A construction method of a muffler and a metasurface muffler

Abstract

The present invention relates to a construction method of a muffler and a metamaterial muffler. The construction method includes obtaining the target frequency band and the target transmission loss of the muffler, constructing the calculation process of the transmission loss of the impedance wall surface of the muffler, and optimizing the structural parameters of the muffler so that the muffler reaches the target transmission loss under the target frequency band. The metamaterial muffler includes a perforated plate, a metal foam, a rigid boundary housing, and a coupled resonator array connected in sequence. The resonator array includes a plurality of coupled resonator units connected in sequence, and each coupled resonator unit includes a plurality of neck-embedded Helmholtz resonators coupled in parallel. Compared with the prior art, the present invention realizes the efficient and accurate optimization design of the structure of the muffler. The proposed metamaterial muffler supports a dense mode density and highly adjustable internal losses, and provides a new way for broadband designable timbre.

Description

Technical Field

[0001] The present invention relates to the technical field of mufflers, and in particular, to a construction method of a muffler and a meta-muffler. Background Art

[0002] Timbre is a fundamental aspect of sound, which is naturally a concept closely related to broadband sound. It is usually considered to be determined by the inherent characteristics of passive mechanical systems. This is because timbre manipulation has always been challenging due to the dispersive nature of resonance, which hinders broadband wave modulation. The latest progress in acoustic metamaterials has greatly enriched the wave processing methods by enhancing performance and reducing size. Due to the development of additive manufacturing technology, it is more feasible to construct acoustic devices based on high-performance metamaterials, leading to various functions such as negative refraction, super-resolution imaging, and deep sub-wavelength absorption. Although most acoustic metamaterials are still limited by strong resonance dispersion and are designed for wave operations at single frequencies or relatively narrow frequency bands, broadband absorbing metamaterials provide new ideas for understanding resonance control and pave the way for broadband timbre manipulation.

[0003] With its unique strong enhancement of the sound field and sub-wavelength structural scale, the initial design of absorbing metamaterials is very effective for narrowband performance. To achieve broadband sound absorption / attenuation, an effective method is to combine a series of absorbing elements with different frequencies. Despite remarkable achievements in broadband high-efficiency sound absorption / attenuation, there is still a large gap in the implementation of timbre manipulation because timbre manipulation poses higher requirements for the frequency selectivity and fine modulation of broadband resonance.

[0004] In the process of the structural design of the above muffler, how to provide a design scheme for the muffler to achieve efficient and accurate optimization design calculation is a major technical problem at present. In addition, how to provide a muffler with a strong and well-controlled global coupling that provides a feasible approach for the designable timbre is also a major technical problem at present. Summary of the Invention

[0005] The purpose of the present invention is to overcome the above-mentioned defects existing in the prior art and provide a construction method of a muffler and a meta-muffler that can achieve efficient and accurate optimization design of the muffler.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A construction method of a muffler, comprising the following steps:

[0008] Obtain the target frequency band and target transmission loss of the muffler, construct the calculation process of the transmission loss of the impedance wall of the muffler, and by optimizing the structural parameters of the muffler, make the muffler reach the target transmission loss under the target frequency band.

[0009] Furthermore, the calculation process of the transmission loss includes:

[0010] Establish a transcendental equation for calculating the wave number inside the waveguide with the muffler installed on the sidewall by using the impedance boundary;

[0011] According to the transcendental equation, construct expressions for the sound pressures at the front end, inside, and rear end of the waveguide with the muffler installed on the sidewall;

[0012] Construct a system of equations for the coefficients of each order of the sound pressure based on the impedance boundary conditions followed inside the waveguide with the muffler installed on the sidewall, and the continuity of the sound pressure and the normal particle velocity at each position along the long side direction of the muffler;

[0013] Solve the system of equations for the coefficients of each order of the sound pressure under the given incident sound pressure, so as to obtain the calculation result of the transmission loss.

[0014] Furthermore, the m-th order wave vector k in the y direction inside the muffler is obtained from the transcendental equation ym , and then according to , the m-th order wave vector in the z direction inside the muffler is obtained as k zm , where k is the air wave number, and construct expressions for the sound pressures at the front end, inside, and rear end of the waveguide with the muffler installed on the sidewall.

[0015] Furthermore, the expressions for the sound pressures at the front end, inside, and rear end of the waveguide with the muffler installed on the sidewall are respectively:

[0016]

[0017]

[0018]

[0019] In the formula, p sample is the sound pressure inside the muffler, p front is the sound pressure at the front end of the muffler, p back is the sound pressure at the rear end of the muffler, k = ω / c0, ω is the circular frequency, c0 is the sound speed in air, y is the long side direction of the muffler, z is the height direction of the muffler, L sample is the length of the muffler, k zm is the m-th order wave vector in the z direction inside the muffler, k ym is the m-th order wave vector in the y direction inside the muffler, k zn is the n-th order wave vector in the z direction at the front and rear ends of the muffler, k yn is the n-th order wave vector in the y direction at the front and rear ends of the muffler, k zn = nπ / W tube , n = 0, 1, 2,..., W tubeis the width of the pipe cross-section, n is the order, A m is the m-th order sound pressure coefficient propagating in the positive y-direction inside the muffler, B m is the m-th order sound pressure coefficient propagating in the negative y-direction inside the muffler, C n is the n-th order sound pressure coefficient propagating in the positive y-direction at the front end of the muffler, D n is the n-th order sound pressure coefficient propagating in the negative y-direction at the front end of the muffler, E n is the n-th order sound pressure coefficient propagating in the positive y-direction at the rear end of the muffler, F n is the n-th order sound pressure coefficient propagating in the negative y-direction at the rear end of the muffler, j is the imaginary unit, i.e., j 2 = -1.

[0020] Furthermore, the calculated cut-off order is greater than the propagable order, and the cut-off order is the sum of m and n.

[0021] Furthermore, the expression of the system of equations for each order coefficient of the sound pressure is:

[0022] MR C = C in

[0023] In the formula, the coefficient matrix M can be determined by given the structural parameters of the waveguide and the muffler, and the muffler is installed on the waveguide to collect the performance parameters of the muffler; the sound pressure parameter C can be obtained by given the incident sound pressure in ; solving the system of equations to obtain the vector R composed of the amplitude coefficients of the sound pressure at the front end, inside and rear end of the waveguide with the metamaterial muffler installed on the side wall C .

[0024] Furthermore, the calculation result of the sound energy flux is obtained from each amplitude coefficient, so as to calculate the incident energy flux and the transmitted energy flux, and then calculate the transmission loss. The calculation expression of the transmission loss is:

[0025]

[0026] In the formula, t is the transmission coefficient and TL is the transmission loss.

[0027] The present invention also provides a metamaterial muffler constructed by using the construction method of a muffler as described above, including a perforated plate, a metal foam, a rigid boundary shell and a coupled resonator array connected in sequence. The resonator array includes a plurality of coupled resonator units connected in sequence, and each coupled resonator unit includes a plurality of neck-embedded Helmholtz resonators coupled in parallel. The structural parameters of the perforated plate, the metal foam, the rigid boundary shell and the coupled resonator array are obtained by using the construction method of a muffler as described in any one of claims 1-7.

[0028] Furthermore, the rigid boundary housing is provided with a plurality of unit housings, which correspond to the resonator units one by one. The number of the metal foams is multiple, and each metal foam is respectively installed in the corresponding unit housing.

[0029] Furthermore, the metal foam is a nickel metal foam prepared by an electroplating sintering process.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] (1) According to the target frequency band and target transmission loss of the metamaterial muffler, the present invention adjusts the structural parameters of the metamaterial muffler, calculates the corresponding transmission loss, and continuously optimizes to meet the target requirements, so as to achieve different design goals. The proposed transmission loss calculation process is based on impedance boundary conditions, sound pressure, and normal particle velocity continuity to establish and solve equations, and the calculation process is efficient and accurate.

[0032] (2) The present invention proposes a metamaterial muffler that supports dense mode density and tunable internal loss, and provides a new way for broadband designable timbre. The dense mode density causes strong global coupling and is finely modulated under the guidance of the theoretical model, effectively suppressing resonance dispersion and providing suitable frequency selection wave operation ability for timbre tuning.

[0033] (3) This embodiment proposes three design schemes for the metamaterial muffler. The first metamaterial muffler achieves an average transmission loss of 28.4 dB in the range of 500 - 3200 Hz and has a deep sub-wavelength thickness of 53.5 mm. The second metamaterial muffler further realizes controllable sound attenuation in the range of 500 - 3200 Hz with a thickness of 43.4 mm. Finally, the third designed metamaterial muffler has a thickness of 44.4 mm, and by playing the functions of alleviating, highlighting, and silencing in the fundamental frequency and harmonic frequency ranges, it achieves the strict goal of designable timbre in the range of 500 - 3200 Hz under the controllable sound attenuation efficiency.

[0034] (4) The present invention provides new insights for global coupling modulation to suppress resonance dispersion, and proposes a general and effective method for manipulating mode density distribution, coupling effect, and intrinsic loss through acoustic metamaterial mufflers. These results will contribute to the development of multifunctional and efficient mufflers for aeroengines and ventilation systems, and open up a way for the research of designable timbre. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic structural diagram of a metamaterial muffler provided in an embodiment of the present invention;

[0036] Figure 2In it, (a) is a schematic diagram showing the change of the transmission loss (TL) characteristic with the mode density and frequency provided in the embodiment of the present invention, ρ mode ranges from 2.4 to 8.8; γ n and Γ n are respectively set to 0.03ω n and 0.06ω n ; The three dashed lines respectively represent typical sparse, medium and dense mode densities, and the corresponding TL curves are shown in (b);

[0037] Figure 3 is a schematic diagram of experimental data of a metamaterial muffler with high-efficiency acoustic attenuation provided in the embodiment of the present invention. In the figure, (a) is the theoretical (line) and experimental (circle) TL of the metamaterial muffler at 500 - 3200 Hz. (b) The theoretical (line) and experimental (circle) transmission coefficient, absorption coefficient and reflection coefficient of the metamaterial muffler under grazing incidence of sound waves. The inset is a picture of the experimental sample. (c) The theoretical (line) and experimental (circle) acoustic resistance and acoustic reactance of the metamaterial muffler. (d) The sound pressure amplitude |p| distribution of the metamaterial muffler at each frequency point marked with a pentagram in (a);

[0038] Figure 4 is a schematic diagram of experimental data of a metamaterial muffler with controllable efficiency acoustic attenuation provided in the embodiment of the present invention. In the figure, (a) The dark lines and circles respectively represent the theoretical and experimental TL of the metamaterial muffler; The light solid line represents the theoretical TL of the muffler without metal foam; The thicknesses of the coupled resonator array, metal foam and perforated plate are 27.4 mm, 15 mm and 1 mm respectively (inset). (b) The theoretical (line) and experimental (circle) acoustic resistance and acoustic reactance of the metamaterial muffler. The dark solid line and the light solid line respectively represent the theoretical acoustic resistance and acoustic reactance of the metamaterial muffler without metal foam;

[0039] Figure 5 is a schematic diagram of experimental data of realizing a designed timbre with a multifunctional metamaterial muffler provided in the embodiment of the present invention. In the figure, (a) The theoretical (line) and experimental (circle) TL of the metamaterial muffler. The TL targets (dashed lines) of the metamaterial muffler in the ranges of 500 - 930 Hz, 930 - 1720 Hz and 1720 - 3200 hz are 18 dB, 3 dB and 35 dB respectively, and the corresponding transmission coefficients are 0.016, 0.5 and 0.003 (the black dashed lines in (b)). The inset is the experimental sample. (b) The theoretical (line) and experimental (circle) transmission coefficients of the metamaterial muffler under grazing incidence of sound waves. The colored dashed lines represent the transmission coefficients of NEHR. The dotted line represents the transmission coefficient of the single perforated plate and its back cavity with a 14 - mm - thick metal foam. (c) The theoretical (line) and experimental (circle) acoustic resistance and acoustic reactance of the metamaterial muffler. (d) The sound pressure amplitude |p| distribution of the metamaterial muffler at each frequency point marked with a pentagram in (a);

[0040] Figure 6 Schematic diagram of a global factor as a function of modal density and frequency provided in an embodiment of the present invention, where the frequency band is selected between 200 - 800 Hz; ρ mode varies from 2.4 to 8.8; γ n and Γ n are 0.03ω n and 0.06ω n ;

[0041] Figure 7 Schematic diagram of TL curves provided in an embodiment of the present invention when the intrinsic loss Γ n is equal to γ n , 3γ n and 5γ n respectively, where the frequency band is selected between 200 - 800 Hz, and the radiation loss γ n = 0.03ω n ;

[0042] In the figure, 1, perforated plate; 2, metal foam; 3, rigid boundary housing; 4, coupled resonator array; 401, embedded square cross-section neck; 402, rectangular cross-section cavity. Detailed implementation manners

[0043] 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.

[0044] 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 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.

[0045] It should be noted that: like 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.

[0046] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the inventive product is customarily placed during use. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention.

[0047] It should be noted that the terms "first" and "second" are only used for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present application, "a plurality" means two or more, unless otherwise specifically defined.

[0048] In addition, terms such as "horizontal" and "vertical" do not mean that the components are required to be absolutely horizontal or hanging vertically, but may be slightly inclined. For example, "horizontal" only means that its direction is more horizontal relative to "vertical", and does not mean that the structure must be completely horizontal, but may be slightly inclined.

[0049] Embodiment 1

[0050] This embodiment provides a method for constructing a muffler, including the following steps:

[0051] Obtain the target frequency band and target transmission loss of the muffler, construct the calculation process of the transmission loss of the impedance wall surface of the muffler, and by optimizing the structural parameters of the muffler, make the muffler reach the target transmission loss under the target frequency band.

[0052] The calculation process of the transmission loss includes:

[0053] Use the impedance boundary to establish a transcendental equation for calculating the wave number inside the waveguide with the muffler installed on the side wall;

[0054] According to the transcendental equation, construct the expressions of the sound pressure at the front end, inside and rear end of the waveguide with the muffler installed on the side wall;

[0055] According to the impedance boundary conditions followed inside the waveguide with the muffler installed on the side wall, and the continuity of the sound pressure and normal particle velocity at each position along the long side direction of the muffler, construct a system of equations for the coefficients of each order of the sound pressure;

[0056] When a given incident sound pressure is provided, solve the system of equations for the coefficients of each order of the sound pressure, so as to obtain the calculation result of the transmission loss.

[0057] The m-th order wave vector k in the y direction inside the muffler is obtained from the transcendental equation ym , and then according to , the m-th order wave vector in the z direction inside the muffler is obtained as k zm , where k is the air wave number, and expressions for the sound pressure at the front end, inside, and rear end of the waveguide with the muffler installed on the sidewall are constructed.

[0058] This solution proposes to calculate the corresponding transmission loss by adjusting the structural parameters of the muffler according to the target frequency band and target transmission loss of the muffler, and continuously optimize to meet the target requirements, so as to achieve different design goals. The proposed transmission loss calculation process is based on impedance boundary conditions and the continuity of sound pressure and normal particle velocity to establish and solve equations, and the calculation process is efficient and accurate.

[0059] Preferably, to provide a muffler that provides a feasible way for a powerful and well-controlled global coupling to provide a designable timbre, and optimize the design in cooperation with the above-mentioned muffler construction method, this embodiment also provides a metamaterial muffler, as Figure 1 shown, including a perforated plate 1, a metal foam 2, a rigid boundary housing 3, and a coupled resonator array 4 connected in sequence. The coupled resonator array 4 includes a plurality of coupled resonator units connected in sequence, and each coupled resonator unit includes a plurality of neck-embedded Helmholtz resonators (NEHR) coupled in parallel.

[0060] The rigid boundary housing 3 is provided with a plurality of unit housings, which correspond to the resonator units one by one. The number of metal foams 2 is a plurality, and each metal foam 2 is installed in a corresponding unit housing. During the test, the rigid boundary housing 3 can be made of a 3D printing material - resin, which is convenient for production and manufacturing. In actual use, the materials such as the coupled resonance cavity array and the rigid boundary housing 3 in the structure are replaced with metal materials.

[0061] Each resonator unit has the same structure. Each neck-embedded Helmholtz resonator in each resonator unit can have different shapes or sizes, but the overall thickness of the resonator unit is the same. The neck-embedded Helmholtz resonator includes a rectangular cross-section cavity 402 and an embedded square cross-section neck 401.

[0062] In this embodiment, the bottom of the metamaterial muffler is composed of 8 identical units in the y direction. Each unit of the metamaterial muffler is composed of 16 NEHRs and has the same thickness. The details of the NEHR are as Figure 1 shown in the right subfigure, which is composed of a rectangular cross-section cavity 402 and an embedded square cross-section neck 401.

[0063] Above the NEHR, the metal foam is located between the resonator array and the perforated plate, and can provide efficient modulation of the intrinsic loss of the metamaterial muffler. The flow resistance of the metal foam is 1500 Pa·s / m 2 , which is separated by each unit housing. The top of the metamaterial muffler is a perforated plate, which can effectively protect the internal materials and prevent the generation of secondary noise on the surface of the metamaterial muffler. The nickel metal foam prepared by the electroplating sintering process has excellent acoustic and mechanical properties such as effective sound dissipation, good strength and stiffness. At the same time, compared with traditional sponges, metal foams can also be used in extreme environments such as low temperature and high temperature. The other parts of the metamaterial muffler are manufactured by using laser stereolithography and photosensitive resin, such as ultraviolet curable resin, through additive manufacturing technology (3D printing), and the manufacturing accuracy is 0.1 mm.

[0064] In this embodiment, by constructing the theoretical model of the above-mentioned metamaterial muffler, the performance of this metamaterial muffler is analyzed, and the design of three different effects of the metamaterial muffler is realized, which are specifically as follows.

[0065] I. Theoretical Model

[0066] The designable timbre fundamentally requires excellent resonance modulation ability. To achieve this goal, a theoretical model is established using the coupled mode theory. This theoretical model comprehensively describes the interaction between resonance modes from the basic properties of radiation and thermoviscous dissipation of each resonance mode, thereby revealing the potential physical picture of global coupling and providing a modulation method of global coupling for timbre modulation.

[0067] Assume that a resonance system supports N coherently coupled modes, and the evolution of the amplitude of the nth mode with time can be expressed as

[0068]

[0069] where represents the amplitude of the nth mode, j is the unit imaginary number, ω n is the resonance frequency of the nth mode, γ n and Γ n are the corresponding radiation loss and intrinsic loss respectively, is the incident wave. The last term on the right side of formula (1) represents the interaction between the nth mode and other modes, that is, the global coupling effect. The time evolution of the amplitudes of these N modes is and there is a Hamiltonian matrix

[0070]

[0071] and the inhomogeneous term

[0072] Eliminating the time factor term ejωt , and by solving the Hamiltonian equations, we can obtain

[0073]

[0074] In addition, the reflection coefficient r of the coupled system can be written as

[0075]

[0076] The blank between the mode amplitude and the surface acoustic impedance can be eliminated by formula (4) because the acoustic impedance can be expressed as Z = (1 + r) / (1 - r), thus leading to

[0077]

[0078] In this paper, the sound attenuation characteristics of the metamaterial muffler are evaluated by the transmission loss (TL). TL is calculated from the surface acoustic impedance Z using the mode matching method (see calculation method A for details). Therefore, through the connection of formula (5), how resonance modulation affects the sound attenuation characteristics can be revealed. Specifically, TL can be expressed as a function of ω, ω n , γ n , Γ n , that is, TL = f(ω, ω n , γ n , Γ n ), (n = 1, 2,..., N). In addition, the mode density can be defined as

[0079]

[0080] where ω n,max and ω n,min are the maximum and minimum values among the N mode resonance frequencies, First, the influence of the mode density on the global coupling was studied in method B, and the results show that a dense mode density can excite stronger global coupling. Therefore, although the dispersive nature of resonance is inevitable, when the global coupling is strong enough, it may greatly suppress the dispersion of individual resonances and control the overall acoustic characteristics of the entire coupled system. Based on this property, this embodiment further studies the influence of the mode density on TL.

[0081] Without loss of generality, this embodiment first considers a coherent coupled mode system with 16 modes, where the eighth mode ω8 = 2π×400 Hz, and the ratio of two adjacent modes is σ, that is Figure 2 (a) depicts the evolution of the TL curve with the change of the mode density, where the frequency band is selected in 200 - 800 Hz, γ n is 0.03ω n , Γ n is 2γ n, and σ varies from 1.1 to 1.4, i.e., ρ mode ranges from 2.4 to 8.8, where and N = 16. As the mode density increases, TL gradually increases, and the fluctuations of the curve significantly decrease. In this embodiment, three typical values are selected to represent the sparse mode density (ρ mode = 2.5), the medium mode density (ρ mode = 3.9), and the medium mode density (ρ mode = 7.4), corresponding to Figure 2 (a) the three dashed lines. It can be intuitively seen that when the system has a sparse mode density, due to the scattering characteristics of resonance, TL is low and there are large oscillations Figure 2 (b)]. However, when the system has a denser mode density, higher and smoother TL curves can be achieved. These results indicate that the dense mode density can provide new opportunities to control the resonant dispersion of sound in a wide band. It should be noted that adding porous materials such as metal foams can also increase the working frequency bandwidth of each resonance, thereby increasing the mode density and suppressing the resonant dispersion (see the calculation method C for details). In the following, the global coupling of the metamaterial muffler will be modulated to achieve the design goals of efficient broadband sound attenuation, efficient control of sound attenuation, and a designable timbre

[0082] Calculation method A: The mode matching method analyzes the transmission loss of the impedance wall

[0083] If there is no metamaterial muffler, there are four rigid walls, which is a square waveguide. The frequencies discussed here are below the cut-off frequency (00 order). In other words, there are only plane waves within the waveguide. The sound pressure is (omitting e jωt ) with the dispersion relation k = ω / c0. Where ω is the circular frequency and c0 is the speed of sound in air. However, when the muffler under test is installed on one side wall of the sample part of the pipeline, the impedance on one side wall will generate higher-order z-direction (perpendicular to the impedance wall) wave modes near the entire sample part and the joints between the rigid wall and the impedance wall. Now the sound pressures in the sample part and before and after the sample can be expressed as follows:

[0084]

[0085]

[0086]

[0087] The length of the sample part L sample = 400mm. And there is a dispersion relation The z-direction beam k zn = nπ / W tube, n = 0, 1, 2,.... For the sample part, the impedance boundary condition p / v z = Z (there are specific methods in the prior art for calculating impedance). On the surface of the impedance wall The impedance boundary condition derives the relationship between k zm and k ym as a transcendental equation, and only their numerical solutions can be obtained. Now, truncate the order of the wave mode at n Max = M, m Max = M respectively, in order to perform numerical calculations with satisfactory accuracy. According to the continuity of the sound pressure and the normal particle velocity at y = 0

[0088] p front = p sample , (A4)

[0089] v z,front = v z,sample . (A5)

[0090] Multiply both sides of equation (A4) by each function of the series {cos(k zm′ z)}, and then integrate it over its square cross-section or only over its width in the z direction. Finally, exchange the integral and summation operators, and obtain

[0091]

[0092] For simplicity, define

[0093]

[0094]

[0095] Therefore, a system of equations is obtained

[0096] P 1L (C + D) = P 1R (A + B). (A9)

[0097] Similarly, multiply both sides of equation (A5) successively by {cos(k zn′ z)|k zn′ = n'π / W tube}, and exchange the operators in the same way to obtain

[0098] V 1L (C - D) = V 1R (A - B), (A10)

[0099] where

[0100]

[0101] Similarly, according to y = Lsample Local continuity condition

[0102]

[0103] Obtain two other sets of equations

[0104]

[0105] where

[0106]

[0107]

[0108] After arranging (A9), (A10) and (A13), we can get

[0109]

[0110] There is no reflection at the end of the waveguide or it is known that F = RE (R can be 0). (A16) can be written in the form of a set of equations

[0111]

[0112] In the experiment, due to the well-designed end muffler, the end reflection R is very close to zero. Even in the absence of a muffler, it can be obtained through two different end conditions.

[0113] (A17) can be briefly recorded as

[0114] MR C = C in

[0115] where

[0116]

[0117] Given the incident sound pressure C, the amplitudes of each order (A, B, D, E) can be calculated by solving equation (A17).

[0118] The sound energy flux is defined as The skill in calculating it is to sum up the energy fluxes of all orders. So far, the incident, reflected and transmitted energy fluxes (I in , I re , I tr ) and the reflection, transmission, absorption coefficients and transmission loss (r, t, α, TL) can be obtained

[0119]

[0120] Calculation method B: Influence of mode degree on global coupling

[0121] A global factor (Fno) is introduced to evaluate the impact of global coupling on the entire system, defined as

[0122]

[0123] where

[0124]

[0125] is the modal amplitude when the last term of formula (1) is missing, that is, at this time it is local resonance. Substituting formulas (3) and (B2) into (B1), we can get

[0126]

[0127] According to the above formula, the cloud diagram of the global factor as a function of modal density and frequency is as Figure 6 shown. As Figure 6 shown, with the increase of modal density, the global coupling of the corresponding system is enhanced. These results indicate that relatively denser modal density can support a stronger impact of global coupling on each mode. In addition, by comparing Figure 2 it can be clearly found that the transmission loss is positively correlated with the global factor. This supports achieving perfect acoustic energy dissipation by constructing a system with denser modes to support stronger global coupling. On the contrary, almost lossless transmission of acoustic energy can be achieved by constructing a very sparse modal density. In this way, the dissipation and propagation of sound waves can be effectively regulated, thereby realizing arbitrarily designed timbres.

[0128] Calculation method C: Modulation of the transmission loss curve by intrinsic loss

[0129] This calculation method demonstrates the modulation of the transmission loss by the intrinsic loss of a system with medium modal density to illustrate the necessity of introducing metal foam in the configuration of this embodiment. As Figure 7 shown, in this embodiment, a frequency band between 200 - 800 Hz is selected, γ n = 0.03ω n and medium modal density (ρ mode= 3.9). By adjusting the magnitude of the inherent loss, the variation of the transmission loss curve was observed. It can be clearly seen that when the inherent loss increases, the oscillation of the transmission loss curve decreases significantly, and the trough gradually disappears. However, in order to achieve flexible control of the inherent loss, a better method is to introduce a resistive material such as metal foam in the configuration of this embodiment. This proves that using metal foam to provide additional intrinsic loss to pursue a flat transmission loss curve is a very effective method. At the same time, since the requirement for the number of modes is reduced, fewer coupling resonators can be used to achieve broadband sound attenuation, thereby reducing the structural complexity. In addition, metal foam has excellent mechanical properties and good stability in high and low temperature environments, which is difficult to achieve for traditional sponges. This also makes the metamaterial muffler more robust in various extreme environments.

[0130] II. Three different designs

[0131] This embodiment provides three metamaterial mufflers with different effects to verify the theoretical model and demonstrate the design concept of this structure. The design goals of the three metamaterial mufflers are becoming more and more stringent. Finally, through effective modulation of the frequency-selective distribution of the modal density, a designable timbre is achieved.

[0132] 2.1. Achieving broadband sound attenuation with a metamaterial muffler

[0133] Under the guidance of the above design concept, a broadband sound attenuation metamaterial muffler was designed with the highest TL in the target band as the goal. The target frequency band was set at 500 - 3200 Hz, and the thickness was limited within the deep sub-wavelength range. Then, the structural parameters were optimized to achieve the goal of making the average TL as large as possible, where the expected minimum TL was set to be greater than 10 dB. As Figure 3 (a) shows, the metamaterial muffler exhibits excellent attenuation performance in the range of 500 - 3200 Hz, with an average TL of 28.4 dB. The maximum value is 85.7 dB at 1920 Hz, and the minimum value is 10.0 dB at 500 Hz. The experimental results are consistent with the theoretical results in most trends, but there are also some deviations, which may be due to the fact that the high TL is too susceptible to background noise and the sealing conditions of the experimental device may not be perfect. In addition, Figure 3 (b) illustrates that most of the energy of the grazing incident sound wave is absorbed by the metamaterial muffler, and only a small part is reflected.

[0134] The total thickness of the metamaterial muffler is 53.5 mm, which is only 1 / 13 of the wavelength at 500 Hz. The thicknesses of the perforated plate, metal foam, and coupled resonator array are 1 mm, 26 mm, and 26.5 mm respectively, where the perforation rate of the perforated plate is 28%, and the perforation aperture is 1 mm. The acoustic resistance and acoustic reactance of the metamaterial muffler are respectively around 1 and 0 Figure 3(c). Only slight oscillations can be observed, indicating that the metamaterial muffler significantly suppresses resonance dispersion. In addition, to more intuitively demonstrate the sound attenuation ability of the metamaterial muffler, the distribution of the sound pressure amplitude |p| in the pipe at the four frequency points selected by the asterisks in Figure 3 (a) is shown in Figure 3 (d). The theoretical results clearly show that sound energy is strongly dissipated during the propagation along the metamaterial muffler.

[0135] 2.2. Efficiency-Controllable Sound Attenuation

[0136] In this section, a more stringent design goal is set, requiring efficiency-controllable sound attenuation. This goal is achieved by a metamaterial muffler with a NEHR having a medium mode density but the global coupling strength of the entire system is enhanced by metal foam. In other words, in this design, metal foam plays a crucial role in controlling the sound attenuation efficiency of the broadband.

[0137] As shown in Figure 4 (a), when there is no metal foam, the TL curve shows strong fluctuations (light solid line), which is due to the NEHR having a medium mode density (there are 16 NEHR modes in this broadband frequency range, ρ mode = 3.4). As mentioned above, this medium mode density cannot support strong global coupling to suppress resonance dispersion. Here, metal foam is used to ideally enhance the intrinsic loss (Γ n ), mainly to modulate the global coupling to suppress oscillations (the demonstration can also be seen in Computational Method C). After introducing metal foam, the fluctuations of the TL curve become smoother, and the sound attenuation efficiency in the range of 500 - 3200 Hz is controlled to be around 12 dB to a considerable extent ( Figure 4 (a) dark solid line). In addition, as shown in Figure 4 (b), the impedance distribution of this efficiency-controllable metamaterial muffler is different from that of the metamaterial muffler with the highest possible TL shown in Figure 3 (c). The obvious weakening of the curve fluctuations after introducing metal foam also confirms the reduction of resonance dispersion.

[0138] 2.3. Designable Timbre

[0139] The above two designs verify the concept of this embodiment that uses dense mode density to induce strong global coupling and thereby suppress resonant dispersion. In this subsection, the design goal is to manipulate sound, including attenuating, highlighting, and silencing different broadband overtones, i.e., the designable timbre. To this end, the design goal of the third metamaterial muffler is to achieve transmission losses of 18 dB, 3 dB, and 35 dB at 500 - 930 Hz (fundamental frequency), 930 - 1720 Hz (first overtone), and 1720 - 3200 Hz (second overtone), respectively. This goal requires not only strong and tunable global coupling in different overtone ranges.

[0140] Since the proposed metamaterial muffler has excellent mode density modulation ability, NEHR is designed to support dense mode density and sparse mode density in the fundamental frequency range and the first overtone range, respectively. For the second overtone range, with a very high sound attenuation target, the strong synergistic effect of NEHR, MPP, and metal foam provides an effective solution to this challenging topic. As Figure 5 (a) shows, the theoretical and experimental results of TL significantly achieve the goal at different overtones. It should be noted that the goal of the second overtone (transmission loss of 35 dB) actually requires a transmission coefficient as low as about 0.003. Therefore, a relatively slight change in the transmission coefficient will cause a significant fluctuation in the corresponding TL curve, as Figure 5 (a) shows. Nevertheless, the goal of the "silencing" function can still be well achieved in the second overtone. The total thickness of the multifunctional metamaterial muffler is 44.4 mm, consisting of a coupled resonator array of 29.4 mm, metal foam of 14 mm, and a perforated plate with a perforation rate of 8% of 1 mm.

[0141] The transmission curves of the components of the metamaterial muffler intuitively reflect the above design concept of this embodiment. As Figure 5 (b) shows, it can be observed that NEHR has a very dense mode density (ρ mode = 8.2) in the fundamental frequency band (500 - 930 Hz), and here the perforated plate and metal foam have a negligible impact. The first overtone band (930 - 1720 Hz) is set to have a slightly modulated and relatively prominent function for this overtone. Therefore, a mode distribution void (ρ mode = 0) is designed to lift the main limitation of sound propagation in this band. In the second overtone band (1720 - 3200 Hz), the metal foam and the perforated plate play a dominant role in strong dissipation. At the same time, several NEHR resonance modes promote a more drastic change in the transmission characteristics near the initial boundary in this frequency band, enhancing the energy dissipation.

[0142] In addition, the impedance profile of the metasurface muffler also verifies the extraordinary manipulation of resonances, where the dense mode density flattens the impedance curve, while the voids in the mode distribution give rise to large antiresonance-induced fluctuations( Figure 5 (c)). Figure 5 (d) Intuitively illustrates the effect of the tunable timbre by showing the sound pressure distributions at four selected frequencies. When sound waves pass through the metasurface muffler, the timbre of the transmitted wave is tuned as expected, achieving the desired effects of attenuation (600 Hz), prominence (1200 Hz), and silence (2400 Hz) at the corresponding overtones. Overall, guided by the above design concept, the designed multifunctional metasurface muffler effectively regulates the global coupling and finally realizes the tunable timbre.

[0143] III. CONCLUSION

[0144] In summary, this embodiment theoretically and experimentally studies the physical mechanism of global coupling in timbre modulation and proposes a multifunctional acoustic metasurface muffler that can support dense mode density and highly tunable intrinsic losses to verify the above theoretical results and achieve the ultimate goal of tunable timbre. Using the coupled-mode theory, the fundamental radiation and dissipation characteristics of resonances are essentially linked to the acoustic impedance and transmission loss. This theory reveals the influence of the mode density distribution on the global coupling strength and provides a platform for the efficient design of broadband frequency-selective sound attenuation performance. Three design schemes are proposed, comprehensively demonstrating the advantages of the fine modulation of global coupling in the design of multifunctional metasurface mufflers. The first metasurface muffler achieves an average transmission loss of 28.4 dB in the range of 500 - 3200 Hz and has a deep subwavelength thickness of 53.5 mm. The second metasurface muffler further realizes the controllable sound attenuation in the range of 500 - 3200 Hz with a thickness of 43.4 mm. Finally, the third designed metasurface muffler has a thickness of 44.4 mm and achieves the strict goal of tunable timbre in the range of 500 - 3200 Hz with controllable sound attenuation efficiency by playing the functions of attenuation, prominence, and silence in the fundamental and overtone frequency ranges.

[0145] This scheme provides new insights into suppressing resonance dispersion by global coupling modulation and proposes a general and effective method to manipulate the mode density distribution, coupling effect, and intrinsic losses through acoustic metasurface mufflers. These results will contribute to the development of multifunctional and efficient mufflers for aeroengines and ventilation systems and open up a way for the research of tunable timbre.

[0146] 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 efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the prior art shall fall within the protection scope determined by the claims.

Claims

1. A method for constructing a muffler, characterized in that, It includes the following steps: Obtain the target frequency band and target transmission loss of the muffler, construct the calculation process of the transmission loss of the impedance wall surface of the muffler, and make the muffler reach the target transmission loss under the target frequency band by optimizing the structural parameters of the muffler; The structural parameters of the muffler include the thicknesses of the perforated plate, metal foam, and coupled resonator array, as well as the perforation rate and perforation aperture of the perforated plate; The calculation process of the transmission loss includes: Use the impedance boundary to establish a transcendental equation for calculating the wave number inside the waveguide with the muffler installed on the sidewall; According to the transcendental equation, construct the expressions of the sound pressure at the front end, inside, and rear end of the waveguide with the muffler installed on the sidewall; According to the impedance boundary conditions followed inside the waveguide with the muffler installed on the sidewall, and the continuity of the sound pressure and normal particle velocity at each position along the long side direction of the muffler, construct a system of equations for the coefficients of each order of the sound pressure; Under the given incident sound pressure, solve the system of equations for the coefficients of each order of the sound pressure, so as to obtain the calculation result of the transmission loss; The m-th order wave vector k in the y direction inside the muffler is obtained from the transcendental equation ym , and then according to , the m-th order wave vector in the z direction inside the muffler is obtained as k zm , where k is the air wave number, and expressions for the sound pressure at the front end, inside, and rear end of the waveguide with the muffler installed on the sidewall are constructed; The expressions of the sound pressure at the front end, inside, and rear end of the waveguide with the muffler installed on the sidewall are respectively: where p sample is the sound pressure inside the muffler, p front is the sound pressure at the front end of the muffler, p back is the sound pressure at the rear end of the muffler, k = ω / c0, ω is the circular frequency, c0 is the speed of sound in air, y is the long side direction of the muffler, z is the height direction of the muffler, L sample is the length of the muffler, k zm is the m-th order wave vector in the z direction inside the muffler, k ym is the m-th order wave vector in the y direction inside the muffler, k zn is the n-th order wave vector in the z direction at the front and rear ends of the muffler, k yn is the n-th order wave vector in the y direction at the front and rear ends of the muffler, k zn = nπ / W tube , n = 0, 1, 2,..., W tube is the width of the pipe cross-section, n is the order number, A m is the m-th order sound pressure coefficient propagating in the positive y direction inside the muffler, B m is the m-th order sound pressure coefficient propagating in the negative y direction inside the muffler, C n is the n-th order sound pressure coefficient propagating in the positive y direction at the front end of the muffler, D n is the n-th order sound pressure coefficient propagating in the negative y direction at the front end of the muffler, E n is the n-th order sound pressure coefficient propagating in the positive y direction at the rear end of the muffler, F n is the n-th order sound pressure coefficient propagating in the negative y direction at the rear end of the muffler, j is the imaginary unit, i.e., j 2 = -1; The expression of the constructed system of equations for the coefficients of each order of the sound pressure is: MR C = C in In the formula, the coefficient matrix M can be determined by given structural parameters of the waveguide and the muffler. The muffler is installed on the waveguide to collect the performance parameters of the muffler; the sound pressure parameter C can be obtained by given incident sound pressure in ; solving the system of equations to obtain the vector R composed of the amplitude coefficients of the sound pressure at the front end, inside and rear end of the waveguide with the muffler installed on the side wall C ; Obtain the calculation result of the sound energy flow from the coefficients of each amplitude, thereby calculate the incident energy flow and the transmitted energy flow, and further calculate the transmission loss. The calculation expression of the transmission loss is: In the formula, t is the transmission coefficient, and TL is the transmission loss.

2. The construction method of a muffler according to claim 1, characterized in that, The calculated cut-off order is greater than the propagable order, and the cut-off order is the sum of m and n.

3. A meta - muffler constructed by using a construction method of a muffler as described in any one of claims 1 - 2, characterized in that, It includes a perforated plate, a metal foam, a rigid boundary housing, and a coupled resonator array connected in sequence. The resonator array includes a plurality of coupled resonator units connected in sequence. Each coupled resonator unit includes a plurality of neck-embedded Helmholtz resonators coupled in parallel. The structural parameters of the perforated plate, metal foam, rigid boundary housing, and coupled resonator array are obtained by using a construction method of a muffler as described in any one of claims 1-2.

4. The metasurface muffler according to claim 3, wherein The rigid boundary housing is provided with a plurality of unit housings, which correspond to the resonator units one by one. The number of metal foams is a plurality, and each metal foam is installed in a corresponding unit housing.

5. The metasurface muffler according to claim 3, wherein, The metal foam is a nickel metal foam prepared by an electroplating sintering process.

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