A metasurface acoustic liner and its design method

Abstract

The present invention relates to a metamaterial acoustic liner and its design method. The bottom of the metamaterial acoustic liner is a coupled resonance cavity array formed by arranging multiple NEHRs in parallel, and metal foam is placed between the resonance cavity array and the MPP. When constructing the acoustic liner, the metal foam plays an important role in realizing the over-damping condition and suppressing impedance oscillation, which helps the acoustic liner achieve a broadband sound absorption effect without sound absorption troughs while realizing the optimal thickness. As a verification, the present invention designs a metamaterial acoustic liner with a thickness close to the causality limit, and the results show that the acoustic liner can achieve high-efficiency sound absorption in the frequency band ranging from 800 Hz to 3200 Hz. The work of the present invention enriches the design concept of acoustic liners, provides an effective method for constructing broadband acoustic liners that suppress sound absorption troughs, and is expected to be widely applied in the field of noise control.

Description

Technical Field

[0001] The present invention relates to the field of aero-engines, and more particularly to a metamaterial acoustic liner and a design method thereof. Background Art

[0002] Acoustic liners are widely used in the fields of noise reduction of aero-engines and ventilation systems. Researchers have developed and attempted acoustic liner technologies using a variety of different materials and design methods. Traditional acoustic liners are usually composed of multiple layers of micro-perforated plates and honeycomb cavities. Such single-degree-of-freedom or multi-degree-of-freedom acoustic liners have significant sound absorption effects within a single or multiple narrow frequency bands, but they cannot meet the increasingly stringent broadband sound absorption requirements in the aviation field. In addition, when eliminating the influence of low-frequency noise, traditional acoustic liners usually require more layers of micro-perforated plates or honeycomb cavity structures, and their large volume has great limitations in practical applications.

[0003] In order to further reduce the thickness of the acoustic liner and broaden its working frequency band, researchers have proposed a new type of metamaterial acoustic liner by combining acoustic metamaterials and acoustic metasurfaces. Acoustic metamaterials and metasurfaces are usually composed of sub-wavelength-scale resonance units, and these resonance units have excellent acoustic wave manipulation capabilities, showing great application potential in the field of efficient sound absorption and noise reduction. In particular, in recent years, there has been an endless stream of research on the coupling effects of resonant acoustic metamaterials and metasurfaces, which provides a research basis for realizing broadband and compact acoustic structures. However, the interaction caused by the resonance between structures will lead to anti-resonance phenomena, which makes the sound absorption of the overall structure worse at certain frequencies and affects the sound absorption effect of the acoustic liner in the broadband. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above-mentioned defects existing in the prior art and provide a metamaterial acoustic liner and a design method thereof to improve the sound insulation effect of the overall structure.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A metamaterial acoustic liner includes a resonance cavity array, metal foam, and a micro-perforated plate. The resonance cavity array, metal foam, and micro-perforated plate are sequentially stacked, and the resonance cavity array includes a plurality of internally inserted tube-type resonance cavities coupled in parallel.

[0007] A design method of the above-mentioned metamaterial acoustic liner includes establishing a theoretical model of the metamaterial acoustic liner based on the acoustic grating diffraction theory, calculating the sound absorption coefficient of the metamaterial acoustic liner, and thus obtaining the optimal structural parameters of the metamaterial acoustic liner through optimization calculation.

[0008] Further, the establishment process of the theoretical model of the metamaterial acoustic liner includes:

[0009] Define the air domain above the micro-perforated plate as Region I, the location of the micro-perforated plate as Region II, the metal foam as Region III, and the resonant cavity array as Region IV; calculate the sound pressure and corresponding velocity in each region when a plane wave with an incident angle of θ i is incident. According to the boundary conditions, the sound pressure and the normal particle velocity are continuous at the upper and lower interfaces of the micro-perforated plate and the surface of the resonant cavity array, so as to determine the limiting conditions of the sound pressure and velocity at each interface, and finally obtain the sound absorption coefficient of the metamaterial acoustic liner.

[0010] Furthermore, the optimal structural parameters include the length a of the resonant cavity array, the width b of the resonant cavity array, the thickness L of the resonant cavity array, the thickness D of the metal foam, the thickness t of the micro-perforated plate p , the length a p of the resonant cavity unit p , the width b a of the resonant cavity unit a , the height l p of the inner insert pipe in the resonant cavity unit

[0011] Furthermore, the calculation expressions for the sound pressure in Regions I and III are as follows:

[0012]

[0013]

[0014] where m = 0, ±1,... ±M, n = 0, ±1,... ±N, M is the total number of scattering wave modes in the x direction, and N is the total number of scattering wave modes in the y direction; and are the amplitudes of the incident wave and the reflected wave respectively, represents the amplitude of the sound wave in the metal foam, and the superscripts + and - indicate that the sound wave propagates along the positive and negative directions of the z-axis; k x,m = k0cosα + mG x , k y,n = k0cosβ + nG y and represent the wave vector components in the x, y, and z directions in Region I respectively, k0 is the wave vector of the incident wave in air, represents the reciprocal lattice vector; α, β, γ represent the angles between the wave vector and the positive directions of the x, y, and z axes respectively; and represent the wave vector components in the x, y, and z directions in Region III respectively, is the wave vector when the sound wave propagates in the metal foam.

[0015] Furthermore, the Delany-Bazley empirical model is selected for calculation

[0016]

[0017] where f represents the frequency, R f represents the flow resistance of the metal foam, ω is the angular frequency, c is the speed of sound in air, ρ0 is the mass density of air, and j is the imaginary part symbol.

[0018] Furthermore, according to the relationship between the sound pressure and the normal particle velocity the corresponding velocities in regions I and III are obtained:

[0019]

[0020]

[0021] where ρ0 and ρ f represent the mass density of air and the equivalent mass density of the metal foam respectively, and ω is the angular frequency.

[0022] Furthermore, the sound pressure and the normal particle velocity in the perforations of the micro-perforated plate are expressed as:

[0023]

[0024]

[0025] where k pj and ρ pj represent the complex wave vector and the equivalent mass density in the aperture of the micro-perforated plate respectively, represents the amplitude of the sound wave in the aperture, the subscript j represents the j-th aperture, and the subscript p represents that the corresponding physical quantity is the quantity in the perforated area of the micro-perforated plate.

[0026] Furthermore, the sound pressure and velocity at each interface of the metamaterial acoustic liner should satisfy:

[0027]

[0028]

[0029]

[0030] where x pj ,y pj and d prepresent the x-axis, y-axis coordinates and diameter of the center of the j-th hole on the micro-perforated plate respectively; J is the total number of perforations on the micro-perforated plate; Ω = {(x, y)|0 < x < a, 0 < y < b} represents the position of regions I and II in the x-y plane; the perforation rate of the MPP where S Ω = ab and are the area of one period of the metasurface acoustic liner and the cross-sectional area of the j-th perforation respectively; is the position of the upper orifice of the square inner insert tube of the i-th NEHR in the x-y plane; I is the total number of NEHRs, z = 0, z = h f and z = h f + h p represent the upper surface of the NEHRs, the lower surface and the upper surface of the micro-perforated plate respectively, h f = D, h p = t p .

[0031] Calculate the expressions of the sound pressure and velocity in all regions of the metasurface acoustic liner, and then calculate the inhomogeneous linear equations for the scattering problem when the incidence is according to the continuity conditions. The expression of this inhomogeneous linear equation is:

[0032]

[0033]

[0034]

[0035] where, λ mn = (n + N + 1 - 1)(2M + 1)+(m + M + 1) is the serial number of the diffraction order; H and H pa are two diagonal matrices, and the diagonal elements are and The element expression of the matrix is

[0036]

[0037]

[0038] where j = 1, 2, …, J, λ m,n = 1, 2, …, λ M,N , λ m ′, n′ = 1, 2, …, λ M,N ;

[0039] where T pf and T are diagonal elements of and Two diagonal matrices;

[0040] Furthermore, the impedance of the upper nozzle of the i-th resonator is calculated by using the transfer matrix method.

[0041] Furthermore, the sound absorption coefficient of the meta-acoustic liner is expressed as:

[0042]

[0043] In the formula, A- is the amplitude of the incident wave, A + is the amplitude of the reflected wave, θ r is the angle of the incident wave, θ i is the angle of the reflected wave.

[0044] Compared with the prior art, the present invention has the following advantages:

[0045] (1) The present invention designs a meta-acoustic liner composed of multiple parallel-coupled internal inserted Helmholtz resonators (NEHR), micro-perforated plates (MPP), and a layer of metal foam. Most previous research work has ignored the influence of the evanescent wave mode on the structure surface. In this paper, the acoustic grating diffraction theory is used to explain the propagation of high-order mode waves in the acoustic liner structure, so that the coupling effect between the components of the acoustic liner can be described more accurately, thereby improving the sound absorption effect of the overall structure.

[0046] (2) In addition, it should be emphasized that the metal foam not only has excellent mechanical and acoustic properties in the field of aeroacoustics applications, but also can regulate the inherent loss of the acoustic liner to suppress the anti-resonance to cause sound absorption valleys, thereby helping the acoustic liner to achieve nearly perfect sound absorption effect with a nearly thinnest thickness. The design method of combining resistive materials and reactive materials enables the meta-acoustic liner to achieve high-efficiency broadband sound absorption with a light, thin and simple configuration.

[0047] (3) The introduction of the metal foam and MPP in the present invention reduces the number of NEHRs below. Some previous resonant structures may require a lot of structures in parallel to achieve a similar sound absorption effect. In comparison, the structure of the present invention is more convenient for processing and manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of the meta-acoustic liner including the components and their arrangements of each part and the structural schematic of a single NEHR structure;

[0049] Figure 2 Schematic diagram of the acoustic liner partition; h f and h p are the thicknesses of the metal foam and MPP respectively. Regions Ⅰ, Ⅱ, Ⅲ, and Ⅳ represent the regions above the acoustic liner, MPP, metal foam, and NEHR array respectively;

[0050] Figure 3 The acoustic liner dominated by the resonance effect; (a) Theoretical (solid line) and experimental (circles) sound absorption coefficients, (b) Theoretical (solid line) and experimental (circles) acoustic resistance and acoustic reactance curves, (c) Reflection characteristics of the acoustic liner in the complex frequency plane;

[0051] Figure 4 The metamaterial acoustic liner with metal foam; (a) Experimental sample, (b) Theoretical (solid line) and experimental (circles) sound absorption curves, where red and black represent the acoustic liner and the metal foam alone respectively, (c) Acoustic resistance and acoustic reactance curves of the acoustic liner (solid line for theory, circles for experiment), (d) Reflection characteristics of the acoustic liner in the complex frequency plane;

[0052] Figure 5 The sound absorption effect of the acoustic liner with metal foam at different incident angles;

[0053] Figure 6 The pressure sound fields on the MPP surface and the NEHRs surface (f = 2400 Hz), (a) The acoustic liner without metal foam, (b) The acoustic liner with metal foam;

[0054] In the figure, region is the area, Resistance is the acoustic resistance, Reactance is the acoustic reactance, and surface is the surface. Detailed implementation manners

[0055] To make the objectives, 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 with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations.

[0056] Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0057] It should be noted that: Similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0058] Embodiment 1

[0059] This embodiment provides a metamaterial acoustic liner based on a combination of metal foam, perforated plate, and resonance cavity array, which is composed of multiple parallel-coupled inner-intubated Helmholtz resonators (NEHRs), a micro-perforated plate (MPP), and a layer of metal foam. Most previous research work has ignored the influence of the evanescent wave mode on the structure surface. In this paper, the acoustic grating diffraction theory is used to explain the propagation of high-order mode waves in the acoustic liner structure, so that the coupling effect between the components of the acoustic liner can be described more accurately, thereby improving the sound absorption effect of the overall structure. In addition, it should be emphasized that metal foam not only has excellent mechanical and acoustic properties in the field of aeroacoustics applications, but also can regulate the inherent loss of the acoustic liner to suppress the absorption trough caused by anti-resonance, thereby helping the acoustic liner achieve nearly perfect sound absorption effect with a nearly minimum thickness. The design method of combining resistive materials and reactive materials enables the metamaterial acoustic liner to achieve high-efficiency broadband sound absorption with a light, thin, and simple configuration.

[0060] I. Theory and Model

[0061] The acoustic liner configuration with metal foam is shown as Figure 1 follows. Its bottom is a coupled resonance cavity array composed of multiple NEHRs arranged in parallel, and the metal foam is placed between the resonance cavity array and the MPP. The NEHR with significant impedance adjustment function consists of a cavity with a rectangular cross-section (depth L, side lengths a p and b p ) and an inner tube with a square cross-section (tube length l a , side length d p ). By reasonably designing the coupling relationship between these NEHRs and the coupling relationship between the NEHR array, metal foam, and MPP, the overall acoustic liner can provide appropriate broadband impedance conditions, which enables people to freely design the front-end acoustic system. High-order mode sound waves often exist in the form of evanescent waves. In previous theoretical research work, the influence of high-order mode waves is usually ignored. In fact, in acoustic structure components, especially at the interface between different media, there is a certain coupling effect between structure components or there is a transverse energy flow exchange between unit structures, which is mainly caused by the existence of high-order evanescent waves. Ignoring this part of the effect will affect the overall design efficiency. In order to comprehensively consider the combined action of propagating wave mode and evanescent wave mode, a theoretical model of the metamaterial acoustic liner is established in this paper based on the acoustic grating diffraction theory.

[0062] The optimal structural parameters to be obtained through this theoretical model include the length a of the resonance cavity array, the width b of the resonance cavity array, the thickness L of the resonance cavity array, the thickness D of the metal foam, the thickness t p of the micro-perforated plate, the length a p of the resonance cavity unit, the width b p of the resonance cavity unit, and the height l of the inner intubation in the resonance cavity unita , the side length d of the inserted pipe in the resonant cavity unit a , the pore diameter d of the perforated panel p and the porosity ε of the perforated panel. The parameters of each unit in the resonant cavity array are independent of each other.

[0063] When a plane wave is incident on the structure surface, the acoustic grating diffraction theory explains different diffraction effects by decomposing the propagating mode components and evanescent mode components. Combining the design of this article and the Fourier transform method, the acoustic wave propagation of different modes can be calculated. Therefore, the sound pressure and particle velocity can be expressed as the superposition of multiple different modes. If the region is divided into four parts as shown in Figure 2 , the air domain above the MPP is region Ⅰ, the location of the MPP is region Ⅱ, the metal foam is region Ⅲ, and the resonant cavity array is region Ⅳ. Then when a plane wave with an incident angle of θ i is incident, the sound pressure in regions Ⅰ and Ⅲ can be expressed as:

[0064]

[0065]

[0066] where m = 0, ±1, K ± M, n = 0, ±1, K ± N. and are the amplitudes of the incident wave and the reflected wave respectively, represents the acoustic wave amplitude in the metal foam, and the superscript +(-) indicates that the acoustic wave propagates along the positive (negative) direction of the z-axis. k x,m = k0cosα + mG x , k y,n = k0cosβ + nG y and represent the wave vector components in the x, y, and z directions in region Ⅰ respectively, k0 is the wave vector of the incident wave in air, represents the reciprocal lattice vector. α, β, γ represent the angles between the wave vector and the positive directions of the x, y, and z axes respectively. Similarly, and represent the wave vector components in the x, y, and z directions in region Ⅲ respectively, is the wave vector when the acoustic wave propagates in the metal foam, and the Delany-Bazley empirical model is selected here to calculate

[0067]

[0068] where f represents the frequency, R f represents the flow resistance of the metal foam. According to the relationship between the sound pressure and the normal particle velocity Combining the sound pressure expressions (1) and (2), the corresponding velocity can be obtained:

[0069]

[0070]

[0071] where ρ0 and ρ f represent the mass density of air and the equivalent mass density of the metal foam respectively, and ω is the angular frequency. Since the perforation diameter of the MPP is only 1 mm, which is much smaller than the wavelength of the target frequency, it can be considered that only the fundamental mode of sound wave exists in each aperture. That is to say, the sound pressure and the normal particle velocity in the MPP perforation can be expressed as:

[0072]

[0073]

[0074] where k pj and ρ pj represent the complex wave vector and the equivalent mass density in the MPP aperture respectively, represents the amplitude of the sound wave in the aperture, and the subscript j represents the j-th aperture.

[0075] According to the boundary conditions, the sound pressure and the normal particle velocity should be continuous at the upper and lower interfaces of the MPP and the surface of the NEHR array, so as to ensure the efficient absorption of sound waves. That is to say, the sound pressure and velocity at each interface should satisfy:

[0076]

[0077]

[0078]

[0079] where x pj , y pj and d p represent the x-axis, y-axis coordinates and diameter of the center of the j-th hole on the MPP respectively. J is the total number of perforations on the MPP. Ω = {(x, y)|0 < x < a, 0 < y < b} represents the position of regions Ⅰ and Ⅱ in the x-y plane. Obviously, the perforation rate of the MPP where S Ω = ab and are the area of one period of the meta-acoustic liner and the cross-sectional area of the j-th perforation respectively. is the position of the upper orifice of the square inner tube of the i-th NEHR in the x-y plane. I is the total number of NEHRs. As Figure 1 shown, z = 0, z = hf and z = h f +h p respectively represent the upper surface of the NEHRs, the lower surface and the upper surface of the MPP. Similarly Figure 1 By comparison, it can be seen that h f = D, h p = t p . Next, first use the boundary conditions on the upper surface of the MPP (i.e., at z = h f +h p ).

[0080] Substitute formulas (1) and (6) into the first formula of formula (8), and combine with the orthogonality relation of waveguide modes to obtain

[0081]

[0082] where, when the summation order in formulas (1 - 4) is truncated at λ M,N λ m,n = (n + N + 1 - 1)(2M + 1)+(m + M + 1) is the serial number of the diffraction order. and can be and expressed as

[0083]

[0084] where H and H pa are two diagonal matrices, and the diagonal elements are respectively and The element expression of the matrix is

[0085]

[0086]

[0087] where j = 1,2,L,J, λ m,n = 1,2,L,λ M,N .

[0088] Similarly, substituting formula (4) and formula (7) into (8), we can get

[0089]

[0090] where

[0091]

[0092]

[0093] Here λ m′,n′ ​=1, 2, …, λ M,N 。

[0094] Similarly, for the lower surface of the MPP (z = h f ), using the boundary condition (8), we can obtain

[0095]

[0096]

[0097] where T pf and T are two diagonal matrices with diagonal elements being and respectively. Here

[0098] It should be emphasized that for the surface of the NEHR, since the size of the inner pipe orifice is much smaller than the minimum wavelength of the frequency band we are studying, in order to simplify the calculation, the transfer matrix method is adopted here

[38] to calculate the impedance of the upper orifice of the i-th NEHR Combined with the fifth equation in formula (8), we can obtain

[0099]

[0100] According to formula (2) and formula (18), we can get

[0101]

[0102] Similarly, substituting formula (19) into the sixth equation of formula (8), we can get

[0103]

[0104] where

[0105]

[0106] where

[0107]

[0108] is an identity matrix of dimension λ M,N ×λ M,N .

[0109] For all the above formulas, and respectively represent the orthogonal function systems in regions I and III, where

[0110]

[0111]

[0112] Equations (9), (13), (16), (17), and (20) give the non - homogeneous linear equations for the scattering problem when the incidence is , that is

[0113] M C R = A in (25)

[0114] where

[0115]

[0116]

[0117] and

[0118]

[0119] When the sound wave is normally incident on the surface of the metasurface acoustic liner, that is, setting the amplitude of the reflected wave can be solved as To ensure numerical convergence of the calculation, the summation in equations (1 - 4) is truncated at N = M = 24, that is, λ M,N = 2401.

[0120] Combining the above calculations, the sound absorption coefficient of the metasurface acoustic liner can be expressed as

[0121]

[0122] where A -(+) and θ i(r) represent the amplitude and angle of the incident (reflected) wave, respectively.

[0123] II. Results and Discussion

[0124] Guided by the above theoretical model, this paper first explored the acoustic liner structure dominated by resonance effects, which consists of a coupled resonator array and MPP. The resonator array with a thickness of 19 mm is composed of 16 NEHRs, the MPP with a thickness and perforation diameter of 1 mm has a perforation rate of 7.5%, and there is a 20 - mm cavity between the resonator array and MPP. The experimental samples are made of photosensitive resin using 3D printing technology. The experiment is carried out in a square impedance tube with a side length of 50 mm, and two 1 / 4 - inch microphones ( type - 4187) are used to measure the amplitude and phase of the sound field. The sound absorption coefficient and acoustic impedance value of the experimental samples can be obtained by analyzing the measured signals. The experimental results are as Figure 3As shown, the resonance-dominated acoustic liner has good performance in the target frequency band, but there are obvious troughs in the absorption curve, which may significantly affect the overall absorption efficiency of the acoustic liner in practical applications. In fact, the decrease of these absorption peaks is attributed to the anti-resonance caused by the interaction between resonance structures. Figure 3 The drastic oscillations in the acoustic resistance and acoustic reactance curves in (b) also illustrate the influence of anti-resonance. Figure 3 The theoretical curves and experimental curves in (a) and (b) are basically in agreement, indicating that the theoretical model proposed in this paper can well explain the response effect of this acoustic liner structure to sound waves in the target frequency band.

[0125] In addition to the intuitive absorption curve, this paper further explores the properties of the acoustic liner in the complex frequency (wavelength) plane from the perspective of causality. The imaginary part of the frequency can represent the potential dissipation property of the acoustic system. If the imaginary part of the frequency is considered in the calculation, the frequency can be correspondingly replaced by the complex form f' = f e + jf i , where f e represents the frequency including the inherent loss of the acoustic liner, and f i represents the additional complex frequency. Figure 3 The natural logarithm of the reflection coefficient r' of the resonant acoustic liner is plotted in (c), where the black contour lines represent the positions with an absorption coefficient of 0.997. The black line and the points inside it are the "zeros". From Figure 3 (c), it can be seen that the zero positions corresponding to this acoustic liner are almost all located in the upper half of the complex frequency plane, and the overall system is in an underdamped state. Fundamentally speaking, the causality constraint for a linear time-invariant system is:

[0126]

[0127] where D and D min represent the actual thickness and the minimum thickness of the absorption structure. λ n represents the zero in the lower half of the complex wavelength plane, corresponding to the zero in the upper half of the complex frequency plane [28,33] . Equation (30) indicates that Figure 3 the zeros in the upper half space in (c) mean that the structure has not reached the optimal design.

[0128] To suppress the absorption trough caused by anti-resonance and to make the metasurface acoustic liner closer to the minimum thickness restricted by causality, this paper adds metal foam to the resonant acoustic liner. Such porous medium materials can more effectively regulate the inherent loss of the structure. As Figure 4 (a) shows, the selected nickel metal foam is placed between the resonance cavity array and the MPP, and its flow resistance is 1500 Pa·s / m 2 . Using the same experimental method as before, the absorption effect of the metasurface acoustic liner with the metal foam structure is measured asFigure 4 As shown in (b) and (c). In the target frequency band, the absorption curve has almost no oscillation, and the average absorption coefficient reaches 0.96. Figure 4 (d) shows the reflection of this acoustic lining structure in the complex frequency plane. It can be clearly seen from the figure that the metal foam moves the overall zero point downward to the lower half plane, which indicates that the modulation of the overall structural loss by the metal foam makes the system in an overdamped state. Therefore, the acoustic lining achieves high-efficiency broadband absorption with a thickness close to the causality limit. Except for the case of normal incidence, as Figure 5 shown, this acoustic lining also has good performance at different incident angles.

[0129] Figure 6 Shows the sound field distribution at the cross-section of two acoustic linings for a more intuitive illustration of the interaction between the metal foam and the resonance cavity at anti-resonance. The magnitude and direction of the local sound intensity are represented by black arrows in the figure, which is convenient for observing the transverse energy exchange at different interfaces of the structure. Through Figure 6 (a) and (b), it can be clearly seen that there is a transverse energy flow transport between the resonance units, and the inherent loss provided by the metal foam can effectively suppress the anti-resonance generated by the interaction of the resonance structures, improving the absorption efficiency at the original absorption trough.

[0130] III. Conclusion

[0131] This paper studies the performance of acoustic linings with metal foam both theoretically and experimentally. The introduction of metal foam provides a new degree of freedom for regulating the inherent loss of the acoustic lining. Reasonably designing and regulating the inherent loss of the system can effectively suppress the anti-resonance of the system and can adjust the position of the zero point in the complex frequency plane to make the system in an overdamped state. In addition, different from previous studies, this paper establishes a theoretical model of the acoustic lining based on the acoustic grating diffraction theory. This method comprehensively considers the fundamental wave mode and high-order wave mode in the system, reveals the absorption mechanism of the broadband noise reduction acoustic lining, and helps researchers complete the on-demand design of the acoustic lining with higher efficiency. The designed acoustic lining structure in this paper achieves high-efficiency absorption from 800 Hz to 3200 Hz with a thickness of only 40 mm. Given the excellent mechanical properties of the acoustic lining material itself and the good broadband absorption effect, this research is expected to be applied to the field of aviation noise absorption and reduction.

[0132] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative labor. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention 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 protection scope determined by the claims.

Claims

1. A design method of a metasurface acoustic liner, characterized in that The meta-acoustic liner includes a resonance cavity array, metal foam, and a micro-perforated plate. The resonance cavity array, metal foam, and micro-perforated plate are stacked in sequence. The resonance cavity array includes a plurality of internally inserted tube-type resonance cavities coupled in parallel. The design method includes establishing a theoretical model of the meta-acoustic liner based on the acoustic grating diffraction theory, calculating the sound absorption coefficient of the meta-acoustic liner, and thus obtaining the optimal structural parameters of the meta-acoustic liner through optimization calculations. The process of establishing the theoretical model of the meta-acoustic liner includes: Define the air domain above the micro-perforated plate as Region Ⅰ, the location of the micro-perforated plate as Region Ⅱ, the location of the metal foam as Region Ⅲ, and the resonance cavity array as Region Ⅳ; Calculate the sound pressure and the corresponding velocity in each region when a plane wave with an incident angle of is incident. According to the boundary conditions, the sound pressure and the normal particle velocity are continuous at the upper and lower interfaces of the micro-perforated plate and the surface of the resonance cavity array, so as to determine the limiting conditions of the sound pressure and velocity at each interface, and finally obtain the sound absorption coefficient of the metamaterial acoustic liner; The optimal structural parameters include the length of the resonant cavity array a , the width of the resonant cavity array b , the thickness of the resonant cavity array L , the thickness of the metal foam D , the thickness of the micro-perforated plate t p , the length of the resonant cavity unit a p , the width of the resonant cavity unit b p , the height of the inner tube in the resonant cavity unit l a , the side length of the inner tube in the resonant cavity unit d a , the pore diameter of the micro-perforated plate d p and the perforation rate of the micro-perforated plate ε ; The calculation expressions for the sound pressure in regions I and III are: Among them, , , is x the total number of modes of the scattered wave in the direction, y is and are the amplitudes of the incident wave and the reflected wave respectively, represents the acoustic wave amplitude in the metal foam, and the superscripts + and - represent that the acoustic wave propagates along the z axis in the positive and negative directions; , and respectively represent the wave vector components in region Ⅰ in the x , y , z directions, k 0 is the wave vector of the incident wave in air, G ( ) represents the reciprocal lattice vector; α , β , γ respectively represent the angles between the wave vector and the positive directions of the x , y , z axes; , and respectively represent the wave vector components in region Ⅲ in the x , y , z directions, is the wave vector when the acoustic wave propagates in the metal foam.

2. The method according to claim 1, characterized in that, Select the Delany-Bazley empirical model for calculation : wherein f represents the frequency, represents the flow resistance of the metal foam, is the angular frequency, is the speed of sound in air, is the mass density of air, is the imaginary part symbol.

3. The method according to claim 1, characterized in that According to the relationship between the sound pressure and the normal particle velocity The corresponding velocities in regions I and III are obtained: where and represent the mass density of air and the equivalent mass density of the metal foam, respectively, is the angular frequency.

4. The method according to claim 1, wherein The sound pressure and normal particle velocity in the perforations of the micro-perforated plate are expressed as: wherein and respectively represent the complex wave vector and the equivalent mass density in the aperture diameter of the micro-perforated plate, represents the acoustic wave amplitude in the aperture diameter, and the subscript j represents the j th aperture diameter, and the subscript p represents that the corresponding physical quantity is the quantity in the perforated area of the micro-perforated plate.

5. The method according to claim 4, characterized in that, The sound pressure and velocity at each interface of the meta-acoustic liner should satisfy: Among them , and respectively represent the j -axis, x -axis coordinates and the diameter of the center of the y -th hole on the micro-perforated plate; J is the total number of perforations on the micro-perforated plate; represents the positions of regions Ⅰ and Ⅱ on the x-y plane; the perforation rate of the MPP , where and are respectively the area of one period of the meta-acoustic liner and the cross-sectional area of the j -th perforation; is the position of the upper orifice of the square inner insert tube of the i -th NEHR on the x-y plane; I is the total number of NEHRs, and respectively represent the upper surface of the NEHRs, the lower surface and the upper surface of the micro-perforated plate, , ; Calculate the expressions of sound pressure and velocity in all regions of the metasurface acoustic liner, and then calculate the inhomogeneous linear equations for the scattering problem when the incident wave is . The expression of this inhomogeneous linear equation set is as follows: Among them, and ; is the serial number of the diffraction order; and are two diagonal matrices, and the diagonal elements are respectively and ; the element expression of the matrix is Among them and , ; Among them and ; and are two diagonal matrices whose diagonal elements are and ; .

6. The method according to claim 5, characterized in that The sound absorption coefficient of the meta-acoustic liner is expressed as: In the formula, is the amplitude of the incident wave, is the amplitude of the reflected wave, is the angle of the incident wave, is the angle of the reflected wave.

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