustic black hole sound absorber structure with a Helmholtz silencer, characterized in that it includes a cross-shaped baffle, an end-step cylindrical cavity, four groups of 1 / 4 annular thin plate arrays, two single-degree-of-freedom Helmholtz silencers and a double-degree-of-freedom Helmholtz silencer, wherein the cross-shaped baffle is located in the end-step cylindrical cavity to divide it into four independent 1 / 4 cylindrical cavities with the same cross-sectional area and different lengths, the four groups of 1 / 4 annular thin plate arrays include four groups of annular thin plate arrays with different numbers of 1 / 4 annular thin plates, the four groups of 1 / 4 annular thin plate arrays are respectively located in four 1 / 4 cylindrical cavities with different lengths, the lengths of the four groups of 1 / 4 annular thin plate arrays are respectively the same as the lengths of the four 1 / 4 cylindrical cavities with different lengths, the plate thickness and spacing of the four groups of 1 / 4 annular thin plate arrays are equal, and the inner diameter of the 1 / 4 annular thin plate in the 1 / 4 annular thin plate array satisfies Where r0 represents the inner diameter of the annular thin plate with the smallest inner diameter, R represents the outer diameter of the annular thin plate, L represents the total length of the 1 / 4 annular thin plate array, and x represents the distance between any 1 / 4 annular thin plate in the 1 / 4 annular thin plate array and the 1 / 4 annular thin plate with the largest inner diameter. The outer diameter of the 1 / 4 annular thin plate array is the same as the inner diameter of the stepped cylindrical cavity at the end, and two single-degree-of-freedom Helmholtz mufflers and a double-degree-of-freedom Helmholtz muffler are connected in series at the end of the three groups of shorter 1 / 4 annular thin plate arrays.

[0006] Furthermore, the thickness of the cross-shaped partition is not greater than 2 mm, the cross-shaped partition is fixed inside the end stepped cylindrical cavity, the center line of the cross-shaped partition coincides with the center line of the end stepped cylindrical cavity, and the cross-shaped partition divides the end stepped cylindrical cavity into four completely independent 1 / 4 cylindrical cavities with the same cross-sectional area and different lengths. The length of the cross-shaped partition is not less than the length of the 1 / 4 cylindrical cavity.

[0007] Furthermore, four groups of 1 / 4 annular thin plate arrays are respectively fixed in 1 / 4 cylindrical cavities of the same length, the spacing between adjacent annular thin plates in the 1 / 4 annular thin plate array is the same, and the thickness of each 1 / 4 annular thin plate is the same and does not exceed 2 mm.

[0008] Furthermore, two single-degree-of-freedom Helmholtz silencers and a double-degree-of-freedom Helmholtz silencer are connected in series at the end of three groups of shorter 1 / 4 annular thin plate arrays. The back cavity bottom area of ​​the single-degree-of-freedom Helmholtz silencer and the double-degree-of-freedom Helmholtz silencer is the same, and the neck size, neck length and back cavity height are different. The inner diameter and outer diameter of the back cavity of the single-degree-of-freedom Helmholtz silencer and the double-degree-of-freedom Helmholtz silencer are respectively the same as the inner diameter and outer diameter of the terminal stepped cylindrical cavity. The total length of the single-degree-of-freedom Helmholtz silencer and the double-degree-of-freedom Helmholtz silencer connected in series with their corresponding 1 / 4 annular thin plate arrays does not exceed the length of the longest 1 / 4 annular thin plate array, and the necks of the single-degree-of-freedom Helmholtz silencer and the double-degree-of-freedom Helmholtz silencer can extend into the back cavity or toward the outside of the back cavity.

[0009] Furthermore, the cross-shaped partition, the end stepped cylindrical cavity, the four groups of 1 / 4 annular thin plate arrays, the two single-degree-of-freedom Helmholtz mufflers and the double-degree-of-freedom Helmholtz mufflers are integrally formed through 3D printing or connected and fixed by using strong glue, welding or bolts.

[0010] Furthermore, a method for designing an acoustic black hole sound absorber structure with a Helmholtz muffler comprises the following steps:

[0011] In the first step, when the sound wave is incident vertically, the transfer function of the sound pressure and sound volume velocity at the sound wave entrance and end of the 1 / 4 acoustic black hole absorber structure composed of a 1 / 4 annular thin plate array and a 1 / 4 cylindrical cavity is

[0012]

[0013] Where, M is the number of 1 / 4 annular thin plates in the 1 / 4 acoustic black hole absorber structure; is the wave number; h i+1 is the distance between two adjacent annular thin plates; is the area of ​​the opening of the i+1th 1 / 4 annular thin plate; Z0=ρ0c0 is the impedance of air; is the cavity admittance, where V i+1 It is the volume of the hollow cone part between two adjacent 1 / 4 annular thin plates.

[0014] When the sound wave is incident vertically, the transfer function of sound pressure and sound volume velocity when propagating in a single Helmholtz muffler is:

[0015] T HR =T neck T cavity (2)

[0016] Where, T neck is the transfer function of the Helmholtz muffler neck; T cavity is the transfer function of the back cavity of the Helmholtz muffler

[0017]

[0018]

[0019] Where, L neck is the length of the Helmholtz muffler neck; S neck is the cross-sectional area of ​​the Helmholtz muffler neck; L cavity is the length of the back cavity of the Helmholtz muffler; S cavity is the cross-sectional area of ​​the back cavity of the Helmholtz muffler.

[0020] The transfer function of a 1 / 4 acoustic black hole absorber structure connected in series with n Helmholtz silencers is:

[0021]

[0022] The effective acoustic impedance of a structure consisting of a 1 / 4 acoustic black hole absorber and n (n ≥ 0) Helmholtz silencers in series is

[0023]

[0024] By designing a parallel coupling structure of four groups of 1 / 4 acoustic black hole absorbers and n Helmholtz silencers in series, the total effective acoustic impedance after combination is

[0025]

[0026] In the formula, Z1, Z2, Z3, and Z4 are the acoustic impedances corresponding to the structure of four groups of 1 / 4 acoustic black hole absorbers and n Helmholtz silencers in series. The sound absorption coefficient of the acoustic black hole absorber structure with Helmholtz silencers is obtained from formula (7):

[0027]

[0028] Where S = πR 2 is the total area that allows sound waves to be incident vertically, where R is the inner diameter of the cylindrical cavity.

[0029] In the second step, based on the change of the above impedance value with the structural size of the Helmholtz silencer, the structural length of the Helmholtz silencer connected in series at the end of the 1 / 4 acoustic black hole absorber is designed through series and parallel coupling design to optimize the sound absorption coefficient of the acoustic black hole absorber structure with the Helmholtz silencer.

[0030] Compared with the prior art, the advantages of the present invention are: the present invention proposes an acoustic black hole sound absorber structure with a Helmholtz silencer, which has a wide-band sound absorption effect and a Helmholtz silencer that has a good sound absorption effect at low frequencies. The structure is not only simple in structure, but also has a stable wide-band sound absorption effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a structural schematic diagram of the present invention;

[0032] Figure 2 It is a schematic diagram of the cross-shaped partition structure of the present invention;

[0033] Figure 3 This is a schematic diagram of the end stepped cylindrical cavity structure of the present invention;

[0034] Figure 4 This is a schematic diagram of the structure of four groups of 1 / 4 annular thin plate arrays of the present invention;

[0035] Figure 5 It is a schematic diagram of the structure of the first single-degree-of-freedom Helmholtz muffler of the present invention;

[0036] Figure 6 It is a schematic diagram of the structure of a second single-degree-of-freedom Helmholtz muffler of the present invention;

[0037] Figure 7 It is a schematic diagram of the structure of the dual-degree-of-freedom Helmholtz muffler of the present invention;

[0038] Figure 8 The curves of the sound absorption coefficient of the acoustic black hole sound absorber structure with a Helmholtz muffler of the present invention and the traditional acoustic black hole sound absorber structure of the same length as the incident noise frequency;

[0039] In the figure: 1. Cross-shaped partition, 2. End stepped cylindrical cavity, 3. 1 / 4 ring thin plate array, 4. Single-degree-of-freedom Helmholtz muffler, 5. Double-degree-of-freedom Helmholtz muffler. DETAILED DESCRIPTION

[0040] The present invention is further described below with reference to the accompanying drawings and specific examples, but is not intended to be a limitation of the present invention.

[0041] like Figures 1 to 7As shown, an acoustic black hole sound absorber structure with a Helmholtz silencer comprises a cross-shaped baffle 1, an end stepped cylindrical cavity 2, four groups of 1 / 4 annular thin plate arrays 3, two single-degree-of-freedom Helmholtz silencers 4 and a double-degree-of-freedom Helmholtz silencer 5, wherein the cross-shaped baffle 1 is located in the end stepped cylindrical cavity 2 to divide it into four independent 1 / 4 cylindrical cavities with the same cross-sectional area and different lengths, the four groups of 1 / 4 annular thin plate arrays 3 include four groups of annular thin plate arrays with different numbers of 1 / 4 annular thin plates, the four groups of 1 / 4 annular thin plate arrays 3 are respectively located in four 1 / 4 cylindrical cavities with different lengths, the lengths of the four groups of 1 / 4 annular thin plate arrays 3 are respectively the same as the lengths of the four 1 / 4 cylindrical cavities with different lengths, the plate thicknesses and spacings of the four groups of 1 / 4 annular thin plate arrays are equal, and the inner diameters of the 1 / 4 annular thin plates in the 1 / 4 annular thin plate arrays 3 satisfy Where r0 represents the inner diameter of the annular thin plate with the smallest inner diameter, R represents the outer diameter of the annular thin plate, L represents the total length of the 1 / 4 annular thin plate array 3, and x represents the distance between any 1 / 4 annular thin plate in the 1 / 4 annular thin plate array 3 and the 1 / 4 annular thin plate with the largest inner diameter. The outer diameter of the 1 / 4 annular thin plate array 3 is the same as the inner diameter of the terminal stepped cylindrical cavity 2, and two single-degree-of-freedom Helmholtz mufflers 4 and a double-degree-of-freedom Helmholtz muffler 5 are connected in series at the end of the three groups of shorter 1 / 4 annular thin plate arrays.

[0042] Furthermore, the thickness of the cross-shaped partition 1 is not greater than 2 mm, the cross-shaped partition 1 is fixed inside the terminal stepped cylindrical cavity 2, the center line of the cross-shaped partition 1 coincides with the center line of the terminal stepped cylindrical cavity, and the cross-shaped partition 1 divides the terminal stepped cylindrical cavity into four completely independent 1 / 4 cylindrical cavities with the same cross-sectional area and different lengths. The length of the cross-shaped partition 1 is not less than the length of the 1 / 4 cylindrical cavity.

[0043] Furthermore, four groups of 1 / 4 annular thin plate arrays 3 are respectively fixed in 1 / 4 cylindrical cavities of the same length, and the spacing between adjacent annular thin plates in the 1 / 4 annular thin plate array 3 is the same, and the thickness of each 1 / 4 annular thin plate is the same and does not exceed 2 mm.

[0044] Furthermore, two single-degree-of-freedom Helmholtz silencers 4 and a double-degree-of-freedom Helmholtz silencer 5 are connected in series at the ends of three groups of shorter 1 / 4 annular thin plate arrays. The back cavity bottom area of ​​the single-degree-of-freedom Helmholtz silencer 4 and the double-degree-of-freedom Helmholtz silencer 5 is the same, and the neck size, neck length and back cavity height are different. The inner diameter and outer diameter of the back cavity of the single-degree-of-freedom Helmholtz silencer 4 and the double-degree-of-freedom Helmholtz silencer 5 are respectively the same as the inner diameter and outer diameter of the terminal stepped cylindrical cavity 2. The total length of the single-degree-of-freedom Helmholtz silencer 4 and the double-degree-of-freedom Helmholtz silencer 5 connected in series with their corresponding 1 / 4 annular thin plate arrays does not exceed the length of the longest 1 / 4 annular thin plate array, and the necks of the single-degree-of-freedom Helmholtz silencer 4 and the double-degree-of-freedom Helmholtz silencer 5 can extend into the back cavity or toward the outside of the back cavity.

[0045] Furthermore, the cross-shaped partition 1, the end stepped cylindrical cavity 2, the four groups of 1 / 4 annular thin plate arrays 3, the two single-degree-of-freedom Helmholtz mufflers 4 and the double-degree-of-freedom Helmholtz mufflers 5 are integrally formed by 3D printing or connected and fixed by using strong glue, welding or bolts.

[0046] Furthermore, a method for designing an acoustic black hole sound absorber structure with a Helmholtz muffler comprises the following steps:

[0047] In the first step, when the sound wave is incident vertically, the transfer function of the sound pressure and sound volume velocity at the sound wave entrance and end of the 1 / 4 acoustic black hole absorber structure composed of a 1 / 4 annular thin plate array and a 1 / 4 cylindrical cavity is

[0048]

[0049] Where, M is the number of 1 / 4 annular thin plates in the 1 / 4 acoustic black hole absorber structure; is the wave number; h i+1 is the distance between two adjacent annular thin plates; is the area of ​​the opening of the i+1th 1 / 4 annular thin plate; Z0=ρ0c0 is the impedance of air; is the cavity admittance, where V i+1 It is the volume of the hollow cone part between two adjacent 1 / 4 annular thin plates.

[0050] When the sound wave is incident vertically, the transfer function of sound pressure and sound volume velocity when propagating in a single Helmholtz muffler is:

[0051] T HR =T neck T cavity (2)

[0052] Where, T neck is the transfer function of the Helmholtz muffler neck, Tcavity is the transfer function of the back cavity of the Helmholtz muffler

[0053]

[0054] Where, L neck is the length of the Helmholtz muffler neck; S neck is the cross-sectional area of ​​the Helmholtz muffler neck; L cavity is the length of the back cavity of the Helmholtz muffler; S cavity is the cross-sectional area of ​​the back cavity of the Helmholtz muffler.

[0055] The transfer function of a 1 / 4 acoustic black hole absorber structure connected in series with n Helmholtz silencers is:

[0056]

[0057] The effective acoustic impedance of a structure consisting of a 1 / 4 acoustic black hole absorber and n (n ≥ 0) Helmholtz silencers in series is

[0058]

[0059] By designing a parallel coupling structure of four groups of 1 / 4 acoustic black hole absorbers and n Helmholtz silencers in series, the total effective acoustic impedance after combination is

[0060]

[0061] In the formula, Z1, Z2, Z3, and Z4 are the acoustic impedances corresponding to the structure of four groups of 1 / 4 acoustic black hole absorbers and n Helmholtz silencers in series. The sound absorption coefficient of the acoustic black hole absorber structure with Helmholtz silencers is obtained from formula (7):

[0062]

[0063] Where S = πR 2 is the total area that allows sound waves to be incident vertically, where R is the inner diameter of the cylindrical cavity.

[0064] In the second step, based on the change of the above impedance value with the structural size of the Helmholtz silencer, the structural length of the Helmholtz silencer connected in series at the end of the 1 / 4 acoustic black hole absorber is designed through series and parallel coupling design to optimize the sound absorption coefficient of the acoustic black hole absorber structure with the Helmholtz silencer.

[0065] In this embodiment, the total length of the structure is selected to be 90mm, the thickness of the 1 / 4 annular thin plate is 1mm, the spacing between the annular thin plates is 3mm, the number of 1 / 4 annular thin plates in the four groups of 1 / 4 annular thin plate arrays is 30, 25, 20, and 17 respectively, and the maximum inner diameter of the four groups of 1 / 4 annular thin plate arrays is 47.5mm, and the minimum inner diameter is 4.5mm. The geometric dimensions of the two single-degree-of-freedom Helmholtz silencers are as follows: the neck area of ​​the first Helmholtz silencer is 9πmm 2 , the neck length is 6mm, the back cavity length is 10mm; the neck area of ​​the second Helmholtz muffler is 25πmm 2 , the neck length is 3mm, the back cavity length is 4mm; the two neck areas of the double-degree-of-freedom Helmholtz muffler are 25πmm 2 and 9πmm 2 , the corresponding neck lengths are 5mm and 6mm, and the corresponding back cavity lengths are 10mm and 15mm respectively. The first single-degree-of-freedom Helmholtz silencer is connected in series to the end of a 1 / 4 acoustic black hole absorber with 25 plates, the second single-degree-of-freedom Helmholtz silencer is connected in series to the end of a 1 / 4 acoustic black hole absorber with 20 plates, and the double-degree-of-freedom Helmholtz silencer is connected in series to the end of a 1 / 4 acoustic black hole absorber with 17 plates, where the sound wave is transmitted from an area of ​​25πmm 2 The neck is incident on a two-DOF Helmholtz muffler.

[0066] In this embodiment, the sound absorption coefficient curves of the acoustic black hole absorber structure with a Helmholtz muffler described in the present invention and the traditional acoustic black hole absorber are calculated by using the transfer function method, as shown in FIG. Figure 8 From the numerical calculation results, it can be found that the acoustic black hole sound absorber structure with a Helmholtz silencer proposed in the present invention has a sound absorption coefficient greater than 0.5 when the frequency is greater than 315 Hz, while the traditional acoustic black hole sound absorber structure can only achieve a sound absorption coefficient greater than 0.5 when the frequency is greater than 480 Hz, which shows that the acoustic black hole sound absorber structure with a Helmholtz silencer described in the present invention has good broadband sound absorption characteristics.

[0067] The above description is only a preferred embodiment of the present invention, and does not limit the implementation mode and protection scope of the present invention. For those skilled in the art, it should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the description and illustrations of the present invention should be included in the protection scope of the present invention.

Claims

1. An acoustic black hole sound absorber structure with a Helmholtz muffler, characterized in that The invention comprises a cross-shaped baffle (1), an end-step cylindrical cavity (2), four groups of 1 / 4 annular thin plate arrays (3), two single-degree-of-freedom Helmholtz mufflers (4) and a double-degree-of-freedom Helmholtz muffler (5), wherein the cross-shaped baffle (1) is located in the end-step cylindrical cavity (2) to divide the cavity into four independent 1 / 4 cylindrical cavities with the same cross-sectional area and different lengths, the four groups of 1 / 4 annular thin plate arrays (3) contain four groups of annular thin plate arrays with different numbers of 1 / 4 annular thin plates, the four groups of 1 / 4 annular thin plate arrays (3) are respectively located in four 1 / 4 cylindrical cavities with different lengths, the lengths of the four groups of 1 / 4 annular thin plate arrays (3) are respectively the same as the lengths of the four 1 / 4 cylindrical cavities with different lengths, the plate thicknesses and spacings of the four groups of 1 / 4 annular thin plate arrays are equal, and the inner diameters of the 1 / 4 annular thin plates in the 1 / 4 annular thin plate arrays (3) satisfy Wherein r0 represents the inner diameter of the annular thin plate with the smallest inner diameter, R represents the outer diameter of the annular thin plate, L represents the total length of the 1 / 4 annular thin plate array (3), and x represents the distance between any 1 / 4 annular thin plate in the 1 / 4 annular thin plate array (3) and the 1 / 4 annular thin plate with the largest inner diameter; the outer diameter of the 1 / 4 annular thin plate array (3) is the same as the inner diameter of the terminal stepped cylindrical cavity (2), and two single-degree-of-freedom Helmholtz silencers (4) and a double-degree-of-freedom Helmholtz silencer (5) are connected in series at the end of the three groups of 1 / 4 annular thin plate arrays with shorter sizes.

2. The acoustic black hole sound absorber structure with a Helmholtz muffler according to claim 1, characterized in that: The cross-shaped partition (1) has a plate thickness of no more than 2 mm. The cross-shaped partition (1) is fixed inside the end stepped cylindrical cavity (2). The center line of the cross-shaped partition (1) coincides with the center line of the end stepped cylindrical cavity (2). The cross-shaped partition (1) divides the end stepped cylindrical cavity (2) into four completely independent 1 / 4 cylindrical cavities with the same cross-sectional area and different lengths. The length of the cross-shaped partition (1) is no less than the length of the 1 / 4 cylindrical cavity.

3. The acoustic black hole sound absorber structure with a Helmholtz muffler according to claim 1, characterized in that: Four groups of 1 / 4 annular thin plate arrays (3) are respectively fixed in a 1 / 4 cylindrical cavity of the same length, the spacing between adjacent annular thin plates in the 1 / 4 annular thin plate array (3) is the same, and the thickness of each 1 / 4 annular thin plate is the same and does not exceed 2 mm.

4. The acoustic black hole sound absorber structure with a Helmholtz muffler according to claim 1, characterized in that: Two single-degree-of-freedom Helmholtz silencers (4) and a double-degree-of-freedom Helmholtz silencer (5) are connected in series at the ends of three groups of shorter 1 / 4 annular thin plate arrays. The back cavity bottom area of ​​the single-degree-of-freedom Helmholtz silencer (4) and the double-degree-of-freedom Helmholtz silencer (5) is the same, and the neck size, neck length and back cavity height are different. The inner diameter and outer diameter of the back cavity of the single-degree-of-freedom Helmholtz silencer (4) and the double-degree-of-freedom Helmholtz silencer (5) are respectively the same as the inner diameter and outer diameter of the end stepped cylindrical cavity (2). The total length of the single-degree-of-freedom Helmholtz silencer (4) and the double-degree-of-freedom Helmholtz silencer (5) and their corresponding 1 / 4 annular thin plate arrays connected in series does not exceed the length of the longest 1 / 4 annular thin plate array. The necks of the single-degree-of-freedom Helmholtz silencer (4) and the double-degree-of-freedom Helmholtz silencer (5) can extend into the back cavity or toward the outside of the back cavity.

5. The acoustic black hole sound absorber structure with a Helmholtz muffler according to claim 1, characterized in that: The cross-shaped partition (1), the end stepped cylindrical cavity (2), four groups of 1 / 4 annular thin plate arrays (3), two single-degree-of-freedom Helmholtz silencers (4) and a double-degree-of-freedom Helmholtz silencer (5) are integrally formed by 3D printing or connected and fixed by using strong glue, welding or bolts.

6. A method for designing an acoustic black hole sound absorber structure with a Helmholtz muffler, characterized in that: The steps include: In the first step, when the sound wave is incident vertically, the transfer function of the sound pressure and sound volume velocity at the sound wave entrance and end of the 1 / 4 acoustic black hole absorber structure composed of a 1 / 4 annular thin plate array and a 1 / 4 cylindrical cavity is Where M is the number of 1 / 4 annular thin plates in the 1 / 4 acoustic black hole absorber structure; is the wave number; h i+1 is the distance between two adjacent annular thin plates; is the area of ​​the opening of the i+1th 1 / 4 annular thin plate; Z0=ρ0c0 is the impedance of air; is the cavity admittance, where V i+1 is the volume of the hollow cone between two adjacent 1 / 4 annular thin plates; When the sound wave is incident vertically, the transfer function of sound pressure and sound volume velocity when propagating in a single Helmholtz muffler is T HR =T neck T cavity (2) Where, T neck is the transfer function of the Helmholtz muffler neck; T cavity is the transfer function of the back cavity of the Helmholtz muffler Where, L neck is the length of the Helmholtz muffler neck; S neck is the cross-sectional area of ​​the Helmholtz muffler neck; L cavity is the length of the back cavity of the Helmholtz muffler; S cavity is the cross-sectional area of ​​the back cavity of the Helmholtz muffler; The transfer function of a 1 / 4 acoustic black hole absorber structure connected in series with n Helmholtz silencers is: The effective acoustic impedance of a structure consisting of a 1 / 4 acoustic black hole absorber and n (n ≥ 0) Helmholtz silencers in series is By designing a parallel coupling structure of four groups of 1 / 4 acoustic black hole absorbers and n Helmholtz silencers in series, the total effective acoustic impedance after combination is Where Z1, Z2, Z3, and Z4 are the acoustic impedances corresponding to the structure of four groups of 1 / 4 acoustic black hole absorbers and n Helmholtz silencers in series. The sound absorption coefficient of the acoustic black hole absorber structure with Helmholtz silencers is obtained from formula (7): Where S = πR 2 is the total area that allows vertical incidence of sound waves, where R is the inner diameter of the cylindrical cavity; In the second step, based on the change of the above impedance value with the structural size of the Helmholtz silencer, the structural length of the Helmholtz silencer connected in series at the end of the 1 / 4 acoustic black hole absorber is designed through series and parallel coupling design to optimize the sound absorption coefficient of the acoustic black hole absorber structure with the Helmholtz silencer.

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