Active control method for improving low-frequency sound absorption performance of micro-perforated plate sound absorber array under free field vertical incidence excitation

Abstract

The invention provides an active control method for improving the low-frequency sound absorption performance of a micro-perforated panel sound absorber array under free field vertical incidence excitation, and the method comprises the steps: introducing an active control technology into a certain unit in a common large-size MPPA array in engineering, placing a loudspeaker on the rear wall of a cavity of a certain MPPA unit in the array to form an active MPPA unit, and enabling the active MPPA unit to be used as a sound absorber array of a micro-perforated panel. The low-frequency sound absorption performance of a single MPPA unit is improved through active control, meanwhile, by means of the mutual coupling influence of surface normal vibration velocity radiation sound fields between the units in the array, the effect that a certain active MPPA unit in the array works and absorbs sound energy incident to the whole array is achieved, and therefore the maximum improvement of the low-frequency sound absorption performance of the array is achieved at the minimum cost. The invested active control measure is low in cost, and the overall low-frequency sound absorption performance of the array is remarkable, so that the array has important engineering practical value.

Description

Technical Field

[0001] The present invention relates to the technical field of noise control, and in particular to an active control method for improving the low-frequency sound absorption performance of a micro-perforated plate sound absorber array under free-field vertical incident excitation. Background Art

[0002] Noise pollution is one of the four major pollutions in modern times, which can cause serious harm to people's physical and mental health. At present, there are three main methods for controlling noise: one is to control the noise source, the second is to take control measures on the noise propagation path, and the third is to isolate the receiver to reduce the harm of noise to the receiver. Among them, controlling noise on the propagation path is a common and effective measure, including sound absorption, sound insulation, noise elimination, damping and vibration reduction, etc., and using sound-absorbing materials to reduce noise is the most basic technical method in noise control.

[0003] Compared with traditional porous sound-absorbing materials, micro-perforated panels (MPP) have simple structures, are environmentally friendly, and are made of a variety of materials. They can also be used in harsh environments such as high temperature and high humidity. They are known as the new generation of the most promising sound-absorbing structures to replace porous sound-absorbing materials. Micro-perforated panel absorbers (MPPAs) are typical applications of micro-perforated sound-absorbing materials in engineering. MPPAs are composed of micro-perforated panels and their rear cavities. Micro-perforated panels have large acoustic resistance and small acoustic reactance, so they have good sound absorption performance. The resonance sound absorption effect generated by the rear cavity significantly increases the relative velocity between the air medium in the micropores and the panel structure, making MPPA have superior sound absorption performance in a wider frequency band.

[0004] However, for MPPA with characteristic parameters, its effective sound absorption band (band with sound absorption coefficient greater than 0.5) can only be limited to a specific range. In order to effectively broaden the sound absorption band of MPPA, the prior art has proposed many improvement measures. Among them, the most commonly used method is to arrange multiple MPPAs with different cavity depths in parallel to form a large-area MPPA array (C.Wang, L.Huang.On the acoustic properties of parallel arrangement of multiple micro-perforated panel absorbers with different cavity depths.Journal of theAcoustical Society of America,2011,Vol 130,208-218.). It superimposes the effective sound absorption bands of different MPPAs on each other, significantly broadens the total mid-high frequency sound absorption band of the array, but the improvement of low-frequency sound absorption performance is very limited. Increasing the cavity depth of MPPA can effectively absorb sound and tend to the low frequency band, but the bulky MPPA is not convenient for engineering applications. The applicant's previous research disclosed an active micro-perforated plate sound absorber and a method for improving its low-frequency sound absorption performance (CN112951188B). For small-sized MPPA, a point force-controlled elastic plate was introduced. The MPPA cavity acoustic impedance was offset by an active control method to achieve the improvement of low-frequency sound absorption performance, solving the problem of weak low-frequency sound absorption performance of small-sized MPPA units. In actual application, in order to meet the needs of large-area sound absorption, multiple small-sized MPPA units need to be arranged in parallel to form an array. At this time, due to the influence of mutual coupling between different MPPA units, the overall sound absorption performance of the MPPA array is not a simple superposition of unit performance, but a total sound absorption performance under the coupling between units. Therefore, research on improving the low-frequency sound absorption performance of the MPPA array is of great significance to the practical engineering application of this technology. Summary of the invention

[0005] In order to solve the shortcomings of the existing MPPA array in terms of weak low-frequency sound absorption performance under free-field vertical incident excitation, the present invention proposes an active control method for improving the low-frequency sound absorption performance of a micro-perforated plate absorber array under free-field vertical incident excitation. For large-size MPPA arrays commonly used in engineering, active control technology is introduced in a unit in the MPPA array, that is, a loudspeaker is placed on the rear wall of a cavity of a MPPA unit in the array to form an active MPPA unit, and the low-frequency sound absorption performance of a single MPPA unit is improved through active control. At the same time, with the help of the mutual coupling effect of the surface normal vibration velocity radiation sound field between the units in the array, an active MPPA unit in the array is realized to absorb the sound energy incident to the entire array, thereby maximizing the improvement of the array's low-frequency sound absorption performance at the lowest cost. The active control measures invested in the present invention are low-cost, and the overall low-frequency sound absorption performance of the array is significant, so it has important engineering practical value.

[0006] The technical solution of the present invention is:

[0007] A micro-perforated plate sound absorber array is formed by arranging a plurality of micro-perforated plate sound absorbers with different cavity depths in parallel. The micro-perforated plate sound absorber cavities are rigid wall cavities. The front ends of the micro-perforated plates of all the micro-perforated plate sound absorbers are flush, and a loudspeaker is installed on the rear wall of the micro-perforated plate sound absorber with a deeper cavity depth as a secondary control source.

[0008] The active control method for improving the low-frequency sound absorption performance of the micro-perforated plate absorber array under free-field vertical incident excitation comprises the following steps:

[0009] Step 1: Modeling and calculating the sound field in the cavity of each micro-perforated plate sound absorber in the micro-perforated plate sound absorber array according to the geometric model parameters, material parameters, and primary excitation and secondary excitation parameters of the micro-perforated plate sound absorber array, and deriving the sound pressure expression at any position in the cavity of each micro-perforated plate sound absorber;

[0010] Step 2: The reflected sound field of the array surface is characterized by using the sound pressure reflection coefficient that varies with the position of the array surface, the normal vibration velocity of the array surface is solved according to the boundary condition that the normal particle velocity of the micro-perforated plate sound absorber array surface is continuous, and the radiated sound field of the array surface is solved according to the Rayleigh integral formula to obtain the total sound pressure of the incident side sound field;

[0011] Step 3: According to the relationship between the normal vibration velocity of the micro-perforated plate surface in each micro-perforated plate sound absorber in the micro-perforated plate sound absorber array and the sound pressure on both sides of the micro-perforated plate, an equation group satisfied by the sound pressure reflection coefficient of the array surface is established, and at the same time, the surface of the micro-perforated plate sound absorber is discretized to establish a matrix equation satisfied by the sound pressure reflection coefficient at discrete points on the array surface, and the matrix equation is solved to obtain the sound pressure reflection coefficient value at the discrete point;

[0012] Step 4: Taking the sound power absorbed by the micro-perforated plate sound absorber array as the control target, calculate the theoretical optimal control source intensity when the absorbed sound power is maximized, and then obtain the sound absorption coefficient of the micro-perforated plate sound absorber array after control; set the control source intensity to zero, calculate the absorbed sound power, and then obtain the sound absorption coefficient of the micro-perforated plate sound absorber array before control.

[0013] Beneficial Effects

[0014] 1. The present invention forms an active MPPA unit by placing a loudspeaker on the rear wall of a MPPA unit cavity in the array, and by means of the mutual coupling of the surface normal velocity radiation sound field between the units in the array, an active MPPA unit in the array is operated to absorb the sound energy incident to the entire array. This method significantly improves the overall low-frequency sound absorption performance of the array by investing very little active control measures.

[0015] 2. The active MPPA array involved in the present invention significantly improves the low-frequency sound absorption performance of the micro-perforated plate absorber array under free-field vertical incidence conditions. At the same time, combined with the good mid- and high-frequency sound absorption performance of the micro-perforated plate absorber array, it achieves high-efficiency sound absorption in the full frequency band, which has important engineering use value.

[0016] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0018] Figure 1 Schematic diagram of an active MPPA array model of the present invention; wherein a is a side view and b is a front view;

[0019] Figure 2 is a secondary source layout diagram in the present invention;

[0020] Figure 3 This is a comparison chart of the sound absorption coefficient before and after active MPPA array control when the sizes of the two units are both 0.3m×0.2m.

[0021] Figure 4 This is a comparison chart of the sound absorption coefficient before and after active MPPA array control when the size of unit 1 is 0.3×0.15m and the size of unit 2 is 0.3×0.25m. DETAILED DESCRIPTION

[0022] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0023] like Figure 1 As shown, the active 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 micro-perforated plate sound absorber cavity is a rigid wall cavity, the front ends of the micro-perforated plates of the two micro-perforated plate sound absorbers are flush, and a loudspeaker is installed on the rear wall of the unit with a deeper cavity depth as a secondary control source.

[0024] Based on the above active micro-perforated plate sound absorber array, this embodiment proposes an active control method for improving the low-frequency sound absorption performance of the micro-perforated plate sound absorber array under free field vertical incident excitation. The specific implementation steps are as follows:

[0025] Step 1: Determine the sound field expression in the cavity of each MPPA unit of the active micro-perforated plate absorber array.

[0026] In this step, the sound field in the cavity of each MPPA unit in the active micro-perforated plate absorber array is modeled and calculated according to the geometric model parameters, material parameters, and primary and secondary excitation parameters of the active micro-perforated plate absorber array, and the sound pressure expression at any position in the cavity of each MPPA unit is derived.

[0027] The geometric model parameters of the active micro-perforated plate sound absorber array include the length a1 and a2 of the MPPA unit 1 and the MPPA unit 2 in the micro-perforated plate sound absorber array. In this embodiment, a1=a2, the width b1, b2 and the cavity depth D1, D2, and the thickness t of the micro-perforated plate. h , pore diameter d h , and porosity σ.

[0028] The material parameters of the active micro-perforated plate sound absorber array include the density ρ0 and the sound velocity c0 of air, and the viscosity coefficient η of air.

[0029] The primary excitation and secondary excitation parameters of the above-mentioned active micro-perforated plate absorber array include: the primary excitation is a vertically incident plane wave, the amplitude of the plane wave is p0; the position of the secondary control source is (xs, ys, zs), and the intensity of the secondary control source is q(ω).

[0030] The modeling and calculation process of the sound field in the cavity of each MPPA unit is as follows:

[0031] Under the excitation of the primary vertical incident plane wave in the free field and the secondary control source, according to the wave equation satisfied by the sound pressure in the cavity of each MPPA unit in the active micro-perforated plate absorber array and the boundary condition of the normal vibration velocity continuity satisfied on the surface of the micro-perforated plate, the expression of the sound pressure in the cavity of each MPPA unit in the active micro-perforated plate absorber array is derived by using the modal superposition principle. The specific process is:

[0032] The loudspeaker is equivalent to a point sound source. Under the excitation of the primary free-field vertical incident plane wave and the secondary control source, the sound pressure P of the cavity sound field in MPPA unit 1 and MPPA unit 2 in the active micro-perforated plate absorber array is 1,c (x,y,z,t),P 2,c (x, y, z, t) satisfy the following wave equations respectively:

[0033]

[0034] Where Q(x s ,y s ,z s ,t) is the point source intensity, Q(x s ,y s ,z s ,t)=q(ω)e jωt δ(xx s ,yy s ,zz s ), where δ(·) is the Dirac function.

[0035] According to the modal superposition principle, the sound pressure in the cavity of MPPA unit 1 and MPPA unit 2 can be expressed in the form of modal expansion:

[0036]

[0037] Where P 1,uwm (ω) and P 2,uwm (ω) are the modal amplitudes of the (u, w, m)th order acoustic modes in the cavities of MPPA unit 1 and MPPA unit 2, respectively. and are the acoustic mode functions of the two cavities, respectively, expressed as:

[0038]

[0039] U, W, M are the upper limits of the number of modes;

[0040] According to the boundary conditions that the surface of the micro-perforated plate in each MPPA unit cavity meets the normal vibration velocity continuity Where v1(x, y) and v2(x, y) are the normal vibration velocities of the micro-perforated plate surface in MPPA unit 1 and MPPA unit 2, respectively. Using Green's second formula and the orthogonality of the acoustic mode functions of the MPPA unit cavities, the acoustic mode amplitude P can be obtained: 1,uwm (ω) and P 2,uwm The expressions of (ω) are:

[0041] Where ω is the frequency of the primary incident wave excitation, ω 1,uwm With ω2,uwm is the resonant frequency of the (u,w,m)th order acoustic mode in the cavity of MPPA unit 1 and MPPA unit 2, ξ 1,uwm With ξ 2,uwm is the corresponding modal damping ratio, and is the generalized modal mass, v1(x, y) and v2(x, y) represent the normal vibration velocity of the micro-perforated plate surface in MPPA unit 1 and MPPA unit 2.

[0042] Substituting equation (5) into equation (3) and equation (6) into equation (4), we can obtain the sound pressure expression at any point in the sound field of each unit cavity in the array.

[0043] Step 2: Characterize the reflected and radiated sound fields on the surface of the active micro-perforated plate absorber array, and calculate the total sound pressure of the incident side sound field on the array surface.

[0044] In the present invention, the sound pressure reflection coefficient that changes with the position of the array surface is used to characterize the reflected sound field of the array surface, the normal vibration velocity of the array surface is solved according to the boundary condition of the continuity of the normal particle velocity of the active micro-perforated plate sound absorber array surface, and the radiated sound field of the array surface is solved according to the Rayleigh integral formula, so as to obtain the total sound pressure of the incident side sound field;

[0045] Step 2.1: Characterize the acoustic field reflected from the array surface

[0046] Assume that the primary vertical incident plane wave in the free field is a vertical incident plane wave p with amplitude p0 i =p0e j(ωt-kz) , where k = ω / c0 is the wave number; the sound pressure reflection coefficients r1(x, y) and r2(x, y) that vary with the surface position are introduced to characterize the reflected sound field on the surface of MPPA unit 1 and MPPA unit 2, and the sound pressure of the reflected waves on the surface of MPPA unit 1 and MPPA unit 2 is expressed as:

[0047] p 1,r =r1(x,y)p0e j( ωt+kz ) (7)

[0048] p 2,r =r2(x,y)p0e j( ωt+kz ) (8)

[0049] Step 2.2: Characterize the acoustic field radiated from the array surface

[0050] Without considering the normal radiation velocity, according to the boundary condition of the array surface velocity continuity, the superposition value of the incident wave and the reflected wave in the incident side sound field is used to determine the normal particle velocity expression on the surface of MPPA unit 1 and MPPA unit 2 in the array:

[0051]

[0052] According to the Rayleigh integral formula, the sound pressure radiated from the surface vibration velocity of MPPA unit 2 to the surface of MPPA unit 1 and the sound pressure radiated from the surface vibration velocity of MPPA unit 1 to its own surface can be expressed as:

[0053]

[0054] In the formula, r 21 (s) represents the distance from any point on the surface of unit 2 to the (x, y) point on the surface of unit 1; r 11 (s) represents the distance from any point on the surface of element 1 to the point (x,y) on the surface of element 1.

[0055] Similarly, the sound pressure radiated from the surface vibration velocity of MPPA unit 1 to the surface of MPPA unit 2 and the sound pressure radiated from the surface vibration velocity of MPPA unit 2 to the surface of its own unit can be expressed as:

[0056]

[0057] In the formula, r 12 (s) represents the distance from any point on the surface of unit 1 to the (x, y) point on the surface of unit 2; r 22 (s) represents the distance from any point on the surface of unit 2 to the (x,y) point on the surface of unit 2.

[0058] Then the total sound pressure of the sound field on the incident side (z=0) of the surface of MPPA unit 1 and MPPA unit 2 in the array is:

[0059]

[0060] Step 3: Calculate the sound pressure reflection coefficient of the active micro-perforated plate absorber array surface.

[0061] According to the relationship between the normal vibration velocity on the micro-perforated plate surface of MPPA unit 1 and MPPA unit 2 in the array and the sound pressure on both sides of the micro-perforated plate, a group of equations satisfied by the sound pressure reflection coefficient on the array surface is established. At the same time, the unit surface is discretized, and a matrix equation satisfied by the sound pressure reflection coefficient at discrete points on the array surface is established. The matrix equation is solved to obtain the sound pressure reflection coefficient value at the discrete point.

[0062] make and is the normal radiation velocity generated by the normal particle vibration on the surface of MPPA unit 1 and MPPA unit 2. Since the normal radiation velocity caused by the normal vibration of any point on the array surface is not zero only at its own position, and for the convenience of analysis, it is approximately considered Then the total normal vibration velocity on the surface of MPPA unit 1 and MPPA unit 2 is approximately and

[0063] Therefore, the surface normal vibration velocity in MPPA unit 1 and MPPA unit 2 in the array satisfies the following relationship:

[0064]

[0065] Where p 1,c (z=0), p 2,c (z=0) is the acoustic pressure in the cavity of MPPA unit 1 and MPPA unit 2 near the surface of the micro-perforated plate in the array (z=0), z0 is the impedance of the pores on the micro-perforated plate, and when the pore constant satisfies 1<k h <10 o'clock, Where η is the viscosity coefficient of air, k h =(d h / 2) / r visc (ω) is the pore constant, is the thickness of the viscous boundary layer;

[0066] For MPPA unit 1, substitute equations (3), (9) and (15) into equation (17), discretize MPPA unit 1 into M1 discrete surface elements, and discretize MPPA unit 2 into M2 discrete surface elements, with the surface element side length being a. Then, the following relationship can be obtained:

[0067] Ar1+Br2=C+Gq(ω) (19)

[0068] In the formula is the sound pressure reflection coefficient of the discrete points on the surface of MPPA unit 1 and MPPA unit 2. The (i, j)th elements in the coefficient matrices A, B, C, and G are:

[0069]

[0070] In the formula, r(s) i,j is the distance between discrete surface element i and discrete surface element j.

[0071] Similarly, for unit 2, substitute equation (4), equation (10) and equation (16) into equation (18). After combining the two equations, the following relationship can be obtained:

[0072] Dr1+Er2=F (24)

[0073] Where, the (i, j)th elements in the coefficient matrices D, E, and F are:

[0074]

[0075] Combining equations (19) and (24), we can obtain the matrix equations of the sound pressure reflection coefficients r1 and r2 of MPPA unit 1 and MPPA unit 2:

[0076]

[0077] make The sound pressure reflection coefficient can be solved:

[0078]

[0079] Where X1 = x 11 C+x 12 F;X2=x 11 G;X3=x 21 C+x 22 F;X4=x 21 G.

[0080] Step 4: Solve the theoretical optimal control source intensity and calculate the sound absorption coefficient before and after control.

[0081] Taking the sound power absorbed by the active micro-perforated plate sound absorber array as the control target, the theoretical optimal control source intensity when the absorbed sound power is maximized is calculated, and then the sound absorption coefficient of the active micro-perforated plate sound absorber array after control is obtained; the control source intensity is set to zero, the absorbed sound power is calculated, and then the sound absorption coefficient of the active micro-perforated plate sound absorber array before control is obtained.

[0082] The specific process of this step is: taking the absorbed sound power of the active micro-perforated plate absorber array as the control target, and obtaining the optimal secondary control source intensity that maximizes the sound absorption coefficient by maximizing the absorbed sound power; the sound power of the active micro-perforated plate absorber array is:

[0083]

[0084] Where the superscript H represents the conjugate transpose, Re[·] is the real part of the complex number;

[0085] is the sound pressure of the discrete surface elements on the surface of MPPA unit 1 and MPPA unit 2;

[0086] is the particle velocity of the discrete surface element on the surface of MPPA unit 1 and MPPA unit 2.

[0087] Formula (15) and formula (16) can be simplified as:

[0088] p1=I+Jr1+Kr2 (31)

[0089] p2=L+Yr1+Zr2 (32)

[0090] Where the (i)th element in the coefficient vectors I, J, K, L, Y, and Z are:

[0091]

[0092] Substituting equations (31), (32), (9) and (10) into equation (30), the absorbed sound power is expressed as:

[0093] . Π abs =λ1+Re[λ2q(ω)]+Re[λ3q(ω) H ]+Re[λ4q(ω)q(ω) H ]. (39)

[0094] Where, the coefficients λ1, λ2, λ3, and λ4 are:

[0095]

[0096] In the formula, ψ is the element Column vector of .

[0097] It can be seen from equation (39) that the sound power absorbed by the active micro-perforated plate absorber array is a quadratic function of the secondary control source intensity; the control source intensity is expressed in the form of a complex number q(ω) = q R (ω)+jq I (ω), substitute it into equation (39) and calculate the partial derivatives of the real and imaginary parts of the control source intensity respectively; set the partial derivative to 0 and obtain the optimal control source intensity that maximizes the absorbed sound power:

[0098]

[0099] After obtaining the theoretical optimal secondary control source intensity, the sound absorption coefficient of the active micro-perforated plate absorber array after control can be obtained according to the calculation formula of the sound absorption coefficient;

[0100] The sound absorption coefficient of the active micro-perforated plate absorber array is expressed as:

[0101]

[0102] In the formula, Π inc is the incident wave acoustic power,

[0103] Let the control source intensity q(ω) = 0 in formula (39) to obtain the absorbed sound power before control, and calculate the sound absorption coefficient of the MPPA array before control according to formula (45); substitute formula (44) into formula (39) to calculate the absorbed sound power of the MPPA array after control, and then calculate the sound absorption coefficient of the MPPA array after control according to formula (31).

[0104] The following is a specific simulation example:

[0105] 1. Determine the parameters of active MPPA

[0106] like Figure 1 and Figure 2 As shown, one secondary control source is used for control, and the layout of the secondary control source is as follows Figure 2 The geometric parameters, material parameters and primary excitation parameters of the active MPPA array are shown in Tables 1 to 3.

[0107] Table 1 Geometric parameters of active MPPA array

[0108]

[0109]

[0110] Table 2 Material property parameters of active MPPA array

[0111]

[0112] Table 3 Primary excitation and secondary control source parameters

[0113]

[0114] 2. Calculation of the sound absorption coefficient before and after active MPPA array control

[0115] According to the above parameters, the sound absorption coefficient before active MPPA control and the theoretically optimal sound absorption coefficient after control are calculated.

[0116] 3. Simulation results and analysis

[0117] The sound absorption coefficient curves of the active MPPA array before and after control are calculated as shown in the attached figure. Figure 3 As shown in the results, it can be seen that after control, the sound absorption coefficient of the MPPA array under vertical incident excitation is almost close to 1 in a wide low-frequency band, which fully demonstrates the superiority of the active MPPA array in low-frequency sound absorption performance and engineering feasibility.

[0118] When the area of ​​unit 1 is reduced to three quarters of the original area, the sound absorption coefficient curves before and after active MPPA array control are as follows: Figure 4As shown in the figure, the average sound absorption coefficient of the active MPPA array after control is 0.75. It can be seen that although the size of the active unit is reduced, the low-frequency sound absorption performance is still significantly improved, which can provide a reference for practical engineering applications.

[0119] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A micro-perforated plate sound absorber array, characterized in that: The micro-perforated plate sound absorber array is composed of a plurality of micro-perforated plate sound absorbers with different cavity depths arranged in parallel, the micro-perforated plate sound absorber cavity is a rigid wall cavity, the front ends of the micro-perforated plates of all the micro-perforated plate sound absorbers are flush, and a loudspeaker is installed on the rear wall of the micro-perforated plate sound absorber with a deeper cavity depth as a secondary control source.

2. An active control method for improving the low-frequency sound absorption performance of the micro-perforated plate absorber array of claim 1 under free-field vertical incident excitation, characterized in that: The following steps are involved: Step 1: Modeling and calculating the sound field in the cavity of each micro-perforated plate sound absorber in the micro-perforated plate sound absorber array according to the geometric model parameters, material parameters, and primary excitation and secondary excitation parameters of the micro-perforated plate sound absorber array, and deriving the sound pressure expression at any position in the cavity of each micro-perforated plate sound absorber; Step 2: The reflected sound field of the array surface is characterized by using the sound pressure reflection coefficient that varies with the position of the array surface, the normal vibration velocity of the array surface is solved according to the boundary condition that the normal particle velocity of the micro-perforated plate sound absorber array surface is continuous, and the radiated sound field of the array surface is solved according to the Rayleigh integral formula to obtain the total sound pressure of the incident side sound field; Step 3: According to the relationship between the normal vibration velocity of the micro-perforated plate surface in each micro-perforated plate sound absorber in the micro-perforated plate sound absorber array and the sound pressure on both sides of the micro-perforated plate, an equation group satisfied by the sound pressure reflection coefficient of the array surface is established, and at the same time, the surface of the micro-perforated plate sound absorber is discretized to establish a matrix equation satisfied by the sound pressure reflection coefficient at discrete points on the array surface, and the matrix equation is solved to obtain the sound pressure reflection coefficient value at the discrete point; Step 4: Taking the sound power absorbed by the micro-perforated plate sound absorber array as the control target, calculating the theoretical optimal control source intensity when the absorbed sound power is maximized, and then obtaining the sound absorption coefficient of the micro-perforated plate sound absorber array after control; The control source intensity is set to zero, the absorbed sound power is calculated, and then the sound absorption coefficient of the micro-perforated plate sound absorber array mentioned before the control is obtained.

3. The method according to claim 2, characterized in that: In step 1, the process of obtaining the sound pressure expression at any position in the cavity of each micro-perforated plate sound absorber is: Assuming that the micro-perforated plate absorber array has two micro-perforated plate absorbers, the loudspeaker is equivalent to a point sound source. Under the excitation of the primary free field vertical incident plane wave and the secondary control source, the sound pressure P of the cavity sound field in the two micro-perforated plate absorbers is 1,c (x,y,z,t),P 2,c (x, y, z, t) satisfy the following wave equations respectively Where Q(x s ,y s ,z s ,t) is the point source intensity, Q(x s ,y s ,z s ,t)=q(ω)e jωt δ(xx s ,yy s ,zz s ), where δ(·) is the Dirac function; ρ0 is the density of air, c0 is the speed of sound; According to the modal superposition principle, the sound pressure in the cavity of the two micro-perforated plate absorbers is expressed in the form of modal expansion: Where P 1,uwm (ω) and P 2,uwm (ω) are the modal amplitudes of the (u, w, m)th order acoustic modes in the cavities of the two micro-perforated plate absorbers, and are the acoustic mode functions of the two cavities, respectively, expressed as: U, W, M are the upper limits of the number of modes; According to the boundary conditions that the micro-perforated plate surface in the cavity of each micro-perforated plate sound absorber meets the normal vibration velocity continuity Where v1(x, y) and v2(x, y) are the normal vibration velocities of the micro-perforated plate surfaces in the two micro-perforated plate absorbers, respectively. Using Green's second formula and the orthogonality of the acoustic mode functions of the cavity of each micro-perforated plate absorber, the acoustic mode amplitude P is obtained. 1,uwm (ω) and P 2,uwm The expressions of (ω) are: Where ω is the frequency of the primary incident wave excitation, ω 1,uwm With ω 2,uwm is the resonant frequency of the (u,w,m)th order acoustic mode in the cavity of the two micro-perforated plate absorbers, ξ 1,uwm With ξ 2,uwm is the corresponding modal damping ratio, is the generalized modal mass, v1(x, y) and v2(x, y) represent the normal vibration velocity of the micro-perforated plate surface in the two micro-perforated plate absorbers; Substituting equation (5) into equation (3) and equation (6) into equation (4), we can obtain the sound pressure expression at any point in the sound field of each micro-perforated plate absorber in the array.

4. The method according to claim 3, characterized in that: Step 2, the process of obtaining the total sound pressure of the incident side sound field is: Step 2.1: Characterize the acoustic field reflected from the array surface Assume that the primary vertical incident plane wave in the free field is a vertical incident plane wave p with amplitude p0 i =p0e j(ωt-kz) , where k = ω / c0 is the wave number; the sound pressure reflection coefficients r1(x, y) and r2(x, y) that vary with the surface position are introduced to characterize the reflected sound field on the surfaces of the two micro-perforated plate absorbers. The sound pressure of the reflected waves on the surfaces of the two micro-perforated plate absorbers is expressed as: p 1,r =r1(x,y)p0e j(ωt+kz) (7) p 2,r =r2(x,y)p0e j(ωt+kz) (8) Step 2.2: Characterize the acoustic field radiated from the array surface Without considering the normal radiation vibration velocity, according to the boundary condition of the array surface velocity continuity, the normal particle vibration velocity expression of the two micro-perforated plate absorbers in the array is determined by using the superposition value of the incident wave and the reflected wave in the incident side sound field: According to the Rayleigh integral formula, the sound pressure radiated from the surface vibration velocity of the second micro-perforated plate sound absorber to the surface of the first micro-perforated plate sound absorber and the sound pressure radiated from the surface vibration velocity of the first micro-perforated plate sound absorber to its own surface can be expressed as: In the formula, r 21 (s) represents the distance from any point on the surface of the second micro-perforated plate sound absorber to the point (x, y) on the surface of the first micro-perforated plate sound absorber; r 11 (s) represents the distance from any point on the surface of the first micro-perforated plate sound absorber to the point (x, y) on the surface of the first micro-perforated plate sound absorber; The sound pressure radiated from the surface vibration velocity of the first micro-perforated plate sound absorber to the surface of the second micro-perforated plate sound absorber and the sound pressure radiated from the surface vibration velocity of the second micro-perforated plate sound absorber to the surface of its own unit can be expressed as: In the formula, r 12 (s) represents the distance from any point on the surface of the first micro-perforated plate sound absorber to the point (x, y) on the surface of the second micro-perforated plate sound absorber; r 22 (s) represents the distance from any point on the surface of the second micro-perforated plate sound absorber to the point (x, y) on the surface of the second micro-perforated plate sound absorber; Then the total sound pressure of the sound field on the incident side (z=0) of the two micro-perforated plate absorbers in the array is:

5. The method according to claim 4, characterized in that: In step 3, the process of obtaining the sound pressure reflection coefficient value at the discrete point is: Let v rad1 and v rad2 is the normal radiation vibration velocity generated by the normal particle vibration on the surface of the two micro-perforated plate absorbers; The total normal vibration velocity of the two micro-perforated plate absorbers is and Satisfies the following relationship: Where p 1,c (z=0), p 2,c (z=0) is the sound pressure in the cavity of the two micro-perforated plate absorbers in the array close to the surface of the micro-perforated plate (z=0), z0 is the impedance of the pores on the micro-perforated plate, and when the pore constant satisfies 1<k h <10 o'clock, Where η is the viscosity coefficient of air, k h =(d h / 2) / r visc (ω) is the pore constant, is the thickness of the viscous boundary layer; For the first micro-perforated plate sound absorber, substitute equations (3), (9) and (15) into equation (17), discretize the surface of the first micro-perforated plate sound absorber into M1 discrete surface elements, and discretize the surface of the second micro-perforated plate sound absorber into M2 discrete surface elements, with the side length of the surface element being a, and then the following relationship can be obtained: Ar1+Br2=C+Gq(ω) (19) In the formula is the sound pressure reflection coefficient of the discrete points on the surface of the two micro-perforated plate absorbers. The (i, j)th elements in the coefficient matrices A, B, C, and G are: In the formula, r(s) i,j is the distance between discrete surface element i and discrete surface element j; For the second micro-perforated plate sound absorber, substitute equation (4), equation (10) and equation (16) into equation (18). After combining the two equations, the following relationship can be obtained: Dr1+Er2=F (24) Where, the (i, j)th elements in the coefficient matrices D, E, and F are: Combining equations (19) and (24) we can obtain the matrix equations of the sound pressure reflection coefficients r1 and r2 of the two micro-perforated plate absorbers: make Solve for the sound pressure reflection coefficient: Where X1 = x 11 C+x 12 F;X2=x 11 G;X3=x 21 C+x 22 F;X4=x 21 G.

6. The method according to claim 4, characterized in that: In step 4, the process of calculating the sound absorption coefficient of the micro-perforated plate absorber array before and after the control is: The acoustic power of the micro-perforated plate absorber array is: Where the superscript H represents the conjugate transpose, Re[·] is the real part of the complex number; is the sound pressure of discrete elements on the surface of two micro-perforated plate absorbers; is the particle vibration velocity of the discrete surface elements on the surface of the two micro-perforated plate absorbers; Formula (15) and formula (16) can be simplified as: p1=I+Jr1+Kr2 (31) p2=L+Yr1+Zr2 (32) Where the i-th element in the coefficient vectors I, J, K, L, Y, and Z are: Substituting equations (31), (32), (9) and (10) into equation (30), the absorbed sound power is expressed as: P abs =λ1+Re[λ2q(ω)]+Re[λ3q(ω) H ]+Re[λ4q(ω)q(ω) H ]. (39) Where, the coefficients λ1, λ2, λ3, and λ4 are: In the formula, ψ is the element Column vector of ; The control source strength is expressed as a complex number q(ω) = q R (ω)+jq I (ω), substitute it into equation (39) and calculate the partial derivatives of the real and imaginary parts of the control source intensity respectively; set the partial derivative to 0 and obtain the optimal control source intensity that maximizes the absorbed sound power: After obtaining the theoretical optimal secondary control source intensity, the sound absorption coefficient of the active micro-perforated plate absorber array after control can be obtained according to the calculation formula of the sound absorption coefficient; The sound absorption coefficient of the active micro-perforated plate absorber array is expressed as: In the formula, Π inc is the incident wave acoustic power, The lengths of the first micro-perforated plate sound absorber and the second micro-perforated plate sound absorber are respectively a1 and a2, and the widths are respectively b1 and b2; Using formula (39), let the control source intensity q(ω) = 0 to obtain the absorbed sound power before control, and calculate the sound absorption coefficient of the MPPA array before control according to formula (45); substitute formula (44) into formula (39) to calculate the absorbed sound power of the MPPA array after control, and then calculate the sound absorption coefficient of the MPPA array after control according to formula (31).

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