Method for obtaining sound absorption coefficient of composite sound absorption structure with material flow resistance and surface density

Abstract

This invention provides a method for obtaining the sound absorption coefficient of a composite sound-absorbing structure that only requires measuring the material flow resistance and areal density, belonging to the field of sound-absorbing material technology. It includes: step a, obtaining the specific flow resistance and areal density of a flexible sheet-type porous sound-absorbing material; step b, obtaining the specific flow resistance and material thickness of a volumetric porous sound-absorbing material, and calculating the flow resistance of the volumetric porous sound-absorbing material; step c, constructing the transfer matrix of the flexible sheet-type porous sound-absorbing material and the volumetric porous sound-absorbing material; step d, establishing the transfer matrix of the composite sound-absorbing structure and obtaining the sound absorption coefficient; and step e, optimizing the sound absorption coefficient. In this invention, only the specific flow resistance and areal density need to be measured for the flexible sheet-type porous sound-absorbing material, and only the specific flow resistance and thickness parameters need to be measured for the volumetric porous sound-absorbing material. Optimizing the areal density and specific flow resistance for the target sound absorption frequency band can achieve the optimal sound absorption effect in that frequency band, effectively reducing the workload in the selection of sound-absorbing materials.

Description

Technical Field

[0001] This invention relates to the field of sound-absorbing materials technology, and in particular to a method for obtaining the sound absorption coefficient of a composite sound-absorbing structure that only requires material flow resistance and surface density. Background Technology

[0002] Porous sound-absorbing materials (such as micro-perforated panels and sound-absorbing cotton) are widely used in construction, railways, and automobiles to reduce noise levels and improve comfort in people's environments. Currently, porous sound-absorbing materials are mainly divided into two types: sheet-type porous sound-absorbing materials and volumetric porous sound-absorbing materials. The definitions for these two types are as follows: if the wavelength of the sound wave is much greater than the material thickness, the material is a sheet-type porous material; conversely, if the wavelength of the sound wave is much smaller than the material thickness, the material is a volumetric porous sound-absorbing material. Most volumetric porous sound-absorbing materials on the market suffer from poor low-frequency sound absorption. While volumetric porous sound-absorbing materials used alone have good high-frequency sound absorption, their low-frequency sound absorption is poor. In recent years, flexible sheet-type porous materials have attracted widespread attention due to their environmental friendliness, economy, and decorative properties. Flexible, thin-sheet porous materials exhibit excellent sound absorption performance. This is due to two main factors: firstly, the surface of the material has numerous uneven rectangular pits, causing diffuse reflection of sound waves; secondly, the material's interior contains numerous irregular micropores left by interwoven fibers, allowing sound waves to easily penetrate the material's interior and excite the air within these pores, converting sound energy into heat and gradually dissipating it, thus achieving sound absorption and noise reduction. However, flexible, thin-sheet porous sound-absorbing materials are too thin to be used alone; an air layer or other material is required to achieve optimal sound absorption. Therefore, combining flexible, thin-sheet porous sound-absorbing materials with volumetric porous sound-absorbing materials yields better sound absorption performance.

[0003] However, traditional acoustic theoretical models for calculating and optimizing sheet and volumetric composite materials require obtaining nine parameters: material porosity, flow resistance, torsion, viscous characteristic length, thermal characteristic length, Young's modulus, damping loss factor, and volume density. Many of these parameters are difficult to obtain, and measuring all nine parameters is very expensive, which greatly inconveniences the prediction and optimization of the acoustic performance of sheet and volumetric composite sound-absorbing materials.

[0004] Therefore, there is an urgent need for a method for calculating and optimizing the sound absorption performance of composite materials that can significantly reduce the parameters required for predicting and optimizing the sound absorption performance of composite materials, while having similar prediction accuracy as traditional methods. Summary of the Invention

[0005] In view of this, in order to predict and optimize the sound absorption performance of composite sound-absorbing structures combining flexible sheet-type porous sound-absorbing materials and volumetric porous sound-absorbing materials, and to significantly reduce the parameters required for predicting and optimizing the sound absorption performance of composite materials, making them more practical, this invention provides a method for obtaining the sound absorption coefficient of composite sound-absorbing structures that only requires material flow resistance and areal density. Specifically, for flexible sheet-type porous sound-absorbing materials, only the specific flow resistance and areal density need to be measured; for volumetric porous sound-absorbing materials, only the specific flow resistance and thickness parameters need to be measured. By optimizing the areal density and specific flow resistance for the target sound absorption frequency band, the optimal sound absorption effect in that frequency band can be achieved, effectively reducing the workload in the selection of sound-absorbing materials.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for obtaining the sound absorption coefficient of a composite sound-absorbing structure that only requires material flow resistance and areal density, wherein the composite sound-absorbing structure is composed of a flexible sheet-type porous sound-absorbing material and a volumetric profile porous sound-absorbing material, comprising the following steps:

[0008] Step a: Obtain the specific resistance and areal density of the flexible thin-film porous sound-absorbing material;

[0009] Step b: Obtain the specific resistance and thickness of the porous sound-absorbing material in the bulk profile, and calculate the flow resistance ratio of the porous sound-absorbing material in the bulk profile:

[0010] Step c: Construct the transfer matrix of the flexible sheet-type porous sound-absorbing material and the transfer matrix of the volumetric profile porous sound-absorbing material:

[0011] Step d: Establishing the transfer matrix and obtaining the sound absorption coefficient of the composite sound-absorbing structure.

[0012] Based on the incident direction of the sound waves and the order in which the sound waves pass through the material, the following relationship can be established:

[0013]

[0014]

[0015] H 12 =jZ c sin(K c d)+R s1 cos(K c d) (3)

[0016]

[0017] H 22 =cos(K) c d) (5)

[0018] In the above equations (1)-(5), H is the transfer matrix of the composite sound-absorbing structure in step d, M is the transfer matrix of the flexible sheet-type porous sound-absorbing material, P is the transfer matrix of the volumetric profile porous sound-absorbing material, and R s1 K represents the specific resistance value of the flexible sheet-type porous sound-absorbing material obtained in step a. c Z is the propagation constant of the volumetric porous sound-absorbing material. c denoted as the characteristic impedance of the volumetric porous sound-absorbing material, d is the thickness of the volumetric porous sound-absorbing material obtained in step b, and j is the imaginary unit.

[0019] Solving equation (1) yields the surface acoustic impedance of the composite structure shown in equation (6):

[0020]

[0021] In equation (6), Z f The surface acoustic impedance of the composite structure;

[0022] The reflection coefficient and sound absorption coefficient of the composite sound-absorbing structure are calculated according to equations (7) and (8), respectively:

[0023]

[0024] α = 1 - |r| 2 (8)

[0025] In equation (7), r is the reflection coefficient of the composite sound-absorbing structure, α is the sound absorption coefficient of the composite sound-absorbing structure, and ρc is the characteristic impedance of air.

[0026] Step e: Optimize the sound absorption coefficient of the composite sound-absorbing structure:

[0027] The areal density and specific resistance of the flexible sheet-type porous sound-absorbing material at the maximum effective sound absorption area are calculated using equation (9):

[0028]

[0029] In equation (9), A α For the effective sound absorption area, f1 is the lower limit frequency value of the target frequency band, f2 is the upper limit frequency value of the target frequency band, α(f) is the frequency response curve of the sound absorption coefficient, and m2 is the surface density of the flexible thin-film porous sound-absorbing material when the effective sound absorption area is maximized; R s The specific resistance of the flexible thin-film porous sound-absorbing material is the value when the effective sound absorption area is maximized, where df is the derivative with respect to frequency.

[0030] Preferably, in step b, the flow resistivity is calculated as follows:

[0031] σ=R s2 / d (10);

[0032] In equation (10), σ is the flow resistivity in step b, and R s2 The specific resistance value of the porous sound-absorbing material of the volumetric profile obtained in step b.

[0033] Preferably, the transfer matrix of the flexible thin-film porous sound-absorbing material is constructed as follows:

[0034] The transmission matrix of flexible sheet porous sound-absorbing material is constructed based on the impedance characteristics of the pores and the transmission impedance of the flexible sheet porous sound-absorbing material.

[0035] Among them, the impedance characteristics of the pores in flexible thin-film porous sound-absorbing materials

[0036] In equation (11), η is the dynamic viscosity coefficient, σ is the flow resistance, d is the diameter of the hole, and t1 is the material thickness.

[0037] Transmission impedance of flexible thin-film porous sound-absorbing materials

[0038] In equation (12), j is the imaginary unit;

[0039] The impedance characteristic transfer matrix of flexible thin-film porous sound-absorbing materials can be expressed as:

[0040]

[0041] Preferably, based on the DB equivalent model of porous materials, the impedance characteristic transfer matrix of the volumetric porous sound-absorbing material is expressed as:

[0042]

[0043] In equation (13), K c Z is the propagation constant of the volumetric porous sound-absorbing material. c denoted as , where d is the characteristic impedance of the volumetric porous sound-absorbing material, d is the thickness of the volumetric porous sound-absorbing material, and j is the imaginary unit.

[0044] Preferably, the process for constructing the transmission impedance of the pores in the flexible sheet-type porous sound-absorbing material is as follows:

[0045] From the perspective of impedance, when sound pressure is incident perpendicularly, it causes vibration in the flexible, thin-film porous sound-absorbing material. This changes the particle velocity on the surface of the material. According to Newton's laws:

[0046]

[0047] In equation (14), ΔP represents the sound pressure change, m represents the surface density of the flexible sheet-type porous sound-absorbing material, u represents the particle velocity on the surface of the flexible sheet-type porous sound-absorbing material, and t2 represents time. Given the partial derivative of the particle velocity with respect to time, transforming equation (14) to the frequency domain yields its vibration impedance:

[0048] Z m =jωm (15)

[0049] In equation (15), Z m ω is the vibration impedance, j is the imaginary unit, ω is the angular frequency, and m is the surface density.

[0050] Micro-perforated plates have a similar structure to flexible sheet-type porous sound-absorbing materials. The characteristic impedance of micro-perforated plates is transferred to that of flexible sheet-type porous sound-absorbing materials. The impedance formula for micro-perforated plates is as follows:

[0051]

[0052] In equation (16), Z MPP Let t be the impedance of the microperforated plate, and t be the thickness of the microperforated plate. ρ is the porosity, c is the air density, d is the sound velocity, ω is the pore diameter, β is the angular frequency, and η is the porosity constant.

[0053] At low frequencies, omitting the imaginary part in equation (16), the impedance characteristic formula for flexible thin-film porous sound-absorbing materials is simplified from equation (16):

[0054]

[0055] In equation (17), Z Rs Impedance characteristics of flexible thin-film porous sound-absorbing materials;

[0056] The process of constructing the transmission impedance of flexible thin-film porous sound-absorbing materials is as follows:

[0057] Combining equation (15) and equation (17), the transmission impedance of the flexible thin-film porous sound-absorbing material can be obtained:

[0058]

[0059] Preferably, K c and Z c The specific calculation formula is as follows:

[0060]

[0061]

[0062] ω=2πf (21)

[0063] In equations (19), (20), and (21), ρ0, c0, f, σ, and ω represent air density, sound velocity in air, sound frequency, flow resistance of the porous sound-absorbing material, and angular frequency, respectively.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] 1) The flexible sheet-type porous material and the volumetric porous material proposed in this invention only require the measurement of specific flow resistance and areal density for the former and only specific flow resistance and thickness for the latter, which improves the calculation efficiency.

[0066] 2) The areal density and specific resistance values ​​required for measurement in this invention can be used in subsequent optimization of the sound absorption performance of composite structures. Optimizing the areal density and specific resistance values ​​for the target sound absorption frequency band can achieve the best sound absorption effect in that frequency band, effectively reducing the workload in the selection of sound absorption materials. Attached Figure Description

[0067] Figure 1 This is a flowchart illustrating the implementation of the calculation method in this invention;

[0068] Figure 2 This is a model diagram of the composite structure in this invention;

[0069] Figure 3 This is a schematic diagram illustrating the flow resistance measurement principle in this invention;

[0070] Figure 4 This is a comparison chart of experimental and calculated sound absorption effects of the composite structure in this invention;

[0071] Figure 5 This is a calculation diagram showing the optimal sound absorption effect of the composite structure in the 0-1600Hz range, as presented in this invention. Detailed Implementation

[0072] The technical solution of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings.

[0073] like Figure 2 As shown, the present invention provides a method for obtaining the sound absorption coefficient of a composite sound-absorbing structure, which is applied to a composite structure combining a flexible sheet-type porous sound-absorbing material and a volumetric porous sound-absorbing material. The flexible sheet-type porous sound-absorbing material can be a non-woven fabric, and the volumetric porous sound-absorbing material can be volumetric sound-absorbing cotton. In specific implementation, along the incident direction of the sound wave, the sound wave passes through the flexible sheet-type porous material and the volumetric porous material successively. The impedance characteristic transfer matrix M of the flexible sheet-type porous material and the impedance characteristic transfer matrix P of the volumetric porous material are used, and the impedance characteristic transfer matrix H of the composite structure is used. Figure 1 As shown, the method for calculating the sound absorption coefficient of this composite structure includes the following steps:

[0074] Step a: Measurement of surface density and specific flow resistance of flexible thin-film porous sound-absorbing material:

[0075] The specific flow resistance of the flexible sheet-type porous sound-absorbing material is measured using a flow resistance meter, and the mass of the flexible sheet-type porous sound-absorbing material is determined using an electronic balance, thus obtaining the surface density; the principle of flow resistance measurement is as follows: Figure 3 As shown, this is a conventional technical method in this field, and will not be described in detail here.

[0076] Step b: Measurement of acoustic parameters of volumetric porous materials:

[0077] The specific resistance of a volumetric porous sound-absorbing material can be calculated by measuring the specific resistance of the material using a flow resistance meter and measuring the thickness of the material.

[0078] σ=R s2 / d (10);

[0079] In equation (10), σ is the flow resistivity in step b, and R s2 The specific resistance value of the porous sound-absorbing material of the volumetric profile obtained in step b;

[0080] Step c, Construction of the transfer matrix for flexible sheet-type porous sound-absorbing materials and volumetric porous sound-absorbing materials:

[0081] The transfer matrix of the flexible thin-film porous sound-absorbing material is constructed as follows:

[0082] The transmission matrix of flexible sheet porous sound-absorbing material is constructed based on the impedance characteristics of the pores and the transmission impedance of the flexible sheet porous sound-absorbing material.

[0083] Among them, the impedance characteristics of the pores in flexible thin-film porous sound-absorbing materials

[0084] In equation (11), η is the dynamic viscosity coefficient, σ is the flow resistance, d is the diameter of the hole, and t1 is the material thickness.

[0085] Transmission impedance of flexible thin-film porous sound-absorbing materials

[0086] In equation (12), j is the imaginary unit;

[0087] The impedance characteristic transfer matrix of flexible thin-film porous sound-absorbing materials can be expressed as:

[0088]

[0089] Based on the DB equivalent model of porous materials, the impedance characteristic transfer matrix of volumetric porous sound-absorbing materials is expressed as:

[0090]

[0091] In equation (13), K c Z is the propagation constant of the volumetric porous sound-absorbing material. c denoted as the characteristic impedance of the volumetric porous sound-absorbing material, d is the thickness of the volumetric porous sound-absorbing material, and j is the imaginary unit;

[0092] The process of constructing the transmission impedance of the pores in the flexible thin-film porous sound-absorbing material is as follows:

[0093] From the perspective of impedance, when sound pressure is incident perpendicularly, it causes vibration in the flexible, thin-film porous sound-absorbing material. This changes the particle velocity on the surface of the material. According to Newton's laws:

[0094]

[0095] In equation (14), ΔP represents the sound pressure change, m represents the surface density of the flexible sheet-type porous sound-absorbing material, u represents the particle velocity on the surface of the flexible sheet-type porous sound-absorbing material, and t2 represents time. Given the partial derivative of the particle velocity with respect to time, transforming equation (14) to the frequency domain yields its vibration impedance:

[0096] Z m =jωm (15)

[0097] In equation (15), Z m ω is the vibration impedance, j is the imaginary unit, ω is the angular frequency, and m is the surface density.

[0098] The areal density *m* in equation (14) reflects the vibration impedance of the flexible sheet-type porous sound-absorbing material membrane. The transmission impedance of the pores in the flexible sheet-type porous sound-absorbing material should also be considered. Micro-perforated plates have a similar structure to flexible sheet-type porous sound-absorbing materials; therefore, their characteristic impedance can be transferred to that of flexible sheet-type porous sound-absorbing materials. The impedance formula for micro-perforated plates is as follows:

[0099]

[0100] In equation (16), Z MPP Let t be the impedance of the microperforated plate, and t be the thickness of the microperforated plate. ρ is the porosity, c is the air density, d is the sound velocity, ω is the pore diameter, β is the angular frequency, and η is the porosity constant.

[0101] For flexible sheet-type porous sound-absorbing materials, the pores are mostly irregular, with the size of the pores being on the same order of magnitude as their thickness, and the pore diameters are mostly in the micrometer range. Therefore, the porosity constant β is much less than 1. Thus, at low frequencies, omitting the imaginary part in equation (16), the impedance characteristic formula for flexible sheet-type porous sound-absorbing materials is simplified from equation (16):

[0102]

[0103] In equation (17), Z Rs The impedance characteristics of the pores in a flexible, thin-film porous sound-absorbing material;

[0104] The process of constructing the transmission impedance of flexible thin-film porous sound-absorbing materials is as follows:

[0105] Considering the parallel impedance characteristics of the membrane and pores in the flexible sheet-type porous sound-absorbing material, combining equation (15) with equation (17) yields the transmission impedance of the flexible sheet-type porous sound-absorbing material:

[0106]

[0107] In the impedance characteristic transfer matrix of the volumetric porous sound-absorbing material, K c and Z c The specific calculation formula is as follows:

[0108]

[0109]

[0110] ω=2πf (21)

[0111] In equations (19), (20), and (21), ρ0, c0, f, σ, and ω represent air density, sound velocity in air, sound frequency, flow resistance of the porous sound-absorbing material, and angular frequency, respectively.

[0112] Step d: Establishing the transfer matrix of the composite sound-absorbing structure and obtaining its sound absorption performance:

[0113] Based on the incident direction of the sound waves and the order in which the sound waves pass through the material, the following relationship can be established:

[0114]

[0115]

[0116] H 12 =jZ c sin(Kcd)+R s1 cos(K c d) (3)

[0117]

[0118] H 22 =cos(K) c d) (5)

[0119] In the above equations (1)-(5), H is the transfer matrix of the composite sound-absorbing structure in step d, M is the transfer matrix of the flexible sheet-type porous sound-absorbing material, P is the transfer matrix of the volumetric profile porous sound-absorbing material, and R s1 K represents the specific resistance value of the flexible sheet-type porous sound-absorbing material obtained in step a. c Z is the propagation constant of the volumetric porous sound-absorbing material. c denoted as the characteristic impedance of the volumetric porous sound-absorbing material, d is the thickness of the volumetric porous sound-absorbing material obtained in step b, and j is the imaginary unit.

[0120] Let the sound pressure of the incident sound wave and the particle vibration velocity be p1 and v1, respectively; let the sound pressure and particle vibration velocity at the rigid wall at the end of the composite structure be p. n and v n The following equality relationship is satisfied:

[0121]

[0122] Since the end is a rigid wall, therefore:

[0123] v n =0

[0124] Solving equation (1) yields the surface acoustic impedance of the composite structure shown in equation (6):

[0125]

[0126] In equation (6), Z f The surface acoustic impedance of the composite structure;

[0127] The reflection coefficient and sound absorption coefficient of the composite sound-absorbing structure are calculated according to equations (7) and (8), respectively:

[0128]

[0129] α = 1 - |r| 2 (8)

[0130] In equation (7), r is the reflection coefficient of the composite sound-absorbing structure, α is the sound absorption coefficient of the composite sound-absorbing structure, and ρc is the characteristic impedance of air; the comparison results of the experimental test values ​​and the calculated values ​​of the transfer matrix of the composite structure are as follows: Figure 4 As shown;

[0131] Step e: Optimize the sound absorption coefficient of the composite sound-absorbing structure:

[0132] The areal density and specific resistance of the flexible sheet-type porous sound-absorbing material at the maximum effective sound absorption area are calculated using equation (9):

[0133]

[0134] In equation (9), A α For the effective sound absorption area, f1 is the lower limit frequency value of the target frequency band, f2 is the upper limit frequency value of the target frequency band, α(f) is the frequency response curve of the sound absorption coefficient, and m2 is the surface density of the flexible thin-film porous sound-absorbing material when the effective sound absorption area is maximized; R s The specific resistance of the flexible thin-film porous sound-absorbing material is the value when the effective sound absorption area is maximized, where df is the derivative with respect to frequency.

[0135] A α The magnitude of the value reflects the sound absorption effect within the frequency band (f1, f2). Therefore, the optimal sound absorption effect can be achieved by solving for the effective sound absorption area within the target frequency band, considering the surface density m2 and specific resistance R of the flexible thin-film porous sound-absorbing material. s The numerical value. The optimal sound absorption effect within the 0-1600Hz frequency band is as follows: Figure 5 As shown.

[0136] R in step a s1 For the specific flow resistance of the first layer of flexible sheet-like porous sound-absorbing material in the composite sound-absorbing structure, in step e, R s The specific flow resistance of the flexible sheet-type porous sound-absorbing material is obtained through an optimized algorithm. Both are the specific flow resistance of the same object, but the values ​​are different. In other words, the sound absorption coefficient of the composite structure can be changed by adjusting the specific flow resistance of the flexible sheet-type porous sound-absorbing material.

[0137] R s It is based on the effective sound absorption area A α The calculated value is obtained by finding A through an optimization algorithm. α At its maximum, the specific resistance of the flexible sheet-like porous sound-absorbing material in the composite structure is R. s It is related to R s1 The only difference is the numerical value, but both belong to the specific flow resistance of flexible thin-film porous sound-absorbing materials, R. s1 R was measured using a flow resistance meter. s It is derived from an optimization algorithm.

[0138] In step a, the specific resistance R of the flexible thin-film porous sound-absorbing material s1 The surface density (m) is used to simulate the frequency response curve of the sound absorption coefficient of the composite structure.

[0139] In summary, by theoretically calculating the sound absorption coefficient of the composite structure, and then by using an optimization algorithm to calculate the effective sound absorption area for the target frequency band, we can determine the surface density and specific resistance of the flexible thin porous material when the effective sound absorption area is maximized. This allows us to achieve a process of changing the surface density and specific resistance to alter the sound absorption coefficient.

[0140] The above are merely preferred embodiments of the present invention; however, the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and its improved concept, should be covered within the scope of protection of the present invention.

Claims

1. A method for obtaining the sound absorption coefficient of a composite sound-absorbing structure requiring only material flow resistance and areal density, wherein the composite sound-absorbing structure is composed of a flexible sheet-type porous sound-absorbing material and a volumetric profile porous sound-absorbing material, characterized in that... Includes the following steps: Step a: Obtain the specific resistance and areal density of the flexible thin-film porous sound-absorbing material; Step b: Obtain the specific resistance and thickness of the porous sound-absorbing material in the bulk profile, and calculate the flow resistance ratio of the porous sound-absorbing material in the bulk profile: Step c: Construct the transfer matrix of the flexible sheet-type porous sound-absorbing material and the transfer matrix of the volumetric profile porous sound-absorbing material: Step d: Establishing the transfer matrix and obtaining the sound absorption coefficient of the composite sound-absorbing structure. Based on the incident direction of the sound waves and the order in which the sound waves pass through the material, the following relationship can be established: H 12 =jZ c sin(K c d)+R s1 cos(K c d) (3) H 22 =cos(K c d) (5) In the above equations (1)-(5), H is the transfer matrix of the composite sound-absorbing structure in step d, M is the transfer matrix of the flexible sheet-type porous sound-absorbing material, P is the transfer matrix of the volumetric profile porous sound-absorbing material, and R s1 K represents the specific resistance value of the flexible sheet-type porous sound-absorbing material obtained in step a. c Z is the propagation constant of the volumetric porous sound-absorbing material. c Let be the characteristic impedance of the volumetric porous sound-absorbing material, d be the thickness of the volumetric porous sound-absorbing material obtained in step b, and j be the imaginary unit. Solving equation (1) yields the surface acoustic impedance of the composite structure shown in equation (6): In equation (6), Z f The surface acoustic impedance of the composite structure; The reflection coefficient and sound absorption coefficient of the composite sound-absorbing structure are calculated according to equations (7) and (8), respectively: α＝1-|r| 2 (8) In equation (7), r is the reflection coefficient of the composite sound-absorbing structure, α is the sound absorption coefficient of the composite sound-absorbing structure, and ρc is the characteristic impedance of air. Step e: Optimize the sound absorption coefficient of the composite sound-absorbing structure: The areal density and specific resistance of the flexible sheet-type porous sound-absorbing material at the maximum effective sound absorption area are calculated using equation (9): In equation (9), A α For the effective sound absorption area, f1 is the lower limit frequency value of the target frequency band, f2 is the upper limit frequency value of the target frequency band, α(f) is the frequency response curve of the sound absorption coefficient, and m2 is the surface density of the flexible thin-film porous sound-absorbing material when the effective sound absorption area is maximized; R s The specific resistance of the flexible thin-film porous sound-absorbing material is the value when the effective sound absorption area is maximized, where df is the derivative with respect to frequency.

2. The method for obtaining the sound absorption coefficient of a composite sound-absorbing structure based solely on material flow resistance and areal density, as described in claim 1, is characterized in that... In step b, the flow resistivity is calculated as follows: σ=R s2 / d (10); In equation (10), σ is the flow resistivity in step b, and R s2 The specific resistance value of the porous sound-absorbing material of the volumetric profile obtained in step b.

3. The method for obtaining the sound absorption coefficient of a composite sound-absorbing structure based solely on material flow resistance and areal density, as described in claim 1, is characterized in that... The transfer matrix of the flexible thin-film porous sound-absorbing material is constructed as follows: The transmission matrix of flexible sheet porous sound-absorbing material is constructed based on the impedance characteristics of the pores and the transmission impedance of the flexible sheet porous sound-absorbing material. Among them, the impedance characteristics of the pores in flexible thin-film porous sound-absorbing materials In equation (11), η is the dynamic viscosity coefficient, σ is the flow resistance, d is the diameter of the hole, and t1 is the material thickness. Transmission impedance of flexible thin-film porous sound-absorbing materials In equation (12), j is the imaginary unit; The impedance characteristic transfer matrix of flexible thin-film porous sound-absorbing materials can be expressed as:

4. The method for obtaining the sound absorption coefficient of a composite sound-absorbing structure requiring only material flow resistance and areal density as described in claim 1, characterized in that, Based on the DB equivalent model of porous materials, the impedance characteristic transfer matrix of volumetric porous sound-absorbing materials is expressed as: In equation (13), K c Z is the propagation constant of the volumetric porous sound-absorbing material. c denoted as , where d is the characteristic impedance of the volumetric porous sound-absorbing material, d is the thickness of the volumetric porous sound-absorbing material, and j is the imaginary unit.

5. The method for obtaining the sound absorption coefficient of a composite sound-absorbing structure requiring only material flow resistance and areal density, as described in claim 3, is characterized in that... The process of constructing the transmission impedance of the pores in flexible thin-film porous sound-absorbing materials is as follows: From the perspective of impedance, when sound pressure is incident perpendicularly, it causes vibration in the flexible, thin-film porous sound-absorbing material. This changes the particle velocity on the surface of the material. According to Newton's laws: In equation (14), ΔP represents the sound pressure change, m represents the surface density of the flexible sheet-type porous sound-absorbing material, u represents the particle velocity on the surface of the flexible sheet-type porous sound-absorbing material, and t2 represents time. Given the partial derivative of the particle velocity with respect to time, transforming equation (14) to the frequency domain yields its vibration impedance: WITH m =jωm (15) In equation (15), Z m ω is the vibration impedance, j is the imaginary unit, ω is the angular frequency, and m is the surface density. Micro-perforated plates have a similar structure to flexible sheet-type porous sound-absorbing materials. The characteristic impedance of micro-perforated plates is transferred to that of flexible sheet-type porous sound-absorbing materials. The impedance formula for micro-perforated plates is as follows: In equation (16), Z MPP Let t be the impedance of the microperforated plate, and t be the thickness of the microperforated plate. ρ is the porosity, c is the air density, d is the sound velocity, ω is the pore diameter, β is the angular frequency, and η is the porosity constant. At low frequencies, omitting the imaginary part in equation (16), the impedance characteristic formula of the pores in the flexible thin-film porous sound-absorbing material is simplified by equation (16): In equation (17), Z Rs The impedance characteristics of the pores in a flexible, thin-film porous sound-absorbing material; The process of constructing the transmission impedance of flexible thin-film porous sound-absorbing materials is as follows: Combining equation (15) and equation (17), the transmission impedance of the flexible thin-film porous sound-absorbing material can be obtained:

6. The method for obtaining the sound absorption coefficient of a composite sound-absorbing structure requiring only material flow resistance and areal density, as described in claim 4, is characterized in that... K c and Z c The specific calculation formula is as follows: ω=2πf (21) In equations (19), (20), and (21), ρ0, c0, f, σ, and ω represent air density, sound velocity in air, sound frequency, flow resistance of the porous sound-absorbing material, and angular frequency, respectively.

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