Acoustic testing method and system for flexible material

Abstract

The invention relates to an acoustic testing method and system for a flexible material, and the method comprises the steps: placing the flexible material in a sleeve, placing the sleeve in an impedance tube, and constructing the sound wave sound pressure of the flexible material with the sleeve in the impedance tube, the sound wave sound pressure comprises incident sound wave sound pressure and sound wave sound pressure returned after the action of a flexible material; the sound wave sound pressure returned after the action of the flexible material is expressed by Bessel series; constructing an air medium molecule vibration speed according to the sound wave sound pressure represented by the Bessel series; solving the returned sound wave pressure and air medium molecule vibration speed by using the sound wave pressure and the air medium molecule vibration speed represented by the Bessel series; and S5, solving the acoustic impedance rate of the flexible material according to the solved returned sound wave pressure and the air medium molecule vibration speed, and solving the sound absorption coefficient based on the acoustic impedance rate. According to the invention, the acoustic performance of the fluffy porous acoustic material can be effectively tested.

Description

Technical Field

[0001] The present invention relates to the technical field of acoustic material testing, and in particular to an acoustic testing method and system for flexible materials. Background Art

[0002] Impedance tube testing is a widely used method for measuring material acoustic properties, such as acoustic impedance and sound absorption coefficient. Traditional impedance tube testing typically requires the sample to be placed directly inside the tube for measurement. This method is particularly suitable for rigid, regularly shaped samples, ensuring stability and consistency throughout the test.

[0003] However, when the test object is a loose or elastic material (such as a fluffy porous material), the traditional impedance tube testing method (placing the sample directly into the impedance tube for measurement) has obvious limitations and shortcomings. After being placed in the impedance tube, such materials cannot maintain a fixed shape and thickness due to their physical properties (such as low density, high elasticity, and easy deformation). For example, fluffy porous materials may compress or collapse under the action of gravity, and may undergo dynamic deformation under the excitation of air flow or sound waves. These changes lead to differences in the actual state of the sample during each test, significantly reducing the repeatability and reliability of the experiment.

[0004] Furthermore, uncertainty in the sample's state directly impacts the accuracy of acoustic parameter measurements. Variations in sample thickness and shape alter the reflection and transmission characteristics of sound waves on the sample surface, leading to fluctuations in measurement results. This fluctuation not only makes it difficult to effectively compare data between tests but can also obscure the material's true acoustic performance, complicating its evaluation and application. For example, in industrial design, an inability to accurately determine a material's sound absorption coefficient makes it difficult to predict its performance in actual acoustic environments, hindering the optimization of a product's acoustic performance.

[0005] When measuring the acoustic parameters of loose or elastic materials, the existing impedance tube testing method cannot effectively control the state of the sample, resulting in poor experimental repeatability and low data reliability, which limits its further application in related fields. Summary of the Invention

[0006] To this end, the technical problem to be solved by the present invention is to overcome the problem that the impedance tube testing method in the prior art cannot control the state of the sample when measuring the acoustic parameters of loose or elastic materials, resulting in poor experimental repeatability and low data reliability.

[0007] To solve the above technical problems, the present invention provides an acoustic testing method for flexible materials, comprising:

[0008] Step S1: placing a flexible material in a sleeve, and then placing the sleeve inside an impedance tube, to create a sound wave pressure inside the impedance tube with the sleeve flexible material, wherein the sound wave pressure includes the sound pressure of the incident sound wave and the sound pressure of the sound wave returned after being acted upon by the flexible material;

[0009] Step S2: expressing the sound pressure of the sound wave returned after being acted upon by the flexible material using a Bessel series;

[0010] Step S3: constructing the air medium molecular vibration velocity according to the sound pressure of the sound wave represented by the Bessel series;

[0011] Step S4: using the sound pressure of the sound wave and the vibration velocity of the air medium molecules represented by the Bessel series to solve the returned sound pressure of the sound wave and the vibration velocity of the air medium molecules;

[0012] Step S5: Calculate the acoustic impedance of the flexible material based on the calculated sound pressure of the returned sound wave and the vibration velocity of air medium molecules, and calculate the sound absorption coefficient based on the acoustic impedance.

[0013] In one embodiment of the present invention, the sound pressure of the incident sound wave and the sound pressure of the sound wave returned after being acted upon by the flexible material are expressed as:

[0014] P in =p0e jkx (1)

[0015] P re =P r1 +P r2 (2)

[0016] Among them, P in is the incident sound pressure, k is the wave number, p0 is the initial sound amplitude, x is the x-axis coordinate, P re is the sound pressure of the sound wave returned after the flexible material acts on it, P r1 is the sound pressure of the reflected sound wave after passing through the flexible material in the sleeve, P r2 It is the sound pressure of the scattered sound wave after being acted upon by the flexible material.

[0017] In one embodiment of the present invention, in step S2, the sound pressure of the sound wave returned after being acted upon by the flexible material is expressed using a Bessel series, specifically:

[0018] The sound pressure P of the sound wave returned after the flexible material re The reflected sound pressure P r1 Expressed as:

[0019] P r1 =p0e jkx (2.a)

[0020] The sound pressure P of the sound wave returned after the flexible material reThe scattered sound pressure P r2 It can be expressed as a Bessel series:

[0021]

[0022] in, k x is the wave number in the x-axis direction; α n is the nth eigenvalue of the Bessel function; J0 is the 0th order Bessel function; R is the inner radius of the impedance tube; r is the coordinate position of any point in the coordinate system constructed along the direction pointing to the edge of the sleeve with the center of the circle on the front surface of the flexible material as the starting point; A0, A n is the mode coefficient, which determines the amplitude of each mode;

[0023] When λ>>R, λ is the sound length of the sound wave, R is the inner radius of the impedance tube, then the wave number k in the x-axis direction is x Expressed as:

[0024]

[0025] In one embodiment of the present invention, step S3 constructs the air medium molecular vibration velocity based on the sound pressure of the sound wave represented by the Bessel series, specifically:

[0026] From the equation of motion Derive formula (4.b):

[0027]

[0028] Where ρ is the air density; V is the vibration velocity of the air medium molecules to be solved and V represents V x , V x is the vibration velocity of air medium molecules in the horizontal axis direction; P is the sound wave equation and P is expressed in formula (2); t is time, c is the air sound speed;

[0029] Substituting equations (2), (2.a), (2.b), and (3) into equation (4.b) yields equation (6):

[0030]

[0031] In one embodiment of the present invention, step S4 uses the sound pressure of the sound wave and the vibration velocity of the air medium molecules represented by the Bessel series to solve the returned sound pressure of the sound wave and the vibration velocity of the air medium molecules, specifically:

[0032] Since the sleeve is rigid, the boundary condition formula (7) is:

[0033]

[0034] Where R0 is the inner radius of the sleeve, and Equation (7) is expanded into a zero-order Bessel series:

[0035] And compare the coefficients with formula (6) to obtain the coefficients p0A0 and p0A n Value:

[0036]

[0037] Substituting equation (8) into equation (6) yields the vibration velocity of air molecules at x = 0, which satisfies:

[0038]

[0039] Substituting equation (8) into equation (2.b) yields the scattered wave pressure p at x = 0: r2 ,satisfy:

[0040]

[0041] According to the obtained formula (10) and formula (2.a), the sound pressure P of the sound wave returned after the flexible material is obtained re .

[0042] In one embodiment of the present invention, step S5 solves the acoustic impedance of the flexible material based on the solved returned sound wave pressure and the air medium molecule vibration velocity, specifically:

[0043] The acoustic impedance of the flexible material and sleeve combined is measured as follows:

[0044]

[0045] Substituting equations (1), (2), (9), and (10) into equation (11), we obtain equation (12):

[0046]

[0047] The acoustic impedance of the flexible material to be measured is:

[0048]

[0049] Substituting equations (1), (2), (9), and (10) into equation (13), we obtain equation (14):

[0050]

[0051] in, Expressed as:

[0052]

[0053] The acoustic impedance Z′ of the flexible material to be determined is obtained by solving equations (12) and (14) together: s for:

[0054]

[0055] In one embodiment of the present invention, the step S5 is to solve the sound absorption coefficient based on the acoustic impedance, specifically: the acoustic impedance Z′ of the flexible material is used to calculate the sound absorption coefficient. s Solve for the sound absorption coefficient α of flexible materials (吸声系数) for:

[0056]

[0057] To solve the above technical problems, the present invention provides an acoustic testing system for flexible materials, comprising:

[0058] The first construction module is used to place the flexible material in the sleeve, and then place the sleeve inside the impedance tube to construct the sound pressure of the sound wave with the sleeve flexible material in the impedance tube, wherein the sound pressure of the sound wave includes the sound pressure of the incident sound wave and the sound pressure of the sound wave returned after being acted upon by the flexible material;

[0059] The first representation module is used to represent the sound pressure of the sound wave returned after being acted upon by the flexible material using a Bessel series;

[0060] The second building block is used to construct the vibration velocity of air medium molecules according to the sound pressure of the sound wave represented by the Bessel series;

[0061] The first solving module is used to solve the returned sound wave pressure and air medium molecule vibration velocity using the sound wave pressure and air medium molecule vibration velocity represented by the Bessel series;

[0062] The second solving module is used to solve the acoustic impedance of the flexible material according to the solved sound pressure of the returned sound wave and the vibration speed of the air medium molecules, and solve the sound absorption coefficient based on the acoustic impedance.

[0063] To solve the above technical problems, the present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the above-mentioned method for acoustic testing of flexible materials are implemented.

[0064] To solve the above technical problems, the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the above-mentioned method for acoustic testing of flexible materials are implemented.

[0065] The above technical solution of the present invention has the following advantages over the prior art:

[0066] The acoustic testing method for flexible materials constructed by the present invention places the sample to be tested (flexible material) in a sleeve and effectively fixes the sample through the sleeve. The sleeve can accurately control the shape and thickness of the sample to be tested, ensuring that the physical state of the sample remains consistent during each test. This consistency significantly reduces the test error caused by changes in the sample state, making the test results of different times more repeatable and comparable. Researchers can perform analysis based on stable data, thereby more accurately evaluating the acoustic performance of the material, thereby improving the stability and accuracy of the test results.

[0067] The present invention uses the support of the sleeve on the flexible material to accurately measure the acoustic properties of these flexible materials, thereby breaking through the limitations of the traditional impedance tube testing method and significantly expanding its application range;

[0068] The present invention constructs an acoustic testing method for flexible materials, which can ensure that the acoustic testing of flexible materials has higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to make the contents of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings.

[0070] Figure 1 It is a flow chart of the method of the present invention;

[0071] Figure 2 This is a schematic diagram of the sleeve structure in an embodiment of the present invention;

[0072] Figure 3 Schematic diagram of the sound wave pressure in the impedance tube with a sleeve flexible material in an embodiment of the present invention;

[0073] Figure 4 2 is a schematic diagram showing that the flexible material is built into the sleeve in an embodiment of the present invention;

[0074] Figure 5 Schematic diagram of the real part of the acoustic impedance ratio before and after correction in an embodiment of the present invention;

[0075] Figure 6 Schematic diagram of the imaginary part of acoustic impedance ratio before and after correction in an embodiment of the present invention;

[0076] Figure 7 Schematic diagram of the sound absorption coefficient before and after correction in an embodiment of the present invention. DETAILED DESCRIPTION

[0077] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0078] Example 1

[0079] Reference Figure 1 The present invention relates to an acoustic testing method for flexible materials, comprising:

[0080] Step S1: placing a flexible material (e.g., a fluffy porous acoustic material) in a sleeve, and then placing the sleeve inside an impedance tube to create a sound wave pressure inside the impedance tube with the sleeve flexible material, wherein the sound wave pressure includes the incident sound wave pressure and the sound wave pressure returned after being acted upon by the flexible material, and the sleeve is used to fix the flexible material;

[0081] Step S2: expressing the sound pressure of the sound wave returned after being acted upon by the flexible material using a Bessel series;

[0082] Step S3: constructing the air medium molecular vibration velocity according to the sound pressure of the sound wave represented by the Bessel series;

[0083] Step S4: using the sound pressure of the sound wave and the vibration velocity of the air medium molecules represented by the Bessel series to solve the returned sound pressure of the sound wave and the vibration velocity of the air medium molecules;

[0084] Step S5: Calculate the acoustic impedance of the flexible material based on the calculated sound pressure of the returned sound wave and the vibration velocity of air medium molecules, and calculate the sound absorption coefficient based on the acoustic impedance.

[0085] The following is a detailed introduction to this embodiment:

[0086] The schematic diagram of the sleeve (also called sample shell) of this embodiment is shown in Figure 2 , in the shape of a hollow cylinder, and a gap is opened in the length direction of the sleeve, so that the diameter of the sleeve can be slightly larger than the diameter of the impedance tube, and the sleeve has a certain flexibility, so that when the sleeve is placed inside the impedance tube, it can fit closely with the inner wall of the impedance tube.

[0087] like Figure 3 As shown, assuming that the inner radius of the impedance tube is R, the outer wall of the sleeve is close to the inner wall of the impedance tube, then the sleeve (i.e. Figure 3 The outer radius of the sample shell in the sleeve is R, and the inner radius of the sleeve is R0. Since the flexible material (i.e., the sample) is disposed inside the sleeve and closely adheres to the inner wall of the sleeve, the sample radius is considered to be R0 in this embodiment.

[0088] Assume that the sound pressure of the incident sound wave and the sound pressure of the sound wave returned after being acted upon by the flexible material are expressed in the form of formula (1) and formula (2).

[0089] P in =p0e jkx (1)

[0090] P re =P r1 +Pr2 (2)

[0091] Among them, P in is the incident sound pressure, k is the wave number, p0 is the initial sound amplitude, x is the x-axis coordinate, P re is the sound pressure of the sound wave returned after the flexible material acts on it, P r1 is the sound pressure of the reflected sound wave after passing through the flexible material in the sleeve, P r2 It is the sound pressure of the scattered sound wave after being acted upon by the flexible material.

[0092] Step S2 uses the Bessel series to express the sound pressure of the sound wave returned after the flexible material is acted upon, specifically: P r1 and P r2 The specific forms of are shown in formulas (2.a) and (2.b), and P r2 It is expressed as a Bessel series.

[0093] P r1 =p0e jkx (2.a)

[0094]

[0095] in, k x is the wave number in the x-axis direction; α n is the nth eigenvalue of the Bessel function; J0 is the 0th order Bessel function; R is the inner radius of the impedance tube; r is the coordinate position of any point in the coordinate system constructed along the direction pointing to the edge of the sleeve with the center of the circle on the front surface of the flexible material as the starting point; A0, A n is the mode coefficient, which determines the amplitude of each mode.

[0096] When λ>>R, λ is the sound length of the sound wave, and R is the inner radius of the impedance tube, then under the long wave approximation, Figure 3 The wave number k in the x-axis direction x It can be approximately expressed as:

[0097]

[0098] Step S3 constructs the air medium molecular vibration velocity based on the sound pressure represented by the Bessel series, specifically:

[0099] From the equation of motion Equations (4.a) and (4.b) can be derived.

[0100]

[0101] Where ρ is the air density; V is the vibration velocity of the air medium molecules to be solved and V represents V r or Vx , V r is the vibration velocity of air medium molecules in the vertical direction, V x is the vibration velocity of air medium molecules in the horizontal axis direction; P is the sound wave equation and P is expressed in formula (2); t is time, and c is the air sound speed.

[0102] Substituting equation (2) (here, equation (2) already includes equations (2.a), (2.b), and (3)) into equation (4.a) yields equation (5).

[0103]

[0104] When r=R, V r =0 is substituted into formula (5), and we get J1(α n )=0, which proves that α n is the nth eigenvalue of the Bessel function;

[0105] Substituting equation (2) into equation (4.b) yields equation (6).

[0106]

[0107] Step S4 uses the sound pressure of the sound wave and the vibration velocity of the air medium molecules represented by the Bessel series to solve the returned sound pressure of the sound wave and the vibration velocity of the air medium molecules, specifically:

[0108] Since the sleeve is rigid, there is a boundary condition (7).

[0109]

[0110] Expand equation (7) into a zero-order Bessel series:

[0111] And compare the coefficients with formula (6) to obtain the coefficients p0A0 and p0A n The value of , that is, formula (8).

[0112]

[0113] Substituting equation (8) into equation (6) yields the vibration velocity of air medium molecules at x=0, which is equation (9).

[0114]

[0115] Substituting equation (8) into equation (2.b) yields the scattered wave pressure p at x = 0: r2 , that is, formula (10).

[0116]

[0117] So far, this embodiment obtains the sound pressure P of the sound wave returned after the flexible material is acted upon according to the obtained formula (10) and formula (2.a): re .

[0118] In this embodiment, the acoustic impedance of the combination of the test sample and the sleeve, as well as the acoustic impedance of the sample alone, can be calculated based on the calculated sound pressure and x-axis sound velocity. Given that this embodiment can actually measure the actual acoustic impedance of the combination of the test sample and the sleeve, the actual acoustic impedance of the sample alone can be obtained by modifying the theoretical equations described above.

[0119] Step S5 solves the acoustic impedance of the flexible material based on the solved returned sound wave pressure and the vibration velocity of the air medium molecules, specifically:

[0120] If you want to solve the acoustic impedance of the sample to be tested, the acoustic impedance of the combination of the sample to be tested and the sleeve measured in the impedance tube (referring to the far field of the impedance tube) is in the form of formula (11).

[0121]

[0122] Substituting equations (1), (2), (9), and (10) into equation (11) yields equation (12).

[0123]

[0124] At the reflecting surface (the front surface of the sample, i.e., the surface opposite to the rigid wall of the impedance tube), the acoustic impedance of the flexible material to be determined (the acoustic impedance of the object to be measured) is:

[0125]

[0126] Substituting equations (1), (2), (9), and (10) into equation (13) yields equation (14).

[0127]

[0128] Among them, the additional impedance It is in the form of formula (15).

[0129]

[0130] The acoustic impedance ratio (the acoustic impedance ratio of the sample to be tested) Z′ can be obtained by solving equations (12) and (14) together: s It is formula (16).

[0131]

[0132] The acoustic impedance Z' of the sample to be tested s Then the sound absorption coefficient α of the object to be measured can be obtained(吸声系数) It is formula (17).

[0133]

[0134] It should be noted that formula (16) converts the Z of formula (12) into s and Z′ of the theory of formula (14) s In conjunction with the actual measured acoustic impedance of the sample and sleeve (Z s By substituting (16) into formula (16), we can calculate the corrected Z′ s .

[0135] The experimental analysis is as follows:

[0136] Now, a fluffy porous material (called flexible material in this embodiment) is measured. Since it does not have good plasticity, it is supported by a flexible sleeve. Figure 4 shown.

[0137] Now measure the flow resistivity and sound absorption coefficient of the material to be tested plus the sleeve. Since the inner radius of the impedance tube is 29mm and the inner radius of the sleeve is 27mm, the additional impedance can be obtained by formula (15): is 0.0141. Then, the corrected acoustic impedance Z′ can be obtained by using formula (16): s , specifically Figure 5 、 Figure 6 As shown. Figure 5 、 Figure 6 It can be seen that the acoustic impedance of the material with the sleeve is slightly higher than the actual acoustic impedance, indicating that if the fixed sleeve is not corrected, the real and imaginary parts of the directly measured acoustic impedance ratio will be higher than the actual value.

[0138] In this embodiment, the acoustic impedance Z' s The sound absorption coefficient of the sample to be tested can be calculated, such as Figure 7 As shown, from Figure 7 It can be seen that the corrected sound absorption coefficient will fluctuate based on the sound absorption coefficient before correction, indicating that if the fixed sleeve is not corrected, the directly measured sound absorption coefficient is inaccurate.

[0139] Example 2

[0140] This embodiment provides an acoustic testing system for flexible materials, including:

[0141] The first construction module is used to place the flexible material in the sleeve, and then place the sleeve inside the impedance tube to construct the sound pressure of the sound wave with the sleeve flexible material in the impedance tube, wherein the sound pressure of the sound wave includes the sound pressure of the incident sound wave and the sound pressure of the sound wave returned after being acted upon by the flexible material;

[0142] The first representation module is used to represent the sound pressure of the sound wave returned after being acted upon by the flexible material using a Bessel series;

[0143] The second building block is used to construct the vibration velocity of air medium molecules according to the sound pressure of the sound wave represented by the Bessel series;

[0144] The first solving module is used to solve the returned sound wave pressure and air medium molecule vibration velocity using the sound wave pressure and air medium molecule vibration velocity represented by the Bessel series;

[0145] The second solving module is used to solve the acoustic impedance of the flexible material according to the solved sound pressure of the returned sound wave and the vibration speed of the air medium molecules, and solve the sound absorption coefficient based on the acoustic impedance.

[0146] Example 3

[0147] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the flexible material acoustic testing method described in the first embodiment are implemented.

[0148] Example 4

[0149] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the method for acoustic testing of flexible materials described in the first embodiment are implemented.

[0150] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiment of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal translation scripting language JavaScript, etc.

[0151] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0152] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0153] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0154] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0155] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for acoustic testing of flexible materials, characterized by: include: Step S1: placing a flexible material in a sleeve, and then placing the sleeve inside an impedance tube, to create a sound wave pressure inside the impedance tube with the sleeve flexible material, wherein the sound wave pressure includes the sound pressure of the incident sound wave and the sound pressure of the sound wave returned after being acted upon by the flexible material; Step S2: expressing the sound pressure of the sound wave returned after being acted upon by the flexible material using a Bessel series; Step S3: constructing the air medium molecular vibration velocity according to the sound pressure of the sound wave represented by the Bessel series; Step S4: using the sound pressure of the sound wave and the vibration velocity of the air medium molecules represented by the Bessel series to solve the returned sound pressure of the sound wave and the vibration velocity of the air medium molecules; Step S5: Calculate the acoustic impedance of the flexible material based on the calculated sound pressure of the returned sound wave and the vibration velocity of air medium molecules, and calculate the sound absorption coefficient based on the acoustic impedance.

2. The acoustic testing method for flexible materials according to claim 1, characterized in that: The sound pressure of the incident sound wave and the sound pressure of the sound wave returned after the flexible material acts on it are expressed as: P in =p0e jkx (1) P re =P r1 +P r2 (2) Among them, P in is the incident sound pressure, k is the wave number, p0 is the initial sound amplitude, x is the x-axis coordinate, P re is the sound pressure of the sound wave returned after the flexible material acts on it, P r1 is the sound pressure of the reflected sound wave after passing through the flexible material in the sleeve, P r2 It is the sound pressure of the scattered sound wave after being acted upon by the flexible material.

3. The acoustic testing method for flexible materials according to claim 2, characterized in that: In step S2, the sound pressure of the sound wave returned after being acted upon by the flexible material is expressed using the Bessel series, specifically: The sound pressure P of the sound wave returned after the flexible material re The reflected sound pressure P r1 Expressed as: P r1 =p0e jkx (2.a) The sound pressure P of the sound wave returned after the flexible material re The scattered sound pressure P r2 It can be expressed as a Bessel series: in, k x is the wave number in the x-axis direction; α n is the nth eigenvalue of the Bessel function; J0 is the 0th order Bessel function; R is the inner radius of the impedance tube; r is the coordinate position of any point in the coordinate system constructed along the direction pointing to the edge of the sleeve with the center of the circle on the front surface of the flexible material as the starting point; A0, A n is the mode coefficient, which determines the amplitude of each mode; When λ>>R, λ is the sound length of the sound wave, R is the inner radius of the impedance tube, then the wave number k in the x-axis direction is x Expressed as:

4. The acoustic testing method for flexible materials according to claim 3, wherein: The step S3 constructs the air medium molecular vibration velocity based on the sound pressure of the sound wave represented by the Bessel series, specifically: From the equation of motion Derive formula (4.b): Where ρ is the air density; V is the vibration velocity of the air medium molecules to be solved and V represents V x , V x is the vibration velocity of air medium molecules in the horizontal axis direction; P is the sound wave equation and P is expressed in formula (2); t is time, c is the air sound speed; Substituting equations (2), (2.a), (2.b), and (3) into equation (4.b) yields equation (6):

5. The acoustic testing method for flexible materials according to claim 4, characterized in that: The step S4 uses the sound pressure of the sound wave and the vibration velocity of the air medium molecules represented by the Bessel series to solve the returned sound pressure of the sound wave and the vibration velocity of the air medium molecules, specifically: Since the sleeve is rigid, the boundary condition formula (7) is: Where R0 is the inner radius of the sleeve, and Equation (7) is expanded into a zero-order Bessel series: And compare the coefficients with formula (6) to obtain the coefficients p0A0 and p0A n Value: Substituting equation (8) into equation (6) yields the vibration velocity of air molecules at x = 0, which satisfies: Substituting equation (8) into equation (2.b) yields the scattered wave pressure p at x = 0: r2 ,satisfy: According to the obtained formula (10) and formula (2.a), the sound pressure P of the sound wave returned after the flexible material is obtained re .

6. The acoustic testing method for flexible materials according to claim 5, characterized in that: The step S5 solves the acoustic impedance of the flexible material based on the solved returned sound wave pressure and the vibration velocity of the air medium molecules, specifically: The acoustic impedance of the flexible material and sleeve combined is measured as follows: Substituting equations (1), (2), (9), and (10) into equation (11), we obtain equation (12): The acoustic impedance of the flexible material to be measured is: Substituting equations (1), (2), (9), and (10) into equation (13), we obtain equation (14): in, Expressed as: The acoustic impedance Z of the flexible material to be determined is obtained by solving equations (12) and (14) together: ′ s for:

7. The acoustic testing method for flexible materials according to claim 6, characterized in that: The step S5 is to solve the sound absorption coefficient based on the acoustic impedance, specifically: the acoustic impedance Z of the flexible material is used to calculate the sound absorption coefficient. ′ s Solve for the sound absorption coefficient α of flexible materials (吸声系数) for:

8. An acoustic testing system for flexible materials, characterized by: including, characterized by: The first construction module is used to place the flexible material in the sleeve, and then place the sleeve inside the impedance tube to construct the sound pressure of the sound wave with the sleeve flexible material in the impedance tube, wherein the sound pressure of the sound wave includes the sound pressure of the incident sound wave and the sound pressure of the sound wave returned after being acted upon by the flexible material; The first representation module is used to represent the sound pressure of the sound wave returned after being acted upon by the flexible material using a Bessel series; The second building block is used to construct the vibration velocity of air medium molecules according to the sound pressure of the sound wave represented by the Bessel series; The first solving module is used to solve the returned sound wave pressure and air medium molecule vibration velocity using the sound wave pressure and air medium molecule vibration velocity represented by the Bessel series; The second solving module is used to solve the acoustic impedance of the flexible material according to the solved sound pressure of the returned sound wave and the vibration speed of the air medium molecules, and solve the sound absorption coefficient based on the acoustic impedance.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the acoustic testing method for flexible materials according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the acoustic testing method for flexible materials according to any one of claims 1 to 7 are implemented.

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