Method for widening sound absorption frequency band of micro-perforated plate sound absorber array under excitation of free field oblique incidence plane wave

Abstract

According to the method for widening the sound absorption frequency band of the micro-perforated plate sound absorber array under the excitation of the free field oblique incidence plane wave, the coupling sound absorption rule between units in the array is analyzed and fully utilized according to the excitation condition of the free field oblique incidence plane wave; unit structure parameters in the array are subjected to optimization design, the optimal sound absorption performance is achieved, the effective sound absorption frequency band of the MPPA array is greatly widened, and broadband efficient sound absorption of the MPPA array under free field oblique incidence excitation is achieved. The invested cost is low, the sound absorption frequency band broadening effect of the MPPA array is obvious, and therefore the MPPA array has important engineering application value.

Description

Technical Field

[0001] This invention relates to the field of noise control technology, and specifically to a method for broadening the sound absorption frequency band of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation. Background Technology

[0002] With rapid industrial development, noise pollution has become an increasingly prominent problem. Excessive noise not only interferes with residents' work efficiency and sleep quality, but can also cause hearing damage, nervous system weakness, and even affect the normal operation of equipment and induce safety accidents. In noise control engineering, using porous sound-absorbing materials to control the sound propagation path is a widely used method.

[0003] Micro-perforated panels (MPPs) are widely used for noise control in aircraft, ships, ground transportation cabins, and industrial plants due to their cleanliness, environmental adaptability, and excellent mid-to-high frequency sound absorption performance. Micro-perforated panel absorbers (MPPAs) typically consist of a micro-perforated panel and a cavity behind it, utilizing cavity resonance to enhance sound energy dissipation, making them a commonly used sound absorption structure. However, for MPPAs with fixed structural parameters, their effective sound absorption bandwidth (sound absorption coefficient greater than 0.5) is usually limited to a specific frequency range centered on the Helmholtz resonance frequency. To expand the sound absorption bandwidth, existing research has proposed various structural improvement schemes, such as using irregular cavities to enhance the coupling between cavity acoustic modes and micropore vibrations, or combining multiple MPPA units with different cavity depths into an array, achieving broadband sound absorption by superimposing the effective sound absorption bandwidth of each unit.

[0004] Current research on MPPA arrays is largely based on one-dimensional plane wave excitation conditions within a pipe. Under these conditions, a so-called "parallel absorption mechanism" exists, meaning that the coupling between units makes the overall sound absorption performance of the array superior to the sum of the individual unit performances. However, in more practical acoustic environments such as free fields or diffuse fields, the sound absorption characteristics of MPPA arrays and the coupling laws between units remain unclear. Especially under the condition of oblique incidence of plane waves in a free field, the "parallel absorption mechanism" no longer applies, leading to a decrease in array sound absorption performance. In this case, due to local resonance in each unit, its surface impedance exhibits a non-uniform distribution, causing the reflected waves from the unit surface to no longer be plane waves and to scatter towards the incident side and other unit surfaces; simultaneously, the radiated sound field generated by the vibration of each unit also affects other units. This coupling effect between units caused by scattering and radiation has a significant impact on the overall sound absorption performance of the array, and the structural parameters of the units further modulate this coupling effect, thus affecting the effective sound absorption bandwidth of the array.

[0005] Furthermore, in complex chambers or diffuse sound fields, acoustic excitation can be considered as the superposition of multiple obliquely incident plane waves. Therefore, for free-field oblique incidence conditions, in-depth analysis and utilization of the coupling law between units to optimize the structural parameters of the units in the array, in order to improve its sound absorption performance and extend the effective sound absorption frequency band, has significant theoretical and engineering value. Summary of the Invention

[0006] To address the issues of decreased sound absorption performance and narrow bandwidth in existing micro-perforated plate (MPPA) absorber arrays under free-field or diffused-field environments due to the disappearance of the "parallel sound absorption mechanism" and complex coupling between units, this invention proposes a method for broadening the sound absorption bandwidth of MPPA arrays under free-field oblique-incident plane wave excitation, and the resulting optimal array. This method, tailored to the free-field oblique-incident plane wave excitation condition, analyzes and fully utilizes the coupling sound absorption laws between units in the array, optimizes the unit structural parameters to achieve optimal sound absorption performance, and significantly broadens the effective sound absorption bandwidth of the MPPA array, realizing broadband and efficient sound absorption under free-field oblique-incident excitation. This invention requires relatively low cost and achieves a significant widening effect on the MPPA array's sound absorption bandwidth, thus possessing significant engineering application value.

[0007] The technical solution of this invention is as follows:

[0008] In a first aspect, the present invention provides a method for broadening the sound absorption frequency band of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation. The micro-perforated plate sound absorber array is composed of multiple micro-perforated plate sound absorber units with different cavity depths arranged in parallel, the cavity walls of each unit are rigid, and the front ends of all units are aligned. The method includes the following steps:

[0009] Step 1: Establish the acoustic model of the MPPA array. Based on the array's geometric parameters, material parameters, and primary excitation parameters, and using the modal superposition method, establish the sound field model within each unit cavity to obtain the sound pressure expression for any point within each unit cavity.

[0010] Step 2: Establish the total sound field model on the incident side of the MPPA array micro-perforated plate surface. A position-dependent sound pressure reflection coefficient is introduced to characterize the non-uniform reflected sound field. Using the boundary condition of continuous surface normal vibration velocity, combined with the superposition relationship between incident and reflected waves, the normal particle velocity distribution on the surface of each unit is determined. Simultaneously, considering the self-radiated sound field generated by the vibration of each unit surface and the mutual radiation sound field between units, the total sound pressure expression on the incident side of the micro-perforated plate surface of each unit is finally obtained.

[0011] Step 3: Solve for the sound pressure reflection coefficient of the array surface. Combine the acoustic impedance boundary conditions of the micro-perforated plate surface (i.e., the relationship between the normal particle velocity and the sound pressure difference on both sides of the micro-hole) with the total sound field expression obtained in Step 2 to establish a system of equations about the sound pressure reflection coefficient of discrete points on each unit surface. By discretizing the array surface, the system of equations is transformed into matrix equations and solved to obtain the sound pressure reflection coefficient of the array surface under free field oblique incidence conditions.

[0012] Step 4: Optimize array parameters based on the sound absorption law of inter-unit coupling. Based on the sound pressure reflection coefficient of the array surface obtained in Step 3, calculate the overall sound absorption coefficient and sound absorption frequency band of the array. With the optimization goal of maximizing the widening of the effective sound absorption frequency band and improving the average sound absorption coefficient, optimize the structural parameters of the units in the array.

[0013] Secondly, the present invention provides a micro-perforated plate sound absorber array optimized by the above method. The array consists of at least two micro-perforated plate sound absorber units with different cavity depths arranged in parallel. The cavity walls of all units are rigid, the front faces are aligned, and the array does not contain any control source, making it a completely passive sound absorption structure.

[0014] Beneficial effects

[0015] Compared with the prior art, the present invention has the following significant advantages:

[0016] This invention provides a systematic MPPA array design method for free-field oblique incidence acoustic environments. By accurately modeling the scattering and radiation coupling between units and transforming this coupling effect into a design element to improve performance, it overcomes the performance degradation problem of traditional MPPA arrays in this environment, achieving broadband and efficient sound absorption in the frequency band below 1000Hz.

[0017] This invention improves performance by optimizing unit structural parameters without introducing a complex active control system or additional sound-absorbing materials. It inherits the advantages of micro-perforated panels, such as being clean, pollution-free, and highly adaptable to the environment, while significantly reducing the cost of achieving broadband sound absorption. It has extremely high engineering application value.

[0018] The MPPA array designed according to the principles of this invention can maintain excellent broadband sound absorption performance in a range of oblique incident plane wave incident angles from 0° to 80°, making it suitable for complex practical acoustic environments.

[0019] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0020] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0021] Figure 1 This is a schematic diagram of the MPPA array model of the present invention, wherein (a) is a side view and (b) is a front view;

[0022] Figure 2 This is a schematic diagram of an obliquely incident plane wave on the micro-perforated surface of the MPPA array in this invention;

[0023] Figure 3 The incident angles of the obliquely incident plane wave are respectively and The sound absorption coefficient curve of the MPPA array;

[0024] Figure 4 The incident angles of the obliquely incident plane wave are respectively and The sound absorption coefficient curve of the MPPA array. Detailed Implementation

[0025] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0026] like Figure 1 As shown, the micro-perforated plate sound absorber array used in this embodiment is composed of two micro-perforated plate sound absorbers (MPPA unit 1 and MPPA unit 2) with different cavity depths arranged in parallel. The cavity walls of the micro-perforated plate sound absorbers are rigid, and the front ends of the two micro-perforated plate sound absorbers are flush. No control source needs to be introduced into the micro-perforated plate sound absorber.

[0027] Based on the aforementioned MPPA array, this example proposes a method to broaden the sound absorption bandwidth of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation. The specific implementation steps are as follows:

[0028] Step 1: Establish the acoustic model of the MPPA array. Based on the array's geometric parameters, material parameters, and primary excitation parameters, and using the modal superposition method, establish the sound field model within each unit cavity to obtain the sound pressure expression for any point within each unit cavity.

[0029] like Figure 1 As shown, the length and width of MPPA cell 1 (hereinafter referred to as "cell 1") and MPPA cell 2 (hereinafter referred to as "cell 2'") in the MPPA array are respectively... , , and The cavity depths are respectively , Both units use the same MPP parameters. For the thickness of the microperforated plate, For pore diameter, Porosity.

[0030] According to the principle of modal superposition, the sound pressure within the cavities of unit 1 and unit 2 can be expressed in the form of modal expansion:

[0031] (1)

[0032] (2)

[0033] in, , and They are respectively Axial direction, Axial direction and The upper limit of the number of modes in the axial direction. and The first one in the cavity of unit 1 The amplitude of the first sound mode and the first Similarly, the order mode function. and The first one in the cavity of unit 2 The amplitude of the first sound mode and the first Rank mode function. and They are represented as follows:

[0034] (3)

[0035] (4)

[0036] Based on the boundary conditions for the normal vibration velocity of the surface of the micro-perforated plate within the cavity of each unit in the MPPA array:

[0037] (5)

[0038] (6)

[0039] in, and Let be the normal vibration velocities on the surfaces of element 1 and element 2, respectively. Based on Green's second law and the orthogonality of the acoustic modal functions of the cavity, the amplitudes of the acoustic modes in the cavities of element 1 and element 2 can be obtained. and The expressions are as follows:

[0040] (7)

[0041] (8)

[0042] in, air density, The speed of sound in air. The excitation frequency of the primary incident sound wave is... and The first and second cavities in unit 1 and unit 2 are respectively The resonant frequency of the phase mode, and For the corresponding modal damping ratio, and This corresponds to the generalized modal mass.

[0043]

[0044]

[0045] Substituting equations (3) and (7) into equation (1), and equations (4) and (8) into equation (2), we can obtain the sound pressure expressions at any point in the cavity of unit 1 and unit 2.

[0046] Step 2: Establish the total sound field model on the incident side of the MPPA array micro-perforated plate surface. A position-dependent sound pressure reflection coefficient is introduced to characterize the non-uniform reflected sound field. Using the boundary condition of continuous surface normal vibration velocity, combined with the superposition relationship between incident and reflected waves, the normal particle velocity distribution on the surface of each unit is determined. Simultaneously, considering the self-radiated sound field generated by the vibration of each unit surface and the mutual radiation sound field between units, the total sound pressure expression on the incident side of the micro-perforated plate surface of each unit is finally obtained.

[0047] The incident sound field on the micro-perforated surface of each unit of the MPPA array mainly consists of three parts: incident sound pressure. Reflected sound pressure Radiated sound pressure generated by the normal vibration velocity of the micro-perforated surface The radiated sound pressure can be further divided into self-radiated sound pressure and mutual-radiated sound pressure. For a free-field obliquely incident sound wave, its incident sound pressure can be expressed as:

[0048]

[0049] The sound pressure level is the amplitude. For wave number, , and The coordinates on the MPPA surface, Let be the angle of incidence of the incident sound wave. The azimuth angle of the incident sound wave.

[0050] Introducing sound pressure reflection coefficient and To characterize the reflected sound field on the incident side, the reflected sound pressures on the surfaces of element 1 and element 2 can be expressed as follows:

[0051] (9)

[0052] (10)

[0053] Omitted simple harmonic time factor Without considering the normal radiation velocity, based on the boundary condition of continuous normal velocity on the MPPA array surface, the normal particle velocities on the surfaces of element 1 and element 2 can be determined by the superposition of incident and reflected waves in the incident sound field, and can be expressed as:

[0054] (11)

[0055] (12)

[0056] According to the Ruili integral formula, the mutual radiation sound pressure from the surface of unit 2 to the surface of unit 1 is... and the self-radiated sound pressure of the surface of Unit 1 It can be represented as:

[0057] (13)

[0058] (14)

[0059] in, Represents any point on the surface of element 2 to the surface of element 1. Distance between points Represents any point on the surface of element 1 to the surface of element 1 Distance between points.

[0060] Furthermore, based on the Rayleigh integral, the surface of the MPPA array can be discretized into tiny surface elements. Each discrete surface element can then be approximated as a monopole sound source vibration (the size of the discrete surface element should be smaller than the maximum wavelength). The radiated sound pressure on each discrete surface element is composed of the self-radiated sound pressure of the element and the mutual radiated sound pressure of other elements. Therefore, for the self-radiated sound pressure of the surface vibration velocity of element 1 radiating to its own surface... This can be further expressed as:

[0061] (15)

[0062] (16)

[0063] Similarly, for the mutual radiation sound pressure from the surface of unit 2 to the surface of unit 1... It can also be further expressed as:

[0064] (17)

[0065] Consistent with the above, the sound pressure radiated from the surface vibration velocity of element 1 to the surface of element 2, and the sound pressure radiated from the surface vibration velocity of element 2 to its own surface, can also be expressed as:

[0066] (18)

[0067] (19)

[0068] in, Represents any point on the surface of element 1 to the surface of element 2. Distance between points Represents any point on the surface of element 2 to the surface of element 2. Distance between points.

[0069] The sound pressure on the incident side of the surface of element 1 and the surface of element 2 in the MPPA array can be expressed as:

[0070] (20)

[0071] (twenty one)

[0072] Step 3: Solve for the sound pressure reflection coefficient of the array surface. Combine the acoustic impedance boundary conditions of the micro-perforated plate surface (i.e., the relationship between the normal particle velocity and the sound pressure difference on both sides of the micro-hole) with the total sound field expression obtained in Step 2 to establish a system of equations about the sound pressure reflection coefficient of discrete points on each unit surface. By discretizing the array surface, the system of equations is transformed into matrix equations and solved to obtain the sound pressure reflection coefficient of the array surface under free field oblique incidence conditions.

[0073] make and Let be the normal radiation velocity caused by the vibration of normal particles on the surfaces of element 1 and element 2. Since the normal radiation velocity at any point on the MPPA array surface is not zero only at its own position, for ease of analysis, it can be approximated as...

[0074]

[0075]

[0076] The total normal vibration velocity of the surface of element 1 and element 2 is approximately:

[0077] (twenty two)

[0078] (twenty three)

[0079] The surface normal velocity of each element in the MPPA array can be considered as the spatial average velocity of each hole element adjacent to the micro-perforated plate hole:

[0080] (twenty four)

[0081] (25)

[0082] in, and These are the sound pressure levels near the surface of the micro-perforated plate inside the cavities of Unit 1 and Unit 2, respectively. Let the impedance of the microperforated plate surface be the constant when the microperforation constant satisfies the following condition. hour, z 0 = 32 or t h d h 2 ( 1 + k h 2 32 + 2 32 k h d h t h ) + j r 0 oh t h [ 1 + ( 9 + k h 2 2 ) − 1 / 2 + 8 3 π d h t h ] ,in, is the viscosity coefficient of air. The porosity constant is... , The thickness of the viscous boundary layer. .

[0083] Combining equations (22) and (24), and equations (23) and (25) respectively, we obtain the following relationship between the normal vibration velocities of the surfaces of element 1 and element 2:

[0084] (26)

[0085] (27)

[0086] For unit 1, substituting equations (7) and (20) into equation (26), unit 1 is discretized into... A square discrete unit; for unit 2, substitute equations (8) and (21) into equation (27) to discretize unit 2 into There are three square discrete elements. Element 1 and Element 2 can then be expressed by the following relationships:

[0087] (28)

[0088] (29)

[0089] in, r 1 = [ r 1 ( x 1 , y 1 ) , r 1 ( x 2 , y 2 ) , ⋯ r 1 ( x M 1 , y M 1 ) ] H , r 2 = [ r 2 ( x 1 , y 1 ) , r 2 ( x 2 , y 2 ) , ⋯ r 2 ( x M 2 , y M 2 ) ] H These are the sound pressure reflection coefficients at discrete points on the surfaces of element 1 and element 2, respectively. For element 1, the coefficient matrix... , and Zhongde Di The elements are as follows:

[0090] (30)

[0091] (31)

[0092] (32)

[0093] Similarly, for element 2, the coefficient matrix , and Zhongde Di The elements are as follows:

[0094] (33)

[0095] (34)

[0096] (35)

[0097] By combining equations (28) and (29), we can obtain:

[0098] [ A B D E ] [ r 1 r 2 ] = [ C F ] (36)

[0099] The sound pressure reflection coefficient can then be calculated:

[0100] [ r 1 r 2 ] = [ A B D E ] − 1 [ C F ] (37)

[0101] in, [ A B D E ] -1 = [ x 11 x 12 x 21 x 22 ] ,but ; .

[0102] Step 4: Optimize array parameters based on the sound absorption law of inter-unit coupling. Based on the sound pressure reflection coefficient of the array surface obtained in Step 3, calculate the overall sound absorption coefficient and sound absorption frequency band of the array. With the optimization goal of maximizing the widening of the effective sound absorption frequency band and improving the average sound absorption coefficient, optimize the structural parameters of the units in the array.

[0103] According to equations (20) to (23), the acoustic power absorbed by the MPPA array can be obtained as follows:

[0104] ∏ abs = ( ∫ 0 a 1 ∫ 0 b 1 Re [ p 1 ⋅ n 1 H ] dxdy + ∫ 0 a 2 ∫ 0 b 2 Re [ p 2 ⋅ n 2 H ] dxdy ) / 2 (38)

[0105] Among them, superscript Represents conjugate transpose. Re[ · ] This represents taking the real part of the matrix; , , and These represent the sound pressure of the discrete surface element of element 1, the sound pressure of the discrete surface element of element 2, the normal vibration velocity of the discrete surface element of element 1, and the normal vibration velocity of the discrete surface element of element 2, respectively.

[0106] p 1 = [ p 1 ( x 1 , y 1 ), p 1 ( x 2 , y 2 ), ⋯ p 1 ( x M 1 , y M 1 ) ]

[0107] p 2 = [ p 2 ( x 1 , y 1 ), p 2 ( x 2 , y 2 ), ⋯ p 2 ( x M 2 , y M 2 ) ]

[0108] n 1 = [ n 1 ( x 1 , y 1 ), n 1 ( x 2 , y 2 ), ⋯ n 1 ( x M 1 , y M 1 ) ]

[0109] n 2 = [ n 2 ( x 1 , y 1 ), n 2 ( x 2 , y 2 ), ⋯ n 2 ( x M 2 , y M 2 ) ] .

[0110] At this point, the sound absorption coefficient of the MPPA array can be expressed as:

[0111] (39)

[0112] For incident sound power, .

[0113] Under free-field oblique incidence plane wave excitation, with the optimization objective of maximizing the widening of the effective sound absorption bandwidth and improving the average sound absorption coefficient, the structural parameters of the units in the array are optimized. The specific optimization process can be achieved using traditional optimization algorithms, which will not be elaborated here. Taking an array composed of two units as an example, the parameter optimization should follow the following conditions:

[0114] (1) The cavity depths of the two MPPA units in the array should be different. The cavity depth of each unit should be determined according to the target frequency band to ensure that the array obtains broadband sound absorption performance.

[0115] (2) The size design of the two MPPA units in the array should ensure that the area ratio of the unit with larger cavity depth to the unit with smaller cavity depth is 2:1. Since the unit with larger cavity depth has a lower Helmholtz resonant frequency and is in a Helmholtz resonant sound absorption state, the larger normal particle velocity on the surface of the unit makes its radiated sound field to the other units stronger. The strong coupling between the units promotes the sound absorption of the other units, resulting in good sound absorption performance within the effective sound absorption frequency band of the unit. For the unit with smaller cavity depth, its Helmholtz resonant sound absorption frequency is higher. Within the effective sound absorption frequency band of the unit, the higher-order sound modes of the cavity will be excited. The Helmholtz resonant sound absorption effect is weak, and the sound absorption performance is low. Moreover, due to the complex normal particle velocity distribution on the surface of the unit, the radiated sound field from the surface of the unit to the other units is weak, resulting in weak coupling between the units. Considering both of the above factors, to maximize broadband and efficient sound absorption performance, the area occupied by the unit with a deeper cavity should be larger than that of the unit with a shallower cavity, and the area ratio between the two should be 2:1. This condition applies to obliquely incident plane waves with an incident angle of... Change to All of these conditions are met;

[0116] (3) To achieve good broadband sound absorption performance in the frequency band below 1000Hz, the longest side length of the unit in the array should not exceed 0.3m (to ensure that the sound absorption coefficient of the effective sound absorption band of the array is greater than 0.6). The smaller the array size, the smaller the amplitude of the higher-order acoustic modes excited by the unit cavity under oblique incident plane wave excitation, the stronger the Helmholtz resonance sound absorption effect of the unit, and the stronger the mutual radiation between units, thus the stronger the coupling sound absorption performance of the array. As the array size increases, the resonant frequency of the higher-order acoustic modes decreases, the Helmholtz sound absorption effect of the shallow cavity unit weakens, the mutual radiation between units weakens, and the sound absorption performance of the array will decrease, as shown in the attached figure. Figure 3 and attached Figure 4 As shown.

[0117] The final geometric parameters, material parameters, and primary excitation parameters of the MPPA array are shown in Tables 1 to 3.

[0118] Table 1. Geometric parameters of MPPA array

[0119]

[0120] Table 2 MPPA Array Material Parameters

[0121]

[0122] Table 3 Primary Excitation Parameters

[0123]

[0124] The MPPA array parameters above are the optimal parameters selected based on the array design principles of this invention. The calculated sound absorption coefficient curve of the array is shown in the attached figure. Figure 3 and attached Figure 4 As shown in the figure, the results show that when plane waves are incident at different angles, the effective sound absorption bandwidth of the MPPA array can cover most of the frequency band below 1000Hz and the average sound absorption coefficient is greater than 0.6. This is the optimal sound absorption performance that the array can achieve in a free field environment. Therefore, the MPPA array designed according to this invention can significantly broaden its effective sound absorption bandwidth and achieve high-efficiency sound absorption over a wide bandwidth.

[0125] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for broadening the sound absorption bandwidth of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation, characterized in that: The micro-perforated plate sound absorber array is composed of multiple micro-perforated plate sound absorber units with different cavity depths arranged in parallel. The cavity walls of each unit are rigid, and the front faces of all units are aligned. The method includes the following steps: Step 1: Based on the array's geometric parameters, material parameters, and primary excitation parameters, establish the sound field model within each unit cavity to obtain the sound pressure expression for any point within each unit cavity; Step 2: Based on the sound pressure reflection coefficient, the reflected sound field of the array surface is characterized. Using the boundary condition of continuous surface normal vibration velocity, combined with the superposition relationship between incident and reflected waves, the normal particle vibration velocity distribution of each unit surface is determined. Combined with the self-radiated sound field generated by the vibration velocity of each unit surface and the mutual radiation sound field between units, the total sound pressure expression of the incident side of the micro-perforated plate surface of each unit of the array is constructed. Step 3: Combine the acoustic impedance boundary conditions of the micro-perforated plate surface with the total sound field expression obtained in Step 2 to establish a set of equations about the sound pressure reflection coefficients of discrete points on the surface of each unit of the array. By discretizing the array surface, the set of equations is transformed into matrix equations and solved to obtain the sound pressure reflection coefficients of the array surface under free-field oblique incident plane wave excitation. Step 4: Based on the sound pressure reflection coefficient of the array surface obtained in Step 3, calculate the overall sound absorption coefficient and sound absorption frequency band of the array. With the optimization goal of maximizing the widening of the effective sound absorption frequency band and improving the average sound absorption coefficient, optimize the structural parameters of the units in the array.

2. The method for broadening the sound absorption bandwidth of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation as described in claim 1, characterized in that: In step 1, the process of establishing the sound field model within each unit cavity and obtaining the sound pressure expression at any point within each unit cavity is as follows: Let the length and width of MPPA cell 1 and MPPA cell 2 in the MPPA array be respectively... , , and The cavity depths are respectively , Both units use the same MPP parameters. For the thickness of the microperforated plate, For pore diameter, Porosity; According to the principle of modal superposition, the sound pressure within the cavities of unit 1 and unit 2 can be expressed in the form of modal expansion: （1） （2） in, , and They are respectively Axial direction, Axial direction and The upper limit of the number of modes in the axial direction. and The first one in the cavity of unit 1 The amplitude of the first sound mode and the first Rank mode function, and The first one in the cavity of unit 2 The amplitude of the first sound mode and the first Rank mode function; and They are represented as follows: （3） （4） Based on the boundary conditions for the normal vibration velocity of the surface of the micro-perforated plate within the cavity of each unit in the MPPA array: （5） （6） in, and Let the normal vibration velocities of the surfaces of element 1 and element 2 be respectively. Based on Green's second law and the orthogonality of the cavity acoustic modal functions, the acoustic modal amplitudes in the cavities of element 1 and element 2 are obtained. and The expressions are as follows: （7） （8） in, air density, The speed of sound in air. The excitation frequency of the primary incident sound wave is... and The first and second cavities in unit 1 and unit 2 are respectively The resonant frequency of the phase mode, and For the corresponding modal damping ratio, and This corresponds to the generalized modal mass; Substituting equations (3) and (7) into equation (1), and equations (4) and (8) into equation (2), we obtain the sound pressure expressions at any point in the cavity of unit 1 and unit 2.

3. The method for broadening the sound absorption frequency band of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation as described in claim 2, characterized in that: In step 1, the generalized modal mass is 。 4. The method for broadening the sound absorption frequency band of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation as described in claim 2, characterized in that: In step 2, the incident sound field on the surface of each unit's micro-perforated plate consists of three parts: incident sound pressure... Reflected sound pressure Radiated sound pressure generated by the normal vibration velocity of the micro-perforated surface Radiated sound pressure can be further divided into self-radiated sound pressure and mutual-radiated sound pressure. For a sound wave incident obliquely in a free field, its incident sound pressure is expressed as: The sound pressure level is the amplitude. For wave number, , and The coordinates on the MPPA surface, Let be the angle of incidence of the incident sound wave. The azimuth angle of the incident sound wave; Introducing sound pressure reflection coefficient and To characterize the reflected sound field on the incident side, the reflected sound pressures on the surfaces of element 1 and element 2 can be expressed as follows: Mutual radiation sound pressure from the surface of unit 2 to the surface of unit 1 and the self-radiated sound pressure of the surface of Unit 1 Represented as: in, Represents any point on the surface of element 2 to the surface of element 1. Distance between points Represents any point on the surface of element 1 to the surface of element 1 Distance between points; The sound pressure radiated from the surface vibration velocity of element 1 to the surface of element 2 and the sound pressure radiated from the surface vibration velocity of element 2 to its own surface are expressed as follows: in, Represents any point on the surface of element 1 to the surface of element 2. Distance between points Represents any point on the surface of element 2 to the surface of element 2. Distance between points; The sound pressure levels on the incident sides of the surfaces of element 1 and element 2 in the MPPA array are expressed as follows: 。 5. The method for broadening the sound absorption bandwidth of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation according to claim 4, characterized in that: In step 2, the normal particle velocities on the surfaces of element 1 and element 2 are determined by the superposition of the incident and reflected waves in the incident sound field: 。 6. The method for broadening the sound absorption bandwidth of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation as described in claim 5, characterized in that: In step 3, the process of obtaining the acoustic pressure reflection coefficient of the array surface under free-field oblique incidence conditions is as follows: make and Let be the normal radiation velocity caused by the vibration of normal particles on the surfaces of element 1 and element 2, and take . Then the total normal vibration velocity of the surface of element 1 and element 2 is: （22） （23） The surface normal velocity of each element in the MPPA array is the spatial average velocity of each hole element adjacent to the micro-perforated plate hole: （24） （25） in, and These are the sound pressure levels near the surface of the micro-perforated plate inside the cavities of Unit 1 and Unit 2, respectively. The impedance of the microperforated plate surface; Combining equations (22) and (24), and equations (23) and (25) respectively, we obtain the following relationship between the normal vibration velocities of the surfaces of element 1 and element 2: （26） （27） For unit 1, substituting equations (7) and (20) into equation (26), unit 1 is discretized into... A square discrete unit; for unit 2, substitute equations (8) and (21) into equation (27) to discretize unit 2 into There are three square discrete elements; at this time, element 1 and element 2 respectively obtain the following relationships: （28） （29） in, , These are the sound pressure reflection coefficients at discrete points on the surfaces of element 1 and element 2, respectively. For element 1, the coefficient matrix is... , and Zhongde Di The elements are as follows: （30） （31） （32） Similarly, for element 2, the coefficient matrix , and Zhongde Di The elements are as follows: （33） （34） （35） Combining equations (28) and (29), we get: （36） The sound pressure reflection coefficient can then be calculated: （37） in, ,but ; .

7. The method for broadening the sound absorption bandwidth of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation as described in claim 6, characterized in that: In step 3, when the microperforation constant satisfies hour, ,in, is the viscosity coefficient of air. The porosity constant is... , The thickness of the viscous boundary layer. .

8. The method for broadening the sound absorption bandwidth of a micro-perforated plate sound absorber array under free-field oblique incidence plane wave excitation as described in claim 6, characterized in that: In step 4, the acoustic power absorbed by the MPPA array is: （38） Among them, superscript Represents conjugate transpose. This represents taking the real part of the matrix; , , and These represent the sound pressure of the discrete surface element of element 1, the sound pressure of the discrete surface element of element 2, the normal vibration velocity of the discrete surface element of element 1, and the normal vibration velocity of the discrete surface element of element 2, respectively. At this point, the sound absorption coefficient of the MPPA array can be expressed as: （39） For incident sound power, .

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