Multi-free metasurface acoustic liner based on multiple layers and provided with embedded pipe insertion plates and design method
By introducing a double-layer structure and mesh structure in the aerial acoustic lining, the surface impedance and coupling effect of the acoustic lining are optimized, and the shortcomings of the existing acoustic lining in broadband noise reduction are solved, and the efficient wideband sound absorption effect is achieved.
Patent Information
- Application Number
- CN202411650358.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-19
- Publication Date
- 2025-03-28
AI Technical Summary
The existing aerial acoustic lining has frequency limitations in reducing noise, making it difficult to achieve wide-band noise reduction, and traditional honeycomb sandwich acoustic lining has limited noise reduction capabilities at lower frequency noise.
The multi-free superstructure acoustic lining design based on multi-layered multi-layer tube inserts is adopted. By introducing a double-layer structure and mesh structure of the embedded tube, the degree of freedom and surface impedance of the acoustic lining is increased, and the sound absorption performance of the acoustic lining is optimized by using series and parallel coupling effects.
It has achieved a multi-free superstructure acoustic lining with a thinner structure and a better wide frequency sound absorption effect, with an average sound absorption coefficient of more than 0.9 in the frequency band of 1000-5000Hz, which significantly improves the noise reduction effect of traditional acoustic lining.
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Figure CN119724142A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of acoustic lining structures, in particular to a multi-freedom super-structure acoustic lining based on multiple layers with embedded tube inserts and a design method. Background Art
[0002] As the quality of life in society continues to improve, the issue of noise pollution has received increasing attention from the public. Especially in the aviation industry, how to effectively control and reduce the noise generated by high-speed aircraft has become an urgent issue to be solved, and thin, broadband noise-reducing linings are in urgent need of development.
[0003] One of the most commonly used aviation acoustic linings is the perforated plate acoustic lining, which consists of a perforated plate, a cavity and a rigid back plate, and can form a single degree of freedom or a multi-degree of freedom structure. It can achieve good sound absorption in certain specific frequency bands, but due to its low degree of freedom, it can only reduce noise at one or two frequencies and cannot be designed for too many noise frequencies, making it difficult to achieve broadband noise reduction and a good noise reduction effect.
[0004] In addition, the traditional perforated honeycomb sandwich acoustic liner dissipates noise energy based on the Helmholtz resonance cavity principle. When reducing lower frequency noise, a larger resonance cavity volume is required. However, the installation position of the acoustic liner in the nacelle and fan casing is limited, which directly limits the noise reduction ability of the traditional acoustic liner for lower frequency noise. New broadband noise reduction technology needs to be developed urgently to further improve the noise reduction effect of traditional acoustic liner. Summary of the invention
[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a multi-freedom super-structured sound lining and design method based on multiple layers with embedded tube inserts, which has a lighter and thinner structure, good broadband sound absorption effect, and good overall configuration adjustability.
[0006] The purpose of the present invention can be achieved by the following technical solutions:
[0007] A multi-free superstructure acoustic liner based on multiple layers with embedded tube plug plates includes a plurality of honeycomb cavities of equal size connected in parallel with each other, each honeycomb cavity is provided with an upper embedded tube and a lower embedded tube fixed in the cavity, the upper embedded tube is connected to the upper end of the honeycomb cavity, and the side lengths and tube lengths of the tube cavity sections of the upper embedded tubes and the lower embedded tubes corresponding to each honeycomb cavity are different.
[0008] Furthermore, the multi-freedom metaacoustic liner also includes a mesh structure covering the top surface of the honeycomb cavity, which is used to change the surface impedance of the multi-freedom metaacoustic liner.
[0009] Furthermore, the mesh structure is a metal mesh or a textile.
[0010] Furthermore, the honeycomb cavity is a columnar structure with a hexagonal cross-section.
[0011] Furthermore, the hexagon is a regular hexagon.
[0012] Furthermore, the upper embedded tube and the lower embedded tube are both hexagonal columnar structures.
[0013] Furthermore, the hexagon is a regular hexagon.
[0014] Furthermore, one end of each of the honeycomb cavities provided with an upper embedded tube is located on the same plane;
[0015] The lower embedded tubes in each of the honeycomb cavities are located on different planes;
[0016] The metal mesh covers the opening portion of the upper embedded tube.
[0017] Furthermore, the multi-freedom super-structure acoustic liner is used for sound absorption in the frequency band of 1000-5000 Hz, and the number of honeycomb cavities in the multi-freedom super-structure acoustic liner is 4, and the size data combinations of the upper embedded tube cavity cross-sectional side length, upper embedded tube length, lower embedded tube cavity cross-sectional side length, lower embedded tube length and lower embedded tube height of the four honeycomb cavities are 4.1mm, 1.7mm, 1.4mm, 2.1mm, 13.6mm; 4.0mm, 0.8mm, 0.8mm, 7.3mm, 34.0mm; 4.0mm, 2.0mm, 0.8mm, 3.5mm, 19.3mm; 3.4mm, 0.8mm, 3.2mm, 4.5mm, 11.3mm;
[0018] The total height and side length of each honeycomb cavity are 36.7 mm and 6.6 mm respectively; the through-hole mesh number of the metal wire mesh is 500 meshes.
[0019] Furthermore, the multi-freedom super-structure acoustic liner is used for sound absorption in the frequency band of 1000-5000 Hz, and the number of honeycomb cavities in the multi-freedom super-structure acoustic liner is 4, and the size data combinations of the upper embedded tube cavity cross-sectional side length, upper embedded tube length, lower embedded tube cavity cross-sectional side length, lower embedded tube length and lower embedded tube height of the four honeycomb cavities are 3.1mm, 0.8mm, 4.3mm, 1.7mm, 1.9mm; 2.9mm, 1.8mm, 2.2mm, 9.3mm, 15.3mm; 2.7mm, 0.8mm, 2.8mm, 5.2mm, 11.3mm; 3.3mm, 0.8mm, 2.8mm, 5.2mm, 23.6mm;
[0020] The total height and side length of each honeycomb cavity are 39.0 mm and 5.5 mm respectively; the through-hole mesh number of the metal wire mesh is 500 meshes.
[0021] Furthermore, the honeycomb cavities are arranged in parallel in a honeycomb configuration.
[0022] The present invention also provides a design method for a multi-freedom super acoustic liner based on multiple layers with embedded tube inserts as described above, comprising the following steps:
[0023] Construct the surface impedance model of each honeycomb cavity in the multi-freedom meta-acoustic liner, and connect multiple honeycomb cavities in parallel to obtain the overall surface impedance model of the multi-freedom meta-acoustic liner;
[0024] By adjusting the geometric parameters of the overall surface impedance model and utilizing the series and parallel coupling effects, the target sound absorption requirements can be achieved.
[0025] The expression of the surface impedance model of the honeycomb cavity is:
[0026]
[0027] In the formula, Z i is the surface impedance of the ith honeycomb cavity, P t 、V t , P b 、V b are the sound pressure and volume velocity at the bottom and top of the structure, respectively, is the transfer matrix of the upper end of the i-th embedded tube, is the transfer matrix of the middle part of the i-th embedded tube, is the transfer matrix of the side cavity of the i-th embedded tube, M i is the transfer matrix of the cavity corresponding to the i-th embedded tube, EA i is the i-th embedded tube, T is the transfer matrix;
[0028] The overall surface impedance model of the multi-freedom meta-acoustic liner is expressed as:
[0029]
[0030] Where Z is the overall surface impedance of the multi-freedom meta-acoustic liner.
[0031] Compared with the prior art, the present invention has the following advantages:
[0032] (1) The present invention introduces a double-layer structure of embedded tubes on the basis of the traditional honeycomb configuration sound liner, and takes the size of the upper embedded tube and the position and size of the lower embedded tube as designable parameters; the degree of freedom of the sound liner is increased, and more precise control of sound waves can be achieved; and based on the theoretical model, the influence of the embedded tube structure on the sound absorption of the sound liner structure is explored, and the broadband sound absorption capacity of the overall structure is improved. Finally, the coupling effect between the structural monomers successfully developed two structures with excellent sound absorption performance, whose honeycomb cavity edge sizes are 6.6mm and 5.5mm respectively, and the thickness is controlled within 40mm. These sound-absorbing structures show good broadband sound absorption capabilities in the frequency range of 1000-5000Hz, and the average sound absorption coefficient reaches above 0.9.
[0033] (2) Compared with the traditional sound liner, the design of the present invention introduces an embedded tube structure, which greatly improves the overall broadband sound absorption capacity of the sound liner and retains the honeycomb structure. The overall configuration is easy to process and has good application prospects in the field of aviation noise reduction. BRIEF DESCRIPTION OF THE DRAWINGS
[0034] Figure 1 A schematic structural diagram of a double-layer honeycomb acoustic liner based on an embedded tube structure provided in an embodiment of the present invention;
[0035] Figure 2 An exploded view of a honeycomb cavity monomer provided in an embodiment of the present invention;
[0036] Figure 3 A schematic cross-sectional view of a honeycomb cavity monomer provided in an embodiment of the present invention;
[0037] Figure 4 A diagram showing the variation of the single-unit sound absorption (α) with the size of the embedded tube provided in an embodiment of the present invention, including the length of the upper inner tube (l a1 ), length of lower inner tube (l a2 ), upper cavity length (l u );
[0038] Figure 5 The relationship between the sound absorption coefficient (Absorption) and the frequency (Frequency) of a theory and an actual product provided in an embodiment of the present invention, wherein the unit of frequency is Hertz (Hz). DETAILED DESCRIPTION
[0039] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.
[0040] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0041] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.
[0042] In the description of the present invention, it should be noted that the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside", etc. indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings, or are the directions or positional relationships in which the inventive product is usually placed when in use. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as a limitation on the present invention.
[0043] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.
[0044] In addition, the terms "horizontal", "vertical" and the like do not mean that the components are required to be absolutely horizontal or suspended, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.
[0045] Example 1
[0046] like Figure 1 As shown, this embodiment provides a multi-free super-structure acoustic liner based on multiple layers with embedded tube plug plates, including a plurality of honeycomb cavities 1 of equal size connected in parallel with each other, each honeycomb cavity 1 is provided with an upper embedded tube 2 and a lower embedded tube 3 fixed in the cavity, the upper embedded tube 2 is connected to the upper end of the honeycomb cavity 1, and the side lengths and tube lengths of the tube cavity cross-sections of the upper embedded tubes 2 and the lower embedded tubes 3 corresponding to each honeycomb cavity 1 are different.
[0047] This solution introduces a double-layer structure of embedded tubes on the basis of the traditional honeycomb configuration sound liner, and takes the size of the upper embedded tube and the position and size of the lower embedded tube as designable parameters; the degree of freedom of the sound liner is increased, and more precise control of sound waves can be achieved.
[0048] The lower embedded tube 3 can be fixed in the honeycomb cavity 1 through a middle partition with a through hole in the middle. Figure 2 As shown;
[0049] Preferably, the multi-freedom metaacoustic liner also includes a mesh structure covering the top surface of the honeycomb cavity 1 for changing the surface impedance of the multi-freedom metaacoustic liner. The mesh structure may be a metal mesh 4 or a textile.
[0050] It should be noted that in the multi-freedom superstructure acoustic liner of this scheme, the hole shape of the honeycomb cavity 1 is adjustable, the hole diameter is adjustable, and the hole length can also be adjusted;
[0051] The material of the mesh structure covering the top surface of the honeycomb cavity 1 is not limited, as long as it can change the surface impedance; it is not limited whether it exists or not;
[0052] The number of layers of the middle baffles for fixing the lower embedded tube 3 is also adjustable, that is, one or more middle baffles of different heights can be provided to jointly fix the lower embedded tube 3. As an optional embodiment, the honeycomb cavity 1, the upper embedded tube 2 and the lower embedded tube 3 are all columnar structures with hexagonal cross-sections, preferably regular hexagons.
[0053] Each honeycomb cavity 1 is provided with one end of the upper embedded tube 2 which is located on the same plane; the top surface of the honeycomb cavity 1 is a top plate with a through hole in the middle;
[0054] The lower embedded tubes 3 in each honeycomb cavity 1 are located on different planes;
[0055] The metal mesh 4 covers the opening portion of the upper embedded tube 2;
[0056] The honeycomb cavities 1 are arranged in parallel in a honeycomb configuration.
[0057] In this embodiment, each upper embedded tube 2 is fixed at the center of one end of the corresponding honeycomb cavity 1 and is in the same horizontal plane, and the lower embedded tube 3 is also at the center of the horizontal position of the corresponding honeycomb cavity 1 and is in a different horizontal plane.
[0058] like Figure 3 As shown, the side length d of the upper inner tube of each sound-absorbing honeycomb structure is a1 , the side length of the lower layer inner tube d a2 , Length of the upper inner tube l a1 , length of lower layer inner tube l a2, honeycomb cavity side length a, upper honeycomb cavity height Lu, total structure thickness L. The honeycomb acoustic lining structure designed in this embodiment has a wall thickness of t=0.8 mm, and the number of metal wire meshes Mn is 500 meshes.
[0059] This embodiment first provides a double-layer honeycomb acoustic liner based on an embedded tube structure with a honeycomb cavity side length a=6.6mm. The parallel coupling effect of multiple cavities enables the average sound absorption coefficient of the overall acoustic liner structure to reach 0.94 in the frequency band of 1000-5000Hz. The structural parameters of the acoustic liner are shown in Table 1.
[0060] Table 1 Geometric parameters of acoustic lining structure
[0061]
[0062] This embodiment also provides a double-layer honeycomb acoustic liner based on an embedded tube structure with a honeycomb cavity side length a=5.5 mm. The parallel coupling effect of multiple cavities enables the average sound absorption coefficient of the overall acoustic liner structure to reach 0.91 in the frequency band of 1000-5000 Hz. The structural parameters of the acoustic liner are shown in Table 2.
[0063] Table 2 Geometric parameters of acoustic lining structure
[0064]
[0065] The experimental verification was carried out using a square standing wave tube with a side length of 30 mm. The experimental results were compared with the theoretical results. Figure 3 As shown, it can be seen that the experimental results are in good agreement with the theoretical results. The deviations between the experiment and the theory and simulation may come from the errors in sample printing and assembly.
[0066] In order to explain the mechanism of achieving good sound absorption effect, a hybrid metasurface composed of four strong sound absorbing units was first studied. Through analysis on the complex frequency plane, it was found that although each strong sound absorbing unit exhibited a high absorption peak when working alone, after being combined together, the overall absorption performance was not ideal due to the influence of the coherent coupling effect. Therefore, a method of achieving broadband absorption by coupling weak sound absorbing units was proposed. The parallel coupling structure of weak sound absorbing units has obvious advantages in the thickness and coupling adjustment freedom. The structural design adopts the coupling of weak sound absorbing units in series and parallel. The possible relationship between the parameters of the single-layer embedded tube weak sound absorbing unit structure and the sound absorption frequency is first simply explored. Taking the double-layer embedded tube sound lining monomer with structural parameters of [0.8, 27.9, 2.1, 0.9, 5.5, 7.2, 40, 5.5, 0.7] as an example, if only the influence of the introduction of the upper embedded tube is considered, the tube length is increased from 0 to the limit tube length of the structure of 5mm, which can be obtained from Figure 4 It can be observed from a in Figure that the introduction of the upper embedded tube causes the absorption peak to shift to low frequency. Figure 4 b and Figure 4Figure c shows the effect of changing the length of the lower and upper parts of the lower embedded tube. In particular, the introduction of the lower tube of the embedded tube will cause the absorption peak to move to low frequency and change the number of absorption peaks in the target frequency band. Therefore, the adjustable structure of the embedded tube is very high. The sound absorption peaks of multiple coupling units can be staggered to achieve broadband sound absorption.
[0067] This embodiment also provides a design method for a multi-freedom superstructure acoustic liner based on multiple layers with embedded tube inserts as described above, wherein the impedance model of the sound absorbing unit is obtained by a transfer matrix method, comprising the following steps:
[0068] P t 、V t , P b 、V b are the sound pressure and volume velocity at the bottom and top of the structure, respectively. They are connected by the transfer T. This relationship can be expressed as:
[0069]
[0070] The transfer matrix T can be written as:
[0071]
[0072] in are the transfer matrices of each part of the structural unit, representing the modulation effect of the structure on the sound wave. The surface impedance of the final structural unit can be expressed as:
[0073]
[0074] Considering the coupling of multiple monomers, the overall surface impedance of the system is obtained by connecting multiple monomers in parallel, which can be expressed as:
[0075]
[0076] By adjusting the geometric parameters of multiple units and making full use of the series and parallel coupling effects, the bandwidth of the sound absorption structure can be greatly expanded. By modulating the surface impedance of the absorber in a near-continuous resonance mode, the sound absorption structure achieves ultra-wideband impedance matching and finally achieves the target sound absorption.
[0077] like Figure 5 As shown in a and b in the figure, the relationship between the sound absorption coefficient (Absorption) and frequency (Frequency) of the above theoretical design method and the actual product has achieved good consistency.
[0078] This example is based on the traditional honeycomb sound lining, and an embedded tube structure is introduced to form a double-layer honeycomb cavity sound lining. The parameters of each embedded tube are adjustable, and it can be directionally designed. Finally, combined with the coupling effect of the monomer, two structures with excellent sound absorption performance were designed. The dimensions of the honeycomb cavity edges are 6.6mm and 5.5mm respectively, and the thickness is controlled within 40mm. These sound-absorbing structures show good broadband sound absorption capabilities in the frequency band of 1000-5000Hz, and the average sound absorption coefficient exceeds 0.9. The design of this embodiment improves the broadband sound absorption capability of the sound lining through the introduction of the embedded tube structure, and is expected to be used in engineering fields such as aircraft engine noise reduction.
[0079] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.
Claims
1. A multi-freedom super acoustic liner based on multiple layers with embedded tube inserts, characterized in that: The invention comprises a plurality of honeycomb cavities (1) of equal size and connected in parallel with each other, each honeycomb cavity (1) being provided with an upper embedded tube (2) and a lower embedded tube (3) fixed in the cavity, the upper embedded tube (2) being connected to the upper end of the honeycomb cavity (1), and the side length and tube length of the tube cavity section of the upper embedded tube (2) and the lower embedded tube (3) corresponding to each honeycomb cavity (1) being different.
2. A multi-freedom super acoustic liner based on multiple layers with embedded tube inserts according to claim 1, characterized in that: The multi-freedom metaacoustic liner also includes a mesh structure covering the top surface of the honeycomb cavity (1) for changing the surface impedance of the multi-freedom metaacoustic liner.
3. A multi-freedom super acoustic liner based on multiple layers with embedded tube inserts according to claim 2, characterized in that: The mesh structure is a metal wire mesh (4) or a textile.
4. The multi-freedom super acoustic liner based on multiple layers with embedded tube inserts according to claim 1 is characterized in that: The honeycomb cavity (1) is a columnar structure with a hexagonal cross section.
5. The multi-freedom super acoustic liner based on multiple layers with embedded tube inserts according to claim 1 is characterized in that: The upper embedded tube (2) and the lower embedded tube (3) are both hexagonal columnar structures.
6. The multi-freedom super acoustic liner based on multiple layers with embedded tube inserts according to claim 1 is characterized in that: One end of each of the honeycomb cavities (1) provided with the upper embedded tube (2) is located on the same plane; The lower embedded tubes (3) in each of the honeycomb cavities (1) are located on different planes; The metal wire mesh (4) covers the opening portion of the upper embedded tube (2).
7. The multi-freedom super acoustic liner based on multiple layers with embedded tube inserts according to claim 1 is characterized in that: The multi-freedom super-structured acoustic liner is used for sound absorption in the frequency band of 1000-5000 Hz. The number of honeycomb cavities (1) in the multi-freedom super-structured acoustic liner is 4. The size data combinations of the side length of the tube cavity cross section of the upper embedded tube (2), the tube length of the upper embedded tube (2), the side length of the tube cavity cross section of the lower embedded tube (3), the tube length of the lower embedded tube (3) and the height of the lower embedded tube (3) of the four honeycomb cavities (1) are 4.1 mm, 1.7 mm, 1.4 mm, 2.1 mm, 13.6 mm; 4.0 mm, 0.8 mm, 0.8 mm, 7.3 mm, 34.0 mm; 4.0 mm, 2.0 mm, 0.8 mm, 3.5 mm, 19.3 mm; 3.4 mm, 0.8 mm, 3.2 mm, 4.5 mm, 11.3 mm; The total height and side length of each honeycomb cavity (1) are 36.7 mm and 6.6 mm respectively; the through-hole mesh number of the metal wire mesh (4) is 500 meshes.
8. The multi-freedom super acoustic liner based on multiple layers with embedded tube inserts according to claim 1 is characterized in that: The multi-freedom super-structured acoustic liner is used for sound absorption in the frequency band of 1000-5000 Hz. The number of honeycomb cavities (1) in the multi-freedom super-structured acoustic liner is 4. The size data combinations of the side length of the tube cavity cross section of the upper embedded tube (2), the tube length of the upper embedded tube (2), the side length of the tube cavity cross section of the lower embedded tube (3), the tube length of the lower embedded tube (3) and the height of the lower embedded tube (3) of the four honeycomb cavities (1) are 3.1 mm, 0.8 mm, 4.3 mm, 1.7 mm, 1.9 mm; 2.9 mm, 1.8 mm, 2.2 mm, 9.3 mm, 15.3 mm; 2.7 mm, 0.8 mm, 2.8 mm, 5.2 mm, 11.3 mm; 3.3 mm, 0.8 mm, 2.8 mm, 5.2 mm, 23.6 mm; The total height and side length of each honeycomb cavity (1) are 39.0 mm and 5.5 mm respectively; the through-hole mesh number of the metal wire mesh (4) is 500 meshes.
9. The multi-freedom super acoustic liner based on multiple layers with embedded tube inserts according to claim 1, characterized in that: The honeycomb cavities (1) are arranged in parallel in a honeycomb configuration.
10. A design method for a multi-freedom meta-acoustic liner based on multiple layers with embedded tube inserts as claimed in any one of claims 1 to 9, characterized in that: The following steps are involved: Constructing a surface impedance model of each honeycomb cavity (1) in a multi-freedom meta-acoustic liner, and connecting multiple honeycomb cavities (1) in parallel to obtain an overall surface impedance model of the multi-freedom meta-acoustic liner; By adjusting the geometric parameters of the overall surface impedance model and utilizing the series and parallel coupling effects, the target sound absorption requirements can be achieved. The expression of the surface impedance model of the honeycomb cavity (1) is: In the formula, Z i is the surface impedance of the i-th honeycomb cavity (1), P t 、V t , P b 、V b are the sound pressure and volume velocity at the bottom and top of the structure, respectively, is the transfer matrix of the upper end of the i-th embedded tube, is the transfer matrix of the middle part of the i-th embedded tube, is the transfer matrix of the side cavity of the i-th embedded tube, M i is the transfer matrix of the cavity corresponding to the i-th embedded tube, EA i is the i-th embedded tube, T is the transfer matrix; The overall surface impedance model of the multi-freedom meta-acoustic liner is expressed as: Where Z is the overall surface impedance of the multi-freedom meta-acoustic liner.