Prediction method of sound absorption coefficient of quasi-zero stiffness and helmholtz resonator combined structure

Abstract

The application relates to a quasi-zero stiffness and Helmholtz resonant cavity combined structure sound absorption coefficient prediction method, belonging to the field of acoustics. The quasi-zero stiffness and Helmholtz resonant cavity combined structure sound absorption coefficient prediction method comprises the following steps: after a quasi-zero stiffness and Helmholtz resonant cavity combined structure is constructed, a proxy model reflecting the relationship between the structural parameters of the quasi-zero stiffness and the sound impedance rate of the bottom plate of the Helmholtz resonant cavity is constructed, and an analytical model reflecting the relationship between the sound absorption coefficient and the sound impedance rate of the bottom plate of the Helmholtz resonant cavity is constructed; then, the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combined structure is predicted by combining the proxy model and the analytical model; the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combined structure can be quickly and efficiently predicted, so that the low-frequency sound absorption performance and compact size optimization of the combined structure are realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of acoustics, in particular, to a sound absorption coefficient prediction method for a quasi-zero stiffness and Helmholtz resonator combined structure. BACKGROUND

[0002] The Helmholtz resonator structure has become a research object of continuous attention in the fields of acoustics engineering and physics due to its unique acoustic resonance characteristics. The traditional Helmholtz resonator structure can realize the energy aggregation and dissipation regulation of sound waves at a specific frequency through the coupling of the geometric parameters of the cavity and the neck. By finely adjusting the length, diameter or streamline design of the throat pipe and optimizing the cavity volume, shape or built-in acoustic lining, the noise reduction performance of the resonator at the low frequency band can be effectively improved.

[0003] However, while the Helmholtz resonator improves the low-frequency sound absorption performance, it also leads to an increase in the size of the structure, which is contrary to the actual engineering requirements. In the engineering field, it is usually desired that the Helmholtz resonator has a wide sound absorption frequency band and is miniaturized. In order to expand the bandwidth, many researchers form a wideband response spectrum by connecting or connecting multiple Helmholtz resonators with different resonance frequencies (such as different throat pipe lengths or cavity volumes). For the miniaturization design of the Helmholtz resonator structure, it is usually required that the structure has a low dimensionless thickness. However, the resonator structure of the connected or parallel structure cannot achieve this goal. In order to further reduce the dimensionless thickness of the resonator, another feasible solution is to change the acoustic impedance boundary condition of the resonator bottom plate to achieve the characteristics of small size and high sound absorption, that is, to combine the quasi-zero stiffness and Helmholtz resonator structure. However, this new structure is relatively complex, and the time cost of obtaining the sound absorption coefficient by numerical simulation is high. SUMMARY

[0004] The purpose of the present application is to provide a sound absorption coefficient prediction method for a quasi-zero stiffness and Helmholtz resonator combined structure, which can quickly and efficiently predict the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combined structure, and realize the optimization of low-frequency sound absorption performance and compact size of the combined structure.

[0005] The present application is achieved in the following way:

[0006] The present application provides a sound absorption coefficient prediction method for a quasi-zero stiffness and Helmholtz resonator combined structure, comprising the following steps:

[0007] Constructing a combined structure of quasi-zero stiffness and Helmholtz resonator;

[0008] Constructing a proxy model reflecting the relationship between the structural parameters of quasi-zero stiffness and the acoustic impedance rate of the bottom plate of the Helmholtz resonator.

[0009] An analytical model reflecting the relationship between the sound absorption coefficient and the Helmholtz resonator bottom plate acoustic impedance ratio is constructed.

[0010] The sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combined structure is predicted by combining the proxy model and the analytical model.

[0011] In some optional embodiments, the quasi-zero stiffness bottom is connected to the top surface of the Helmholtz resonator bottom plate in the combined structure.

[0012] In some optional embodiments, the quasi-zero stiffness includes a top plate and a hollow conical shell arranged coaxially, and a connecting pipe connected to the top plate and the hollow conical shell at both ends, respectively. The structural parameters of the quasi-zero stiffness include the outer diameter of the connecting pipe, the inner radius of the connecting pipe, the radius of the hollow conical shell internal cavity outside the connecting pipe, the shell thickness, the height of the hollow conical shell internal cavity, and the height of the connecting pipe.

[0013] In some optional embodiments, the following formula is used to reflect the relationship between the structural parameters of the quasi-zero stiffness and the Helmholtz resonator bottom plate acoustic impedance ratio:

[0014] ;

[0015] In the formula, z 4 is the Helmholtz resonator bottom plate acoustic impedance ratio; p 4 is the sound pressure on the surface of the Helmholtz resonator bottom plate, p 0 is the air density, c 0 is the air sound speed, u 4 is the particle acoustic vibration speed of the Helmholtz resonator bottom plate; is the difference in force between two points in the quasi-zero stiffness interval, is the displacement between two points in the quasi-zero stiffness interval; S is the Helmholtz resonator bottom plate area; i is the imaginary unit; is the acoustic angular frequency; is the slope of the two points in the quasi-zero stiffness interval.

[0016] In some optional embodiments, the following formula is used to calculate dF :

[0017] ;

[0018] In the formula, b is the outer diameter of the quasi-zero stiffness connecting pipe; t is the quasi-zero stiffness shell thickness; H is the height of the quasi-zero stiffness connecting pipe;h 1 represents the height of the internal cavity of the quasi-zero stiffness hollow conical shell.

[0019] In some alternative implementations, the following formula reflects the relationship between the sound absorption coefficient and the acoustic impedance of the Helmholtz resonant cavity floor:

[0020] ;

[0021] In the formula, α is the sound absorption coefficient when the incident sound wave is a plane wave; R and X Acoustic impedance and acoustic reactance, respectively, represent dimensionless acoustic impedance.

[0022] In some alternative implementations, the dimensionless acoustic impedance and acoustic impedance are calculated using the following formulas. R and X：

[0023] ;

[0024] ;

[0025] In the formula, p j and u j These represent the sound pressure and sound velocity at various points in the composite structure. j Let 1, 2, 3, 4 represent the top of the throat of the Helmholtz resonant cavity, 2 represent the bottom of the throat of the Helmholtz resonant cavity, 3 represent the area between the bottom of the throat of the Helmholtz resonant cavity and the surface of the quasi-zero stiffness top plate, and 4 represent the bottom plate of the Helmholtz resonant cavity. i For imaginary units; T For the transfer matrix, T hole The transfer matrix of the throat ，T section The transfer matrix at the interface between the larynx and the cavity ，T cavity Let be the transfer matrix of the uniform cross-section cavity between the bottom of the throat of the Helmholtz resonant cavity and the surface of the quasi-zero stiffness top plate.

[0026] The beneficial effects of this application are as follows: The method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combination structure provided in this application, after constructing the combination structure of the quasi-zero stiffness and Helmholtz resonator, respectively constructs a surrogate model reflecting the relationship between the structural parameters of the quasi-zero stiffness and the acoustic impedance of the Helmholtz resonator floor and an analytical model reflecting the relationship between the sound absorption coefficient and the acoustic impedance of the Helmholtz resonator floor. Then, the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combination structure is predicted by combining the surrogate model and the analytical model. This method can quickly and efficiently predict the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combination structure, thereby achieving optimization of the low-frequency sound absorption performance and compact size of the combination structure. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 A flowchart illustrating the method for predicting the sound absorption coefficient of a quasi-zero stiffness and Helmholtz resonant cavity combination structure provided in this application embodiment;

[0029] Figure 2 A schematic diagram of the quasi-zero stiffness and Helmholtz resonator combination structure in the sound absorption coefficient prediction method of the quasi-zero stiffness and Helmholtz resonator combination structure provided in the embodiments of this application.

[0030] Figure 3 A schematic diagram of the Helmholtz resonator structure in the method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combination structure provided in the embodiments of this application.

[0031] Figure 4 A schematic diagram of the quasi-zero stiffness structure in the method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combination structure provided in the embodiments of this application;

[0032] Figure 5 The dynamic characteristic curve of quasi-zero stiffness in the method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combination structure provided in the embodiments of this application;

[0033] Figure 6 The quasi-zero stiffness parameter in the method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combined structure provided in the embodiments of this application. h1. The impact on structural mechanical properties;

[0034] Figure 7 The quasi-zero stiffness parameters of the quasi-zero stiffness and Helmholtz resonator cavity combined structure sound absorption coefficient prediction method provided in the embodiments of this application. b Impact on structural mechanical properties;

[0035] Figure 8 The quasi-zero stiffness parameters of the quasi-zero stiffness and Helmholtz resonator cavity combined structure sound absorption coefficient prediction method provided in the embodiments of this application. r Impact on structural mechanical properties;

[0036] Figure 9 The quasi-zero stiffness parameters of the quasi-zero stiffness and Helmholtz resonator cavity combined structure sound absorption coefficient prediction method provided in the embodiments of this application. H Impact on structural mechanical properties;

[0037] Figure 10 The quasi-zero stiffness parameters of the quasi-zero stiffness and Helmholtz resonator cavity combined structure sound absorption coefficient prediction method provided in the embodiments of this application. L Impact on structural mechanical properties;

[0038] Figure 11 The quasi-zero stiffness parameter in the method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combined structure provided in the embodiments of this application. t Impact on structural mechanical properties;

[0039] Figure 12 Morris sensitivity analysis results in the method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combination structure provided in the embodiments of this application;

[0040] Figure 13 The method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combined structure provided in this application embodiment selects four non-sample schemes outside the parameter range, at the edge of the range, and at the center of the range to construct a validation set to verify the error of the surrogate model.

[0041] Figure 14 A schematic diagram of the Helmholtz resonator node in the method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combined structure provided in the embodiments of this application.

[0042] Figure 15 The method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combination structure provided in the embodiments of this application predicts the sound absorption performance of the quasi-zero stiffness and Helmholtz resonator combination structure.

[0043] Figure 16 A comparison diagram of the predicted sound absorption performance of the quasi-zero stiffness and Helmholtz resonator combination structure and the sound absorption performance of the Helmholtz resonator with an extension tube in the method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combination structure provided in the embodiments of this application. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of this application, but not all embodiments.

[0045] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0046] The following detailed description of the features and performance of the method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combination structure of this application is provided in conjunction with embodiments.

[0047] like Figure 1 As shown in the figure, this application provides a method for predicting the sound absorption coefficient of a quasi-zero stiffness and Helmholtz resonator combined structure, including the following steps:

[0048] Step S1, construct as follows Figure 2 The structure shown is a combination of a quasi-zero stiffness plate and a Helmholtz resonator, with the bottom of the quasi-zero stiffness plate connected to the top surface of the bottom plate of the Helmholtz resonator.

[0049] like Figure 3 As shown, the Helmholtz resonator structure includes a hollow cylinder and a throat located inside the cylinder. The throat is coaxially arranged with the cylinder and its top is connected to the top and bottom wall of the cylinder. The throat connects the inside and outside of the cylinder. The main geometric parameters of the Helmholtz resonator include the top thickness of the cylinder. d =1.01mm, throat length E =12.21mm, throat radius R n =0.93mm, length of the internal resonant cavity of the cylinder l c =18.99mm, radius of the internal resonant cavity of the cylinder R c =5.5mm, cylinder sidewall thickness T=2mm, the Helmholtz resonant cavity is connected to the quasi-zero stiffness via an elastic base plate at the bottom of the cavity.

[0050] like Figure 4 As shown, the quasi-zero stiffness structure includes a top plate and a hollow conical shell arranged coaxially, and connecting pipes at both ends connecting the top plate and the hollow conical shell respectively. The conical shell contains a conical cavity, and the bottom of the connecting pipes communicates with the conical cavity. The main geometric parameters of the quasi-zero stiffness include the outer diameter of the connecting pipes. b =2.5mm, inner radius of connecting pipe r =0.56mm, the radius of the internal cavity of the hollow conical shell outside the connecting pipe L =3.75mm, shell thickness t =0.5mm, internal cavity height of hollow conical shell h 1 = 0.75mm and the height of the connecting pipe H = 2.25mm.

[0051] It is worth noting that, in the dimensional design of the combined structure of the quasi-zero stiffness structure and the Helmholtz resonator, a certain space was deliberately reserved between the throat and the quasi-zero stiffness structure to effectively avoid contact between them. Regarding material selection, the quasi-zero stiffness structure is made of low-density polyethylene foam with an elastic modulus E = 0.01 MPa and a Poisson's ratio... v =0.3, density p =100kg / m 3 The hyperelastic properties of this material can effectively maintain the quasi-zero stiffness state of the hollow conical shell structure, but it is not the only material that can be selected in practice.

[0052] Step S2: Construct a surrogate model that reflects the relationship between the structural parameters of quasi-zero stiffness and the acoustic impedance of the Helmholtz resonant cavity floor.

[0053] S201. The constructed quasi-zero stiffness and Helmholtz resonant cavity combination structure adjusts the acoustic impedance of the Helmholtz resonant cavity floor plate through the dynamic characteristics of the quasi-zero stiffness structure. z 4. It breaks through the limitations of traditional Helmholtz resonators that cannot simultaneously accommodate small size and low resonant frequency.

[0054] Therefore, the dimensionless acoustic impedance of the Helmholtz resonant cavity floor plate z The definition of 4 is:

[0055] (1)

[0056] In the formula, p 4 represents the sound pressure level on the surface of the Helmholtz resonant cavity floor. p 0 represents the density of air. c0 represents the speed of sound in air. u 4 represents the particle acoustic velocity of the bottom plate of the Helmholtz resonant cavity.

[0057] Figure 5 The figure shows the dynamic characteristic curves of a quasi-zero stiffness structure. The AB interval is called the quasi-zero stiffness interval, which is defined as the force difference between points A and B. The displacement between points A and B in the quasi-zero stiffness interval is defined as The slope of line segment AB is defined as Combining the above characteristics and the definition of equation (1), the acoustic impedance of the Helmholtz resonant cavity floor is further obtained. z 4 can be represented as:

[0058] (2)

[0059] In the formula, S The area of ​​the Helmholtz resonant cavity floor plate; i For imaginary units; ω is the angular frequency of the sound wave.

[0060] S202, Parameter sensitivity analysis;

[0061] Six structural parameters for quasi-zero stiffness H , r ,t, L , h 1. b Conduct dynamic characteristic analysis, such as Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 As shown, the results indicate that the two most important parameters affecting the mechanical properties of quasi-zero stiffness structures are: t and h 1. Because changes in these two parameters significantly affect the mechanical range of quasi-zero stiffness; the three relatively minor parameters are... L , b and H ; Structural parameters r It has almost no effect on the quasi-zero stiffness characteristics of the structure. Based on the above structural analysis, for H , r ,t, L , h 1. b Further sensitivity analysis was conducted using the Morris method.

[0062] The Morris method evaluates the average impact of each input parameter on the output response by calculating the elementary effects (EE) of each input parameter. μ* ) and nonlinear / interaction effects ( σ Its core steps include:

[0063] 1. Trajectory Generation: Generate multiple sampling points along a random path in the parameter space, changing the value of only one parameter each time.

[0064] II. Basic Effect Calculation: Calculate the rate of change in output caused by the change of each parameter. EE i :

[0065] (3)

[0066] In the formula, Indicates the model output; Indicates the magnitude of change in the input variable; Indicates input variables;

[0067] III. Sensitivity Ranking: Based on μ* (Main sort) and σ (Secondary sorting) comprehensively determines the importance of the parameters. μ* and σ Represented as:

[0068] (4)

[0069] (5)

[0070] In the formula, R Indicates the number of trajectories. j Indicates the trajectory number.

[0071] Five trajectories were selected, resulting in a total of 35 simulation schemes. These trajectories all employed a random path generation algorithm, achieving a relatively uniform distribution within the parameter space. This design effectively avoids overfitting in nonlinear regions caused by single paths, thereby improving the robustness and generalization ability of the simulation results. Morris sensitivity analysis results are as follows: Figure 12 As shown, the input parameters of each structure are compared with the output parameters. dF mean μ * and standard deviation σ The results showed that: t ( μ *=19.57) is a highly sensitive parameter. h 1( μ *=4.2) L ( μ *=1.6) and H( μ *=1.22) is a medium sensitivity parameter. b ( μ *=0.88) and r ( μ *=0.57) is a low-sensitivity parameter. Combined with the preceding analysis, it can be concluded that... r It is the least sensitive parameter, and its changes have almost no effect on the dynamic characteristics of a zero-stiffness structure. Therefore, it is ignored when constructing the surrogate model.

[0072] S203, Constructing a response surface proxy model

[0073] There are many ways to construct a surrogate model. This application uses a response surface function to construct the surrogate model, which has the advantages of simplicity and accuracy. Given that higher-order polynomials involve a large number of undetermined coefficients, require a large number of test points, and involve the complexity of building and analyzing approximate models, quadratic polynomial regression is adopted. The general form of the quadratic polynomial model is:

[0074] (6)

[0075] In the formula, Indicates design variables, Represents the response variable. represents the regression coefficients of the intercept term, linear term, interaction term, and quadratic term in the response surface surrogate model, respectively, and n represents the number of design variables.

[0076] In 2 L +2 t + b Under a structural constraint of 11 mm, 50 sample schemes were generated using the Latin hypercube sampling method. The finite element method was then used to perform numerical simulations on each scheme to obtain sample data. Based on this sample data, a quadratic polynomial response surface surrogate model was constructed using the least squares method, yielding... dF The regression equation is:

[0077] (7)

[0078] To evaluate the accuracy of the surrogate model, a validation set was constructed using four non-sample scenarios: outside the parameter range, at the edge of the range, and at the center of the range. Figure 13 As shown, the results indicate that within the parameter range, the maximum prediction error of the response surface model is 0.05 N / m, and the relative error is 6.6%; outside the parameter range, the maximum prediction error of the response surface model is 0.11 N / m, and the relative error is 14.8%.

[0079] S3. Construct an analytical model that reflects the relationship between the sound absorption coefficient and the acoustic impedance of the Helmholtz resonant cavity floor plate;

[0080] like Figure 14 The acoustic impedance analytical model of the bottom plate of the Helmholtz resonator is used. The transfer matrix method is used to analyze the acoustic parameters of each point of the Helmholtz resonator. In the figure, 1 represents the top of the throat of the Helmholtz resonator, 2 represents the bottom of the throat of the Helmholtz resonator, and 3 represents the area between the bottom of the throat of the Helmholtz resonator and the surface of the quasi-zero stiffness top plate. Based on the parameter relationship between the nodes and the boundary conditions at node 4, the acoustic impedance at node 1, i.e. the top of the throat of the Helmholtz resonator, is derived by the following formulas (8) and (9).

[0081] (8)

[0082] (9)

[0083] In the formula, p j and u j These represent the sound pressure and sound velocity at various points in the composite structure. j Let 1, 2, 3, 4 represent the top of the throat of the Helmholtz resonant cavity, 2 represent the bottom of the throat of the Helmholtz resonant cavity, 3 represent the area between the bottom of the throat of the Helmholtz resonant cavity and the surface of the quasi-zero stiffness top plate, and 4 represent the bottom plate of the Helmholtz resonant cavity. i For imaginary units; T For the transfer matrix, T hole The transfer matrix of the throat ，T section The transfer matrix at the interface between the larynx and the cavity ，T cavity Let be the transfer matrix of the uniform cross-section cavity between the bottom of the throat of the Helmholtz resonant cavity and the surface of the quasi-zero stiffness top plate.

[0084] The absorption coefficient when the incident sound wave is a plane wave can be calculated using the following formula.

[0085] (10)

[0086] In the formula, α is the sound absorption coefficient when the incident sound wave is a plane wave; R and X Acoustic impedance and acoustic reactance, respectively, represent dimensionless acoustic impedance.

[0087] Step S4: Combine the surrogate model and analytical model to predict the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combination structure.

[0088] The sound absorption coefficient of the combined structure of quasi-zero stiffness and Helmholtz resonator is predicted by combining surrogate and analytical models, as follows: Figure 15 As shown, the peak frequency trend of the simulation results is consistent with the prediction results, with a slight deviation in peak height. The prediction error is 0.088, which meets the prediction accuracy requirements.

[0089] To verify the low-frequency sound absorption performance of the quasi-zero stiffness and Helmholtz resonator combination structure provided in this application, the sound absorption coefficients of the quasi-zero stiffness and Helmholtz resonator combination structure and the Helmholtz resonator with the same parameters and an extension tube were predicted, and the corresponding sound absorption coefficient curves were plotted, as shown below. Figure 16 As shown, under the same size conditions, compared with the Helmholtz resonant cavity with an extension tube, the resonant frequency of the quasi-zero stiffness and Helmholtz resonant cavity combination structure is reduced by 520 Hz, while the peak value remains basically unchanged. Its dimensionless thickness is reduced by an order of magnitude, only 0.12%.

[0090] The sound absorption coefficient prediction method for the quasi-zero stiffness and Helmholtz resonator combined structure provided in this application can well fit the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combined structure by combining a surrogate model and an analytical model. At the same time, the method constructs a mapping relationship between input and output based on the surrogate model, which has the advantages of strong selectivity and applicability. Under the premise that the number of experiments is not less than the number of undetermined coefficients of the response surface function in the surrogate model, the experimental method, experimental scheme and response surface function can be selected independently according to the actual situation, thereby significantly reducing computational resources and time costs. It can quickly fit the sound absorption coefficient curve and construct a surrogate model with low prediction time cost to predict the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combined structure, which is convenient for subsequent optimization design.

[0091] The embodiments described above are some, but not all, of the embodiments of this application. The detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A method for predicting the sound absorption coefficient of a quasi-zero stiffness and Helmholtz resonator combined structure, characterized in that, Includes the following steps: Construct a combined structure of quasi-zero stiffness and Helmholtz resonant cavity; A surrogate model is constructed to reflect the relationship between the structural parameters of quasi-zero stiffness and the acoustic impedance of the Helmholtz resonant cavity floor. The following formula reflects the relationship between the quasi-zero stiffness structural parameters and the acoustic impedance of the Helmholtz resonant cavity floor: ； In the formula, z 4 represents the acoustic impedance of the Helmholtz resonant cavity floor plate; p 4 represents the sound pressure level on the surface of the Helmholtz resonant cavity floor. ρ 0 represents the density of air. c 0 represents the speed of sound in air. u 4 represents the particle acoustic velocity of the bottom plate of the Helmholtz resonant cavity; The difference in force between two points in the quasi-zero stiffness interval. The displacement between two points in the quasi-zero stiffness interval; S The area of ​​the Helmholtz resonant cavity floor plate; i For imaginary units; The angular frequency of the sound wave; The slope of two points in the quasi-zero stiffness interval; An analytical model was constructed to reflect the relationship between the sound absorption coefficient and the acoustic impedance of the Helmholtz resonant cavity floor plate. The following formula reflects the relationship between the sound absorption coefficient and the acoustic impedance of the Helmholtz resonant cavity floor: ； In the formula, α is the sound absorption coefficient when the incident sound wave is a plane wave; R and X Acoustic impedance and acoustic reactance, respectively, represent dimensionless acoustic impedance. The sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combined structure is predicted by combining surrogate and analytical models.

2. The method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combined structure according to claim 1, characterized in that, In the combined structure, the quasi-zero stiffness bottom is connected to the top surface of the bottom plate of the Helmholtz resonant cavity.

3. The method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonant cavity combined structure according to claim 2, characterized in that, The quasi-zero stiffness includes a top plate and a hollow conical shell arranged coaxially, and a connecting pipe connecting the top plate and the hollow conical shell at both ends respectively. The structural parameters of the quasi-zero stiffness include the outer diameter of the connecting pipe, the inner radius of the connecting pipe, the radius of the internal cavity of the hollow conical shell outside the connecting pipe, the shell thickness, the height of the internal cavity of the hollow conical shell, and the height of the connecting pipe.

4. The method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combined structure according to claim 1, characterized in that, Calculate using the following formula dF : ； In the formula, b The outer diameter of the quasi-zero stiffness connecting pipe; t The thickness is quasi-zero stiffness shell thickness; H The height of the quasi-zero stiffness connecting pipe; h 1 represents the height of the internal cavity of the quasi-zero stiffness hollow conical shell.

5. The method for predicting the sound absorption coefficient of the quasi-zero stiffness and Helmholtz resonator combined structure according to claim 1, characterized in that, The acoustic impedance and acoustic reactance of dimensionless acoustic impedance are calculated using the following formulas. R and X： ； ； In the formula, p j and u j These represent the sound pressure and sound velocity at various points in the composite structure; j Let 1, 2, 3, 4 represent the top of the throat of the Helmholtz resonant cavity, 2 represent the bottom of the throat of the Helmholtz resonant cavity, 3 represent the area between the bottom of the throat of the Helmholtz resonant cavity and the surface of the quasi-zero stiffness top plate, and 4 represent the bottom plate of the Helmholtz resonant cavity. i For imaginary units; T For the transfer matrix, T hole The transfer matrix of the throat ，T section The transfer matrix at the interface between the larynx and the cavity ，T cavity Let be the transfer matrix of the uniform cross-section cavity between the bottom of the throat of the Helmholtz resonant cavity and the surface of the quasi-zero stiffness top plate.

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