Complex closed space global low-frequency noise reduction method based on active micro-perforated plate sound absorber

Abstract

According to the complex closed space global low-frequency noise reduction method based on the active micro-perforated plate sound absorber, an active control technology is introduced into a small-size MPPA, the low-frequency acoustic reactance of a cavity of the MPPA is reduced by offsetting the sound field of the cavity of the MPPA, and the sound energy dissipation performance of the MPP is improved by breaking the waveform matching of the sound fields on the two sides of the MPP; the noise of the whole complex closed space is reduced in an active sound absorption mode, and meanwhile the problem that the noise reduction performance of some medium-high frequency resonance frequency points is weak due to coupling of a closed space sound field and an MPPA cavity sound field can be solved. The invested active control measure is low in cost, and the low-frequency noise reduction performance of the complex closed space is remarkable, so that the method has important engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical field of noise control, and in particular to a global low-frequency noise reduction method for a complex enclosed space based on an active micro-perforated plate sound absorber. Background Art

[0002] Reducing low-frequency noise in complex cabins, such as aircraft, manned underwater vehicles, and ground transportation, presents a pressing challenge. The cabin noise level of aircraft, such as passenger aircraft, is a key performance indicator and impacts the product's airworthiness certification. Excessive noise in underwater vehicle cabins disrupts the normal work of occupants, and noise radiated outward through the hull affects its stealth capabilities. Traditional passive noise reduction measures, primarily based on sound absorption and insulation, are effective at controlling mid- and high-frequency noise but less effective at controlling low-frequency noise. Low-frequency noise has a long wavelength, slow attenuation, and long propagation distances, and can cause far greater physical and psychological harm than anticipated. Therefore, developing low-frequency noise reduction solutions for complex, enclosed spaces is crucial.

[0003] Active noise control technology is the primary method for achieving low-frequency noise reduction. For small, regular enclosed spaces or localized noise environments, the cabin sound field resembles a regular standing wave field, and significant full-space noise reduction can be achieved with a small number of secondary sources and error sensors. However, for complex enclosed spaces, especially those with irregular shapes and filled with various devices, the internal sound field distribution is complex and resembles a diffuse field. Achieving comprehensive noise reduction in complex enclosed spaces requires deploying a large number of secondary sources and error sensors, making system implementation complex. For relatively regular enclosed spaces, a method combining sound field separation with active sound absorption has been proposed. Using a dual-microphone approach, the sound field is decomposed into a superposition of incident and reflected plane waves. Secondary sound sources are placed on the cabin walls to actively absorb the reflected waves, thus achieving full-space low-frequency noise reduction with a small number of secondary sources and error sensors. However, for complex sound fields, the dual-microphone approach alone is difficult to separate, and is therefore ineffective for controlling the complex acoustic modes of enclosed spaces.

[0004] The micro-perforated sound-absorbing structure is made of micro-holes in a base material (metal, glass, wood). It has the advantages of being clean and pollution-free, highly adaptable to the environment, and having good mid- and high-frequency sound absorption performance. It is often used for mid- and high-frequency sound absorption and noise reduction in cabins. Micro-perforated panel absorber (MPPA) is a commonly used structure in engineering. It is composed of a micro-perforated panel and its rear cavity. The resonant sound absorption of the rear cavity can improve the sound absorption performance of the MPPA and produce an effective sound absorption frequency band centered on the resonant frequency. By changing the structural parameters of the MPPA or arranging multiple MPPAs in series or in parallel to form an array, its effective sound absorption frequency band can cover mid- and high-frequency bands and achieve good sound absorption performance. However, due to the large low-frequency acoustic impedance in the MPPA cavity, its low-frequency sound absorption performance is relatively weak. At the same time, a more prominent problem with MPPAs for noise reduction in complex enclosed cabins is that the coupling of the cabin sound field with the MPPA cavity sound field results in waveform matching on both sides of the MPP (microperforated plate). This means that the surface sound field vibration mode distribution and size on both sides of the MPP are consistent (there is no sound pressure difference in the sound field on both sides of the MPP), resulting in zero vibration velocity of the air medium particles in the MPP micropores and no sound energy dissipation effect of the MPP. This makes the MPPA's sound absorption and noise reduction effect weak in the low-frequency band and even at some mid- and high-frequency cabin resonance frequencies, seriously restricting its application in cabin noise reduction. Summary of the Invention

[0005] To meet the demand for global low-frequency noise reduction in complex enclosed spaces, the present invention proposes a global low-frequency noise reduction method for complex enclosed spaces based on active micro-perforated plate sound absorbers. This method introduces active control technology into a small-sized MPPA, reduces the low-frequency acoustic reactance of the MPPA cavity by offsetting the MPPA cavity sound field, and improves the acoustic energy dissipation performance of the MPP by breaking the waveform matching of the sound fields on both sides of the MPP. This method reduces the noise of the entire complex enclosed space through active sound absorption, while also resolving the problem of weak noise reduction performance at certain mid- and high-frequency resonance frequencies caused by the coupling between the enclosed space sound field and the MPPA cavity sound field. The active control measures employed in this invention are low-cost, and the low-frequency noise reduction performance in complex enclosed spaces is significant, thus having important engineering application value.

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

[0007] A method for global low-frequency noise reduction in a complex enclosed space based on an active micro-perforated plate sound absorber comprises the following steps:

[0008] Step 1: For the active MPPA structure, a modal expansion expression for the sound pressure at any location in the enclosed space and the MPPA cavity is established based on the MPPA's geometric parameters, material parameters, and enclosed space acoustic field parameters. A matrix equation is established based on the relationship between the normal particle velocity on the microperforated plate surface and the sound pressure in the enclosed space and the sound pressure in the active MPPA cavity. Based on the matrix equation, an expression for the enclosed space acoustic modal amplitude and the acoustic mode in the active MPPA cavity is established.

[0009] Step 2: Based on the acoustic modal amplitude expression of any point in the enclosed space obtained in Step 1, and using the column vectors in the matrix equation obtained in Step 1, with the minimum acoustic potential energy of the enclosed space sound field as the objective function, solve the optimal vibration velocity intensity of the secondary piston source in the active MPPA structure to achieve global low-frequency noise reduction in the enclosed space.

[0010] Furthermore, the active MPPA structure consists of a closed space and an MPPA unit located on a rigid wall of the closed space; a primary source is installed in the closed space, and a loudspeaker is installed on the rear wall of the MPPA unit as a secondary control source.

[0011] Furthermore, the process of establishing the modal expansion expression of the sound pressure at any position in the enclosed space and the MPPA cavity based on the geometric parameters, material parameters and closed space sound field parameters of the MPPA is as follows:

[0012] Establish the sound pressure expression of the sound field in the MPPA cavity:

[0013]

[0014] Where U2 and W2 are the upper limits of the number of modes of the MPPA cavity along the x-axis and y-axis, is the (u2,w2)th order acoustic mode amplitude in the MPPA cavity, is the acoustic mode function of the MPPA cavity:

[0015]

[0016] where a2 and b2 are the dimensions of the active MPPA along the x-axis and y-axis, respectively, and (x, y) is the coordinate of any point in the MPPA cavity;

[0017] Under the excitation of the closed space sound field and the secondary control source, the MPPA cavity acoustic mode amplitude is:

[0018]

[0019] Where ω is the excitation frequency of the primary source, j is the imaginary unit, is the acoustic mode function of the MPPA cavity in the y-axis direction, is the generalized modal mass of the MPPA cavity, is the resonance frequency of the (u2, w2)th order acoustic mode in the MPPA cavity, for The corresponding modal damping ratio, ρ0 and c0 are the air density and the speed of sound in the air, respectively, v(y) is the normal particle velocity on the surface of the micro-perforated plate; v s (ω) is the vibration velocity of the secondary control source, ΔS is the area of ​​the secondary control source, Among them, when y s1 ≤y≤y s2 When χ(y s1 ~y s2 )=1, otherwise χ(y s1 ~y s2 )=0,y s1 with y s2 is the position coordinate of the secondary control source;

[0020] Establish the sound pressure expression of the sound field in the enclosed space:

[0021]

[0022] Among them, U1 and W1 are the upper limits of the number of modes along the x-axis and y-axis in the closed space. is the (u1, w1)th order acoustic mode amplitude in the closed space, is the acoustic modal function of the enclosed space;

[0023] When the enclosed space is excited by the primary source, its acoustic modal amplitude is expressed as:

[0024]

[0025] in is the acoustic modal function in the y-axis direction of the closed space, is the generalized modal mass of the enclosed space, is the resonant frequency of the (u1, w1)th order acoustic mode in the closed space, for Corresponding modal damping ratio, q p (ω) is the primary source intensity, (x p ,y p ) represents the primary source position, y1 and y2 are the position coordinates of the active MPPA on the wall of the closed space.

[0026] Furthermore, based on the relationship between the normal particle velocity on the micro-perforated plate surface and the sound pressure in the enclosed space and the sound pressure in the active MPPA cavity, the process of establishing the matrix equation is as follows:

[0027] The normal particle velocity on the MPP surface satisfies the relationship:

[0028]

[0029] Where σ is the porosity, Z0 is the MPP acoustic impedance, P1(x=0) and P2(x=0) are the acoustic pressures in the closed space and the MPPA cavity, respectively;

[0030] Substitute the sound pressure expression of the sound field in the MPPA cavity and the sound pressure expression of the sound field in the closed space into the MPP surface normal particle velocity expression, and multiply the modal function on both sides of the MPP surface normal particle velocity expression And integrating along the active MPPA surface, we can get:

[0031]

[0032]

[0033] in make

[0034]

[0035] Then the W1 acoustic modes along the y-axis in the closed space satisfy the following matrix equation:

[0036] aA+bB=c+v s (ω)g

[0037] in The elements of matrices a and b are a(w1,w′1) and b(w1,w′2) respectively, and the elements of column vectors c and g are c(w1) and g(w1), where w′1 and w′2 also represent the order;

[0038] Substitute the sound pressure expression of the sound field in the MPPA cavity and the sound pressure expression of the sound field in the closed space into the MPP surface normal particle velocity expression, and multiply the modal function on both sides of the MPP surface normal particle velocity expression And integrating along the active MPPA surface, we can get:

[0039]

[0040]

[0041] in make

[0042]

[0043] Then the W2 acoustic modes along the y-axis in the MPPA cavity satisfy the following matrix equation:

[0044] dA+eB=f+v s (ω)h

[0045] The elements of matrices d and e are d(w′1,w2) and e(w2,w′2), and the elements of column vectors f and h are f(w2) and h(w2).

[0046] Furthermore, the process of establishing the expression of the closed space acoustic mode amplitude and the active MPPA cavity acoustic mode according to the matrix equation is as follows:

[0047] Simultaneous matrix equations aA+bB=c+v s (ω)g and dA+eB=f+v s (ω)h gives the expressions of column vectors A and B as follows:

[0048]

[0049] Let the inverse of the coefficient matrix be the block matrix E1=x1c+x2f,E2=x1g+x2h,E1 and E2 are W1×1 column vectors; F1=x3c+x4f,F2=x3g+x4h,F1 and F2 are W2×1 column vectors. The expressions of the acoustic mode amplitudes at any point in the complex closed space and the active MPPA cavity are obtained as follows:

[0050]

[0051] in and are the elements in column vectors A and B respectively.

[0052] Furthermore, in step 2, based on the acoustic modal amplitude expression of any point in the enclosed space obtained in step 1, and using the column vectors in the matrix equation obtained in step 1, the optimal vibration velocity intensity of the secondary piston source in the active MPPA structure is solved with the minimum acoustic potential energy of the enclosed space sound field as the objective function. The process of achieving global low-frequency noise reduction in the enclosed space is as follows:

[0053] Establish the expression for the acoustic potential energy of a closed space:

[0054]

[0055] in

[0056] E1(w1) and E2(w1) are vectors P 1,b 、P 1,a , E1 and E2, the optimal piston source vibration velocity that minimizes the acoustic potential energy in the enclosed space is obtained as:

[0057] v s (ω)=-[(P 1,a )H ΦP 1,a ] -1 (P 1,a ) -1 ΦP 1,b .

[0058] Beneficial effects

[0059] 1. The present invention introduces active control technology into the MPPA unit to form an active MPPA unit and applies it to low-frequency noise reduction in complex enclosed spaces. This method uses active control technology to suppress the sound field in the MPPA cavity to break the sound field matching on both sides of the MPP, thereby significantly improving the sound energy dissipation performance of the MPP, achieving global low-frequency noise reduction in complex enclosed cabins and noise reduction at some mid- and high-frequency resonance frequency points in the cabin.

[0060] 2. The complex enclosed space noise reduction based on active MPPA units involved in the present invention can achieve full-space low-frequency noise reduction and noise reduction of some mid- and high-frequency resonance frequency points in large-scale complex enclosed spaces through active sound absorption with a small-size structure, which has important engineering application value.

[0061] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0063] Figure 1 This is a schematic diagram of the model of the present invention for low-frequency sound absorption and noise reduction in complex enclosed spaces based on the active MPPA structure.

[0064] Figure 2 This is a comparison chart of the acoustic potential energy in a complex enclosed space before and after control of an active MPPA unit with a size of 0.4m×0.05m. DETAILED DESCRIPTION

[0065] The following describes in detail embodiments of the present invention. The embodiments are exemplary and intended to explain the present invention, but are not to be construed as limiting the present invention.

[0066] Aiming at the demand for global low-frequency noise reduction in complex enclosed spaces, the present invention introduces active control technology into the MPPA structure and applies it to complex enclosed spaces to achieve low-frequency noise reduction. Specifically, the sound field in the MPPA cavity is suppressed through active control, thereby breaking the waveform matching on both sides of the MPP and generating a sound pressure difference on both sides of the MPP, thereby enhancing the sound energy dissipation effect of the MPP and minimizing the sound energy dissipation of the enclosed cabin. The active MPPA structure can achieve full-space noise reduction in any complex enclosed cabin by active sound absorption, and a smaller-sized active MPPA structure can achieve global noise reduction in large enclosed spaces. It can also improve the noise reduction performance of MPPA at certain resonant frequency points in the medium and high frequency bands. This method can not only solve the problem of global low-frequency noise reduction in the cabin, but also greatly simplify the control system structure, and has good application prospects.

[0067] The present invention is directed to an active MPPA, that is, the MPPA cavity is a rigid wall cavity, and a speaker is installed on the rear wall of the MPPA as a secondary control source. Figure 1 As shown, this example is a two-dimensional example. The complex enclosed space is a two-dimensional irregular cavity. The primary source is arranged at the lower left corner of the space. The MPPA is installed on the rigid wall on the right side of the complex enclosed space, and a loudspeaker is installed on the back wall of the MPPA unit as a secondary control source.

[0068] Based on the active MPPA structure described above, the global low-frequency noise reduction method for a complex enclosed space proposed in this embodiment includes the following steps:

[0069] Step 1: Based on the geometric and material parameters of the MPPA and the acoustic field parameters of the complex enclosed space, derive the modal expansion expressions for the acoustic pressure at any location within the complex enclosed space and the MPPA cavity. Based on the relationship between the normal particle velocity on the microperforated plate surface and the acoustic pressure within the complex enclosed space and the active MPPA cavity, establish a matrix equation and derive expressions for the acoustic modal amplitudes of the complex enclosed space and the acoustic modes within the active MPPA cavity.

[0070] The walls of the complex closed cavity and the active MPPA cavity are both rigid. Based on the geometric model parameters, material parameters, and complex closed space parameters of the active MPPA, the closed space sound field (cavity 1 sound field) and the active MPPA cavity sound field (cavity 2 sound field) are modeled and calculated. Expressions for the acoustic modal amplitudes in cavity 1 and cavity 2 and the sound pressure expressions at any position in each cavity are derived.

[0071] First, the sound pressure of the sound field in cavity 2 satisfies:

[0072]

[0073] Where U2 and W2 are the upper limits of the number of modes of the MPPA cavity along the x-axis and y-axis, is the (u2,w2)th order acoustic mode amplitude in cavity 2, is the acoustic mode function of cavity 2:

[0074]

[0075] Where a2 and b2 are the dimensions of the active MPPA along the x-axis and y-axis, respectively. (x, y) are the coordinates of any point within the MPPA cavity. In this embodiment, the x-axis is parallel to the width of the active MPPA cavity, and the y-axis is parallel to the length of the active MPPA cavity.

[0076] Under the excitation of the cavity 1 acoustic field and the secondary control source, the acoustic modal amplitude of cavity 2 is:

[0077]

[0078] Where ω is the excitation frequency of the primary source, j is the imaginary unit, is the acoustic mode function of cavity 2 in the y-axis direction, is the generalized modal mass of cavity 2, is the resonant frequency of the (u2, w2)th order acoustic mode in cavity 2, for The corresponding modal damping ratio, ρ0 and c0 are the air density and the speed of sound in the air respectively, and v(y) is the normal particle velocity on the surface of the micro-perforated plate. s (ω) is the vibration velocity of the secondary speaker (piston source), ΔS is the area of ​​the piston source, When y s1 ≤y≤y s2 When χ(y s1 ~y s2 )=1, otherwise χ(y s1 ~y s2 )=0,y s1 with y s2 is the position coordinate of the piston source.

[0079] For the sound field in cavity 1, the sound pressure satisfies:

[0080]

[0081] Where U1 and W1 are the upper limits of the number of modes of cavity 1 along the x-axis and y-axis, is the (u1, w1)th order acoustic mode amplitude in cavity 1, is the acoustic modal function of cavity 1, which can be obtained by finite element modeling and calculation.

[0082] Since cavity 1 is under the excitation of the primary source, its acoustic mode amplitude can be expressed as:

[0083]

[0084] in is the acoustic mode function of cavity 1 in the y-axis direction, is the generalized modal mass of cavity 1, is the resonant frequency of the (u1, w1)th order acoustic mode in cavity 1, for Corresponding modal damping ratio, q p (ω) is the primary source intensity, (x p ,y p ) represents the primary source position, y1 and y2 are the position coordinates of the active MPPA on the wall of the complex closed space.

[0085] The normal particle velocity on the MPP surface satisfies the relationship:

[0086]

[0087] σ is the porosity, Z0 is the MPP acoustic impedance, P1(x=0) and P2(x=0) are the acoustic pressures on the cavity 1 side and cavity 2 side, respectively. Equation (5) can be expressed as:

[0088] The first step is to substitute equations (1) and (3) into equation (5), and multiply both sides of equation (5) by the modal function And integrating along the active MPPA surface, we can get:

[0089]

[0090]

[0091] in make

[0092]

[0093] Then the W1 acoustic modes along the y-axis in cavity 1 satisfy the following matrix equation:

[0094] aA+bB=c+v s (ω)g (7)

[0095] in The elements of matrices a and b are a(w1, w′1) and b(w1, w′2), and the elements of column vectors c and g are c(w1) and g(w1), where w′1 and w′2 also represent the order.

[0096] The second step is to substitute equations (1) and (3) into equation (5) and multiply both sides of equation (5) by the modal function And integrating along the active MPPA surface, we can get:

[0097]

[0098] in make

[0099]

[0100] Then the W2 acoustic modes along the y-axis in cavity 2 satisfy the following matrix equation:

[0101] dA+eB=f+v s (ω)h (9)

[0102] The elements of matrices d and e are d(w′1,w2) and e(w2,w′2), and the elements of column vectors f and h are f(w2) and h(w2). The simultaneous matrix equations (7) and (9) can be used to derive the expressions of column vectors A and B as follows:

[0103]

[0104] Let the inverse of the coefficient matrix be the block matrix E1 = x1c + x2f, E2 = x1g + x2h, where E1 and E2 are W1×1 column vectors. F1 = x3c + x4f, F2 = x3g + x4h, where F1 and F2 are W2×1 column vectors. Once we have the column vectors E1 and E2, we can use them in step 2 to calculate the acoustic potential energy of the enclosed space.

[0105] The expressions of the acoustic mode amplitudes at any point in a complex enclosed space and an active MPPA cavity can be obtained as follows:

[0106]

[0107] in and are the elements in column vectors A and B respectively.

[0108] Step 2: Based on the acoustic modal amplitude expression of any point in the complex enclosed space obtained in Step 1, using the column vectors E1 and E2 in the matrix equation obtained in Step 1, and taking the minimization of the acoustic potential energy of the enclosed space sound field as the objective function, solve the optimal vibration velocity intensity of the secondary piston source in the active MPPA structure to achieve global low-frequency noise reduction in the complex enclosed space.

[0109] The active MPPA structure is used to absorb sound and reduce the sound field in a complex enclosed space, with the acoustic potential energy of the enclosed space as the objective function:

[0110]

[0111] in

[0112] E1(w1) and E2(w1) are vectors P 1,b 、P 1,a , E1 and E2, the optimal piston source vibration speed that minimizes the acoustic potential energy in the enclosed space is:

[0113] v s (ω)=-[(P 1,a ) H ΦP 1,a ] -1 (P 1,a ) -1 ΦP 1,b (14)

[0114] By using the optimal piston source vibration velocity that minimizes the acoustic potential energy of the enclosed space, the acoustic potential energy of the complex enclosed space before and after control can be obtained to verify the full-space noise reduction performance of the active MPPA structure.

[0115] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative 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 purpose of the present invention.

Claims

1. A global low-frequency noise reduction method for complex enclosed spaces based on active micro-perforated plate sound absorbers, characterized by: The following steps are involved: Step 1: For the active MPPA structure, establish the modal expansion expression of the sound pressure at any position in the enclosed space and the MPPA cavity based on the geometric parameters, material parameters, and acoustic field parameters of the enclosed space. Based on the relationship between the normal particle velocity on the micro-perforated plate surface and the sound pressure in the enclosed space and the sound pressure in the active MPPA cavity, a matrix equation is established; based on the matrix equation, expressions for the acoustic mode amplitude in the enclosed space and the acoustic mode in the active MPPA cavity are established; Step 2: Based on the acoustic modal amplitude expression of any point in the enclosed space obtained in Step 1, and using the column vectors in the matrix equation obtained in Step 1, with the minimum acoustic potential energy of the enclosed space sound field as the objective function, solve the optimal vibration velocity intensity of the secondary piston source in the active MPPA structure to achieve global low-frequency noise reduction in the enclosed space.

2. The method for global low-frequency noise reduction in a complex enclosed space based on an active micro-perforated plate sound absorber according to claim 1, characterized in that: The active MPPA structure consists of a closed space and an MPPA unit located on the rigid wall of the closed space; a primary source is installed in the closed space, and a loudspeaker is installed on the rear wall of the MPPA unit as a secondary control source.

3. The method for reducing global low-frequency noise in a complex enclosed space based on an active micro-perforated plate sound absorber according to claim 2, characterized in that: The process of establishing the modal expansion expression of the sound pressure at any position in the enclosed space and the MPPA cavity based on the geometric parameters, material parameters and closed space sound field parameters of the MPPA is as follows: Establish the sound pressure expression of the sound field in the MPPA cavity: Where U2 and W2 are the upper limits of the number of modes of the MPPA cavity along the x-axis and y-axis, is the (u2,w2)th order acoustic mode amplitude in the MPPA cavity, is the acoustic mode function of the MPPA cavity: where a2 and b2 are the dimensions of the active MPPA along the x-axis and y-axis, respectively, and (x, y) is the coordinate of any point in the MPPA cavity; Under the excitation of the closed space sound field and the secondary control source, the MPPA cavity acoustic mode amplitude is: Where ω is the excitation frequency of the primary source, j is the imaginary unit, is the acoustic mode function of the MPPA cavity in the y-axis direction, is the generalized modal mass of the MPPA cavity, is the resonance frequency of the (u2, w2)th order acoustic mode in the MPPA cavity, for The corresponding modal damping ratio, ρ0 and c0 are the air density and the speed of sound in the air, respectively, v(y) is the normal particle velocity on the surface of the micro-perforated plate; v s (ω) is the vibration velocity of the secondary control source, ΔS is the area of ​​the secondary control source, Among them, when y s1 ≤y≤y s2 When χ(y s1 ~y s2 )=1, otherwise χ(y s1 ~y s2 )=0,y s1 with y s2 is the position coordinate of the secondary control source; Establish the sound pressure expression of the sound field in the enclosed space: Among them, U1 and W1 are the upper limits of the number of modes along the x-axis and y-axis in the closed space. is the (u1, w1)th order acoustic mode amplitude in the closed space, is the acoustic modal function of the enclosed space; When the enclosed space is excited by the primary source, its acoustic modal amplitude is expressed as: in is the acoustic modal function in the y-axis direction of the closed space, is the generalized modal mass of the enclosed space, is the resonant frequency of the (u1, w1)th order acoustic mode in the closed space, for Corresponding modal damping ratio, q p (ω) is the primary source intensity, (x p ,y p ) represents the primary source position, y1 and y2 are the position coordinates of the active MPPA on the wall of the closed space.

4. The method for global low-frequency noise reduction in a complex enclosed space based on an active micro-perforated plate sound absorber according to claim 3, characterized in that: According to the normal particle velocity on the surface of micro-perforated plate and the sound pressure in the closed space and the active The relationship between the sound pressure in the MPPA cavity and the process of establishing the matrix equation is: The normal particle velocity on the MPP surface satisfies the relationship: Where σ is the porosity, Z0 is the MPP acoustic impedance, P1(x=0) and P2(x=0) are the acoustic pressures in the closed space and the MPPA cavity, respectively; Substitute the sound pressure expression of the sound field in the MPPA cavity and the sound pressure expression of the sound field in the closed space into the MPP surface normal particle velocity expression, and multiply both sides of the MPP surface normal particle velocity expression by the modal function And integrating along the active MPPA surface, we can get: in make Then the W1 acoustic modes along the y-axis in the closed space satisfy the following matrix equation: aA+bB=c+v s (ω)g in The elements of matrices a and b are a(w1, w1′) and b(w1, w′2), respectively, and the elements of column vectors c and g are c(w1) and g(w1), where w1′ and w′2 also represent the order; Substitute the sound pressure expression of the sound field in the MPPA cavity and the sound pressure expression of the sound field in the closed space into the MPP surface normal particle velocity expression, and multiply both sides of the MPP surface normal particle velocity expression by the modal function And integrating along the active MPPA surface, we can get: in make Then the W2 acoustic modes along the y-axis in the MPPA cavity satisfy the following matrix equation: dA+eB=f+v s (ω)h The elements of matrices d and e are d(w1′,w2) and e(w2,w′2), and the elements of column vectors f and h are f(w2) and h(w2).

5. The method for global low-frequency noise reduction in a complex enclosed space based on an active micro-perforated plate sound absorber according to claim 4, characterized in that: The process of establishing the expression of the acoustic mode amplitude in the closed space and the acoustic mode in the active MPPA cavity based on the matrix equation is as follows: Simultaneous matrix equations aA+bB=c+v s (ω)g and dA+eB=f+v s (ω)h gives the expressions of column vectors A and B as follows: Let the inverse of the coefficient matrix be the block matrix E1=x1c+x2f,E2=x1g+x2h,E1 and E2 are W1×1 column vectors; F1=x3c+x4f,F2=x3g+x4h,F1 and F2 are W2×1 column vectors. The expressions of the acoustic mode amplitudes at any point in the complex closed space and the active MPPA cavity are obtained as follows: in and are the elements in column vectors A and B respectively.

6. The method for global low-frequency noise reduction in a complex enclosed space based on an active micro-perforated plate sound absorber according to claim 5, characterized in that: In step 2, based on the acoustic modal amplitude expression of any point in the enclosed space obtained in step 1, and using the column vectors in the matrix equation obtained in step 1, the optimal vibration velocity intensity of the secondary piston source in the active MPPA structure is solved with the minimum acoustic potential energy of the enclosed space sound field as the objective function. The process of achieving global low-frequency noise reduction in the enclosed space is as follows: Establish the expression for the acoustic potential energy of a closed space: in E1(w1) and E2(w1) are vectors P 1,b 、P 1,a , E1 and E2, the optimal piston source vibration velocity that minimizes the acoustic potential energy in the enclosed space is obtained as: in s (ω)=-[(P 1,a ) H ΦP 1,a ] -1 (P 1,a ) -1 ΦP 1,b 。

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