阅读说明：本技术 调控夹层板结构低频隔声性能的装置及其参数确定方法 (Device for regulating and controlling low-frequency sound insulation performance of sandwich plate structure and parameter determination method thereof ) 是由 翟国庆 林秦豪 董丽 奚晓斌 佘海林 于 2020-12-18 设计创作，主要内容包括：本发明涉及一种调控夹层板结构低频隔声性能的装置及其参数确定方法,属于吸声和隔声技术领域。装置包括由上而下依次组合的上面板、上框架、柔性板、下框架和下面板,上面板上设有穿孔,柔性板上设有质量块；上框架和下框架结构相同,均由纵横交错的隔板构成,将整个装置分隔成若干周期性单元,每个周期性单元对应具有穿孔和质量块。可在夹层板质量(面密度)和厚度保持不变情况下,提升已有夹层板结构的低频隔声性能,同时可针对装置建立专用声传输理论模型,用于直接计算其隔声量,用于精准调控装置隔声峰所在频率,具有较好的工程应用前景。(The invention relates to a device for regulating and controlling low-frequency sound insulation performance of a sandwich plate structure and a parameter determination method thereof, belonging to the technical field of sound absorption and sound insulation. The device comprises an upper panel, an upper frame, a flexible plate, a lower frame and a lower panel which are sequentially combined from top to bottom, wherein the upper panel is provided with a through hole, and the flexible plate is provided with a mass block; the upper frame and the lower frame are identical in structure and are composed of criss-cross partition plates, the whole device is divided into a plurality of periodic units, and each periodic unit is correspondingly provided with a through hole and a mass block. The low-frequency sound insulation performance of the existing sandwich plate structure can be improved under the condition that the quality (surface density) and the thickness of the sandwich plate are kept unchanged, meanwhile, a special sound transmission theoretical model can be established for the device, the sound insulation quantity of the device can be directly calculated, the frequency of a sound insulation peak of the device can be accurately regulated and controlled, and the device has a good engineering application prospect.)

1. A device for regulating and controlling low-frequency sound insulation performance of a sandwich plate structure is characterized by comprising an upper panel, an upper frame, a flexible plate, a lower frame and a lower panel which are sequentially combined from top to bottom, wherein a through hole is formed in the upper panel, and a mass block is arranged on the flexible plate;

the upper frame and the lower frame are identical in structure and are composed of criss-cross partition plates, the whole device is divided into a plurality of periodic units, and each periodic unit is correspondingly provided with the through hole and the mass block.

2. A device for controlling the low frequency sound insulation properties of a sandwich panel structure according to claim 1, wherein said periodic cells are rectangular, preferably square in shape.

3. The device for regulating and controlling the low-frequency sound insulation performance of the sandwich plate structure according to claim 1, wherein the number of the perforations of the upper panel in each periodic unit is 1-4.

4. A device for regulating and controlling the low frequency sound insulation performance of a sandwich plate structure according to claim 3, wherein the diameter of the through holes is 0.5mm to 5mm, and the distance between the holes is larger than 15 mm.

5. The device for regulating and controlling the low-frequency sound insulation performance of the sandwich plate structure according to claim 1, wherein the flexible plate is a plastic plate made of polyester resin, thermoplastic polyurethane or nylon, and the thickness of the plastic plate is 0.05 mm-0.5 mm.

6. The device for controlling the low frequency sound insulation performance of a sandwich panel structure according to claim 1, wherein the upper frame and the lower frame have the same wall thickness of the partition plate.

7. The device for regulating and controlling the low-frequency sound insulation performance of the sandwich plate structure according to claim 1, wherein the mass block is 0.05 g-2.0 g and made of metal, and is adhered to the center of the flexible plate.

8. A parameter determination method for the device for regulating and controlling the low-frequency sound insulation performance of the sandwich plate structure as claimed in any one of claims 1 to 7 is characterized by comprising the following steps:

1) randomly generating a combination x consisting of N structural parameters by taking the mass and the thickness of the device as constraint conditions_iFormed primary set S₁(x₁，x₂，x₃，......，x_N)；

2) Calculating a primary set S₁In each structural parameter combination x_iIs the objective function f (x)_i) Objective function f (x)_i) Can be determined by the following formula:

f(x_i)＝a₁×TL(f₁)+a₂×TL(f₂)

in the formula, TL (f)₁) And TL (f)₂) Respectively, are the combination x with the ith parameter_iAt frequency f₁And f₂The sound insulation quantity of the position is directly calculated by a special sound transmission theoretical model; a is₁And a₂Are all penalty functions when f₁(or f)₂) At the frequency of the sound-insulating peak of the device, a₁(or a)₂) Taking 1, otherwise, taking 0.1; from f (x)_i) When a is expressed, the expression of₁＝a₂1 and TL (f)₁)+TL(f₂) At maximum, f (x)_i) The maximum value at which the two sound-insulating peaks of the device are at frequencies f₁And f₂；

3) In the first generation set S₁(or kth generation set S_k) Randomly selecting 2 structural parameter combinations x_aAnd x_bEach structural parameter combination x_i(x_aOr x_b) Probability of being selected is X is to be_aAnd x_bEach structural parameter in (1) is interchanged with a probability of 50%, and if the interchange determination of a single structural parameter is performed and the determination result is called 1 interchange operation, x containing j structural parameters is subjected to_iJ interchange operations are executed in total, and two new structure parameter combinations x 'are finally generated after the interchange is completed'_aAnd x'_bRespectively judging the combination x 'of the structural parameters'_aAnd x'_bWhether the constraint conditions of quality and thickness in the step 1) are met, and if the constraint conditions are met, the second generation set S is used as the second generation set S₂(or k +1 th generation set S_k+1) An element of (1); repeating the above operations until the second generation set S₂(or k +1 th generation set S_k+1) The number of the inner elements reaches N;

4) respectively corresponding to the second generation set S with probability p₂(or k +1 th generation set S_k+1) Each structural parameter combination x'_iCarrying out mutation operation, namely randomly selecting 2 structural parameters in the structural parameter combination and replacing the structural parameters with any value meeting constraint conditions;

5) computing a second generation set S₂(or k +1 th generation set S_k+1) Of every structural parameter combination x'_iTarget function f (x'_i) Simultaneously using the primary set S₁(or kth generation set S_k) Middle corresponding objective function value f (x)_i) Largest element replacing second generation set S₂(or k +1 th generation set S_k+1) Middle value corresponds to objective function value f (x'_i) Minimum element to ensure the corresponding objective function value f (x) in each iteration_i) The largest elements are not lost;

6) execution of steps 3) to 5) is referred to as an iteration, and the set S is generated by two iterations in front of and behind₁(or kth generation set S_k) And S₂(or k +1 th generation set S_k+1) In, if set S₁(or kth generation set S_k) The mean value of the objective function f (x') corresponding to all the elements in the set S₂(or k +1 th generation set S_k+1) The difference of the average values of the target functions f (x') corresponding to all the elements is less than a threshold value or iteratesStopping iteration when the number reaches a specified value, and outputting a set S_k+1The structure parameter combination x 'with the maximum objective function value f (x') is the optimal structure parameter combination, otherwise, the step 3) is skipped.

9. The method for determining the device parameters for regulating and controlling the low-frequency sound insulation performance of the sandwich plate structure according to claim 8, wherein in the step 2), the special sound transmission theoretical model is as follows:

wherein TL is the sound insulation quantity of the device,and theta is the pitch angle and azimuth angle of the acoustic incident angle,the angle is a limit pitch angle, and is generally 70-85 degrees under the laboratory condition;the transmission coefficient, which is the acoustic power, can be determined by:

wherein I is the sound pressure amplitude of the incident sound wave, k_zIs the wave number, k, in the z direction of the incident acoustic wave_z，mnThe wave number component of the space harmonic along the z direction, m and n are integers, F_mnTo transmit the modal amplitude of the forward wave in the acoustic field, it can be determined by:

in the formula, i is an imaginary number unit; omega is the angular frequency of the incident wave; rho₀Is the air density; h is₁、h₂、h₃The thicknesses of the upper panel, the flexible plate and the lower panel are respectively; d₁、d₂The heights of the upper frame and the lower frame are respectively; alpha is alpha_3，mnThe panel displacement coefficient of the lower panel can be determined by solving equations (1) to (3):

in the formula, alpha_1，mn、α_2，mnThe displacement coefficients of the upper panel and the flexible board, and alpha_3，mnAre all the quantities to be calculated; m is_iThe subscript i is 1,2,3, which represents the upper panel, the flexible panel and the lower panel (same below), respectively;representing the bending stiffness of the corresponding plate body; e_i、v_i、η_i、h_iRespectively representing the Young modulus, Poisson ratio, loss factor and thickness of the corresponding plate body; δ (·) is a dirac δ function; m is_aThe mass of the mass block; a. b are respectively position coordinates of the mass block; l_xAnd l_yLength and width of the periodic unit respectively; alpha is alpha_m＝k_x+2mπ/l_x；β_n＝k_y+2nπ/l_y；γ＝iωσρ₀/Z₀；ζ＝1-σZ_I/Z₀；η₀Is the viscosity coefficient of air;d_pthe diameter of the small hole of the upper panel; z_IIs Z₀An imaginary part of (d);t_x、t_ythe wall thicknesses of the partition plates in the x direction and the y direction of the upper frame and the lower frame are respectively;

where ρ is_sThe density of the upper and lower frames; e_sIs up and downThe Young's modulus of the frame; g_s＝E_s/2(1+μ)；r_i，x＝ρ_st_xd_i；r_i，y＝ρ_st_yd_i；

10. The method for determining the device parameters for regulating and controlling the low-frequency sound insulation performance of the sandwich plate structure according to claim 8, wherein in the step 4), the value of the probability p is 1-10%.

Technical Field

The invention relates to the technical field of sound absorption and sound insulation, in particular to a device for regulating and controlling low-frequency sound insulation performance of a sandwich plate structure and a parameter determination method thereof.

Background

The sandwich plate structure has the advantages of light weight, high rigidity, good impact resistance and the like, is widely applied to the fields of aerospace, transportation, buildings and the like, but is limited by the law of mass, and the sound insulation performance of the structure in medium and low frequency bands is still insufficient. In general, the sound insulation performance of the sandwich plate structure can be improved by perforating the sound incidence side panel of the sandwich plate, inserting a perforated plate in the middle of the sandwich plate, filling the sandwich plate with porous elastic material or non-bonded particles, and the like. Pannton and Kang et al have studied the amount of sound insulation of a two-layer panel structure lined with a porous elastomeric material using a finite element method, and the results show that filling the porous elastomeric material improves the amount of sound insulation of the structure, especially when it is bonded to only one of the panels. Meng and the like research the acoustic performance of the perforated honeycomb sandwich plate, and theoretical and simulation results show that low-frequency sound absorption peaks can be introduced by adopting the perforated panel, so that the low-frequency sound insulation quantity of the structure is improved. However, due to the insufficient sound absorption performance of the porous elastic material in the low-frequency band, the perforated plate structure has a narrow sound absorption bandwidth, and therefore, the realization of low-frequency band broadband sound insulation under the constraint conditions of thickness and mass is still a great challenge.

In recent years, the advent of acoustic metamaterials and metamorphic surfaces has provided a new approach to the problem of low frequency noise control. Patent application publication No. CN111916040A discloses a membrane type acoustics metamaterial sound absorption and insulation device with perforated plates, and the sound absorption and insulation device replaces the back plate of the perforated plate resonance sound absorption structure with an opening frame, a membrane with a mass block pasted in the middle is fixed on the opening frame, and the low-frequency sound absorption and insulation performance in the structure is improved by coupling the perforated plate resonance sound absorption structure and the membrane type acoustics metamaterial. However, as the back plate of the sandwich plate structure, the rigidity of the film is seriously insufficient, the sound insulation performance of the film is poor, the device only has higher sound insulation amount near the sound insulation peak, and the sound insulation amount of other frequency bands is insufficient.

Another patent application publication No. CN111179895A discloses a lightweight honeycomb-type low-frequency sound-insulating metamaterial structure, which includes an upper frame and a lower frame, an elastic membrane between the two frames, a mass block attached to the membrane, and a homogeneous thin plate covering the outer side of the frames. The frame is composed of a plurality of regularly arranged hexagonal honeycomb units, and the positions of the honeycomb units of the upper layer of frame and the lower layer of frame are in one-to-one correspondence. The device mainly makes most of sound energy reflected through the antiresonance generated at a specific frequency by the thin film pasted with the mass block, and then improves the sound insulation of the device. However, since the membrane is disposed inside the device and the sound-incident side panel is not perforated, most of the sound energy can be directly transmitted to the sound-transmitting side through the structural sound transmission path of the upper panel → the upper and lower frames → the lower panel, the membrane cannot be directly excited by the sound wave, resulting in a limited improvement in the sound insulation of the structure.

The sound insulation device (or structure) can obtain the required sound insulation performance (such as sound insulation quantity, frequency of sound insulation peak and the like) by adjusting the structural parameters of the sound insulation device (or structure). In order to obtain the optimal structural parameter combination under the target sound insulation performance, the conventional method is to traverse and calculate the sound insulation performance under all the structural parameter combinations, and then screen and determine the optimal structural parameter combination on the basis. However, the traversal method is computationally inefficient and time-consuming.

Disclosure of Invention

The invention aims to provide a device and a method for regulating and controlling the low-frequency sound insulation performance of a sandwich plate structure, which can improve the low-frequency sound insulation performance of the existing sandwich plate structure and can accurately regulate and control the frequency of a sound insulation peak of the device.

In order to achieve the above object, in a first aspect, the device for regulating and controlling the low-frequency sound insulation performance of a sandwich plate structure provided by the invention comprises an upper panel, an upper frame, a flexible plate, a lower frame and a lower panel which are sequentially combined from top to bottom, wherein a through hole is formed in the upper panel, and a mass block is arranged on the flexible plate;

the upper frame and the lower frame are identical in structure and are composed of criss-cross partition plates, the whole device is divided into a plurality of periodic units, and each periodic unit is correspondingly provided with the through hole and the mass block.

According to the technical scheme, the low-frequency sound insulation performance of the existing sandwich plate structure can be improved under the condition that the quality (surface density) and the thickness of the sandwich plate are kept unchanged, meanwhile, a special sound transmission theoretical model can be established for the device, the device is used for directly calculating the sound insulation quantity of the device, the frequency of a sound insulation peak of the device is accurately regulated and controlled, and the device has a good engineering application prospect.

Optionally, in one embodiment, the shape of the periodic unit is rectangular, preferably square.

Optionally, in one embodiment, the number of perforations of the upper panel is 1-4 per periodic unit.

Optionally, in one embodiment, the diameter of the perforation is 0.5mm to 5mm, and the hole pitch is greater than 15 mm.

Optionally, in an embodiment, the flexible board is a plastic board made of polyester resin, thermoplastic polyurethane or nylon, and has a thickness of 0.05mm to 0.5 mm.

Optionally, in an embodiment, the wall thickness of the partition plate used for the upper frame and the lower frame is the same.

Optionally, in an embodiment, the mass of the mass block is 0.05g to 2.0g, the material of the mass block is metal such as iron, aluminum, tungsten, and the like, and the mass block is preferably attached to the center of the flexible plate. The shape and the thickness of the upper frame and the lower frame are completely the same, so that each periodic unit can be completely overlapped after the upper frame and the lower frame are overlapped. The thickness of the lower panel is 2-5 mm, the lower panel and the upper panel are same in quality and are made of metal such as aluminum and stainless steel or nonmetal such as acrylic, polyvinyl chloride and epoxy resin.

In a second aspect, in order to accurately regulate and control the frequency of a sound insulation peak of the device, the method for determining parameters of the device for regulating and controlling the low-frequency sound insulation performance of the sandwich plate structure provided by the invention comprises the following steps:

1) the random generation of x is composed of N structural parameter combinations by using the mass (surface density) and thickness of the device as constraint conditions_iFormed primary set S₁(x₁,x₂,x₃,……,x_N)；

2) Calculating a primary set S₁In each structural parameter combination x_iIs the objective function f (x)_i) Objective function f (x)_i) Can be determined by the following formula:

f(x_i)＝a₁×TL(f₁)+a₂×TL(f₂)

in the formula, TL (f)₁) And TL (f)₂) Respectively, are the combination x with the ith parameter_iAt frequency f₁And f₂The sound insulation quantity of the position is directly calculated by a special sound transmission theoretical model; a is₁And a₂Are all penalty functions when f₁(or f)₂) At the frequency of the sound-insulating peak of the device, a₁(or a)₂) Taking 1, otherwise, taking 0.1; from f (x)_i) When a is expressed, the expression of₁＝a₂1 and TL (f)₁)+TL(f₂) At maximum, f (x)_i) The maximum value at which the two sound-insulating peaks of the device are at frequencies f₁And f₂；

3) In the first generation set S₁(or kth generation set S_k) Randomly selecting 2 structural parameter combinations x_aAnd x_bEach structural parameter combination x_i(x_aOr x_b) Probability of being selected isX is to be_aAnd x_bEach structural parameter in (1) is interchanged with a probability of 50%, and if the interchange determination of a single structural parameter is performed and the determination result is called 1 interchange operation, x containing j structural parameters is subjected to_iJ times of interchange operations are executed in total, and after the interchange is completedFinally two new structural parameter combinations x 'are generated'_aAnd x'_bRespectively judging the combination x 'of the structural parameters'_aAnd x'_bWhether the constraint conditions of quality and thickness in the step 1) are met, and if the constraint conditions are met, the second generation set S is used as the second generation set S₂(or k +1 th generation set S_k+1) An element of (1); repeating the above operations until the second generation set S₂(or k +1 th generation set S_k+1) The number of the inner elements reaches N;

4) respectively corresponding to the second generation set S with probability p₂(or k +1 th generation set S_k+1) Each structural parameter combination x'_iCarrying out mutation operation, namely randomly selecting 2 structural parameters in the structural parameter combination and replacing the structural parameters with any value meeting constraint conditions;

5) computing a second generation set S₂(or k +1 th generation set S_k+1) Of every structural parameter combination x'_iTarget function f (x'_i) Simultaneously using the primary set S₁(or kth generation set S_k) Middle corresponding objective function value f (x)_i) Largest element replacing second generation set S₂(or k +1 th generation set S_k+1) Middle value corresponds to objective function value f (x'_i) Minimum element to ensure the corresponding objective function value f (x) in each iteration_i) The largest elements are not lost;

6) execution of steps 3) to 5) is referred to as an iteration, and the set S is generated by two iterations in front of and behind₁(or kth generation set S_k) And S₂(or k +1 th generation set S_k+1) In, if set S₁(or kth generation set S_k) The mean value of the objective function f (x') corresponding to all the elements in the set S₂(or k +1 th generation set S_k+1) If the difference value of the average values of the objective functions f (x') corresponding to all the elements in the set is less than the threshold value or the iteration times reach the specified value, stopping the iteration and outputting a set S_k+1The structure parameter combination x 'with the maximum objective function value f (x') is the optimal structure parameter combination, otherwise, the step 3) is skipped.

In step 2), the special acoustic transmission theoretical model is as follows:

wherein TL is the sound insulation quantity of the device,and theta is the pitch angle and azimuth angle of the acoustic incident angle,the angle is a limit pitch angle, and is generally 70-85 degrees under the laboratory condition;the transmission coefficient, which is the acoustic power, can be determined by:

wherein I is the sound pressure amplitude of the incident sound wave, k_zIs the wave number, k, in the z direction of the incident acoustic wave_z,mnThe wave number component of the space harmonic along the z direction, m and n are integers, F_mnTo transmit the modal amplitude of the forward wave in the acoustic field, it can be determined by:

in the formula, i is an imaginary number unit; omega is the angular frequency of the incident wave; rho₀Is the air density; h is₁、h₂、h₃The thicknesses of the upper panel, the flexible plate and the lower panel are respectively; d₁、d₂The heights of the upper frame and the lower frame are respectively; alpha is alpha_3,mnThe panel displacement coefficient of the lower panel can be determined by solving equations (1) to (3):

in the formula, alpha_1,mn、α_2,mnThe displacement coefficients of the upper panel and the flexible board, and alpha_3,mnAre all the quantities to be calculated; m is_iThe subscript i is 1,2,3, which represents the upper panel, the flexible panel and the lower panel (same below), respectively;representing the bending stiffness of the corresponding plate body; e_i、v_i、η_i、h_iRespectively representing the Young modulus, Poisson ratio, loss factor and thickness of the corresponding plate body; δ (·) is a dirac δ function; m is_aThe mass of the mass block; a. b are respectively position coordinates of the mass block; l_xAnd l_yLength and width of the periodic unit respectively; alpha is alpha_m＝k_x+2mπ/l_x；β_n＝k_y+2nπ/l_y；γ＝iωσρ₀/Z₀；ζ＝1-σZ_I/Z₀； η₀Is the viscosity coefficient of air;d_pthe diameter of the small hole of the upper panel; z_IIs Z₀An imaginary part of (d);t_x、t_ythe wall thicknesses of the partition plates in the x direction and the y direction of the upper frame and the lower frame are respectively; where ρ is_sThe density of the upper and lower frames; e_sYoung's modulus of the upper and lower frames; g_s＝E_s/2(1+μ)；r_i,x＝ρ_st_xd_i；r_i,y＝ρ_st_yd_i；

In the step 4), the value of the probability p is 1-10%.

Compared with the prior art, the invention has the advantages that:

(1) by coupling the perforated plate resonance sound absorption structure and the plate type acoustic metamaterial, the device can obviously improve the low-frequency sound insulation performance of the traditional sandwich plate structure under the condition that the mass (surface density) and the thickness are kept unchanged;

(2) according to the special sound transmission theoretical model established by the invention and verified by simulation and actual measurement, the sound insulation quantity of the device can be rapidly and accurately calculated;

(3) aiming at different sound insulation targets, by utilizing the device-specific sound transmission theoretical model and the parameter optimization calculation method established by the invention, the optimal structural parameter combination can be quickly determined through calculation, and the frequency of a sound insulation peak can be accurately regulated and controlled.

Drawings

FIG. 1 is a schematic view of the overall structure of an apparatus according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a periodic unit according to an embodiment of the present invention;

FIG. 3 is a comparison graph of the results of theoretical calculation and simulation calculation of the sound insulation amount of the device in the embodiment of the present invention;

FIG. 4 is a diagram of an experimental sample of an apparatus according to an embodiment of the present invention;

FIG. 5 is a graph comparing the theoretical calculation of the sound insulation amount of the device and the experimental results in the embodiment of the present invention;

fig. 6 is a plot of sound insulation for the device of the example of the invention at optimum structural parameters.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described with reference to the following embodiments and accompanying drawings. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments without any inventive step, are within the scope of protection of the invention.

Unless defined otherwise, technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs. The use of the word "comprise" or "comprises", and the like, in the context of this application, is intended to mean that the elements or items listed before that word, in addition to those listed after that word, do not exclude other elements or items. The terms "connected" or "coupled" and the like are not restricted to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", and the like are used merely to indicate relative positional relationships, and when the absolute position of the object being described is changed, the relative positional relationships may also be changed accordingly.

Examples

Taking an extra-high voltage converter transformer as an example, the low-frequency component of the generated noise is more obvious, and the generated noise has obvious modulated noise on 100Hz and higher harmonics thereof, and the conventional sound insulation measures are difficult to obtain a better noise reduction effect. Therefore, aiming at low-frequency noise radiated by the extra-high voltage converter transformer, particularly 3 rd harmonic (300Hz) and 4 th harmonic (400Hz) noise, the device of the embodiment is additionally designed outside the converter transformer shell, structural parameters of the device are designed in a targeted mode, and the 300Hz and 400Hz harmonic noise radiated by the device is effectively reduced.

Referring to fig. 1 and 2, the device for regulating and controlling the low-frequency sound insulation performance of the sandwich plate structure in the present embodiment is a sandwich plate structure composed of periodic units 8, and each periodic unit 8 includes a perforated upper panel 1, an upper frame 3, a flexible plate 4 with a mass block 5 adhered at the center, a lower frame 6 and a lower panel 7 which are sequentially combined from top to bottom.

The periodic cells 8 are square in shape with a side length of l. The perforated upper 1, flexible 4 and lower 7 panels each have a thickness h₁、h₂、h₃The center of the perforated upper panel 1 is perforated with 1 small hole with the aperture d_pThe upper frame 3 and the lower frame 6 have the same shape and thicknessEnsuring that each periodic unit is completely superposed after the upper frame and the lower frame are superposed, wherein the thicknesses of the partition walls of the upper frame and the lower frame in the x direction and the y direction are respectively t_x、t_yThe upper frame 3 has a height d₁The lower frame 6 has a height d₂. In a period unit, the mass block 5 stuck on the flexible board 4 is positioned at the right center of the flexible board 4, and the mass of the mass block 5 is m_a. Perforated upper panel 1, upper frame 3, underframe 6 and lower panel 7 all select the preparation of ya keli board for use, and polyester resin flexbile plate is selected for use to flexbile plate 4, and cylindrical iron plate is selected for use to quality piece 5.

Considering the perforated upper panel 1, the flexible sheet 4, the lower panel 7, and the upper and lower frames as Kirchhoff sheets, according to Kirchhoff-Love sheet theory, the vibration control equation of each panel under plane wave excitation is established as follows:

in the above formula, w_iAnd m_i(i ═ 1,2,3, representing the upper panel, the flexible sheet, and the lower panel, respectively) are the deflection and the areal density of the corresponding panel body, respectively;the bending rigidity of the corresponding plate body; e_i、v_i、η_i、h_iRespectively representing the Young modulus, Poisson ratio, loss factor and thickness of the corresponding plate body; l_x、l_yThe lengths of the periodic structure units in the x and y directions are respectively; t is t_x、t_yThe wall thicknesses of the upper and lower frames in the x direction and the y direction respectively; d₁、d₂The heights of the upper frame and the lower frame are respectively; δ (·) is a dirac δ function; p_iAnd (x, y, z; t) (i ═ 1,2,3,4) respectively represent incident-side sound field sound pressure, sound field sound pressure in the cavity i, sound field sound pressure in the cavity ii, and transmission sound field sound pressure.

Andrespectively representing tensile force, bending moment and torque generated by frame stretching, bending and torsional vibration, which can be expressed by equations (4) to (15):

in the formula (I), the compound is shown in the specification, where ρ is_sThe density of the upper and lower frames; e_sYoung's modulus of the upper and lower frames; g_s＝E_s/2(1+μ)；r_i,x＝ρ_st_xd_i；r_i,y＝ρ_st_yd_i；

Suppose a plane simple harmonicThe vibration displacement w of the panel under the excitation of sound waves is incident on the structure according to the Bloch periodic fluctuation theory_i(x, y; t) may be expressed in the form of a spatial harmonic series as follows:

wherein m and n are integers; k is a radical of_x、k_y、k_zWave numbers along x, y, z directions, respectively;k₀＝ω/c₀the wave number of air; omega is angular frequency; c. C₀Is the speed of sound in air;and θ are the pitch and azimuth angles, respectively, of the acoustic incident angle (see fig. 1).

Sound pressure P of each sound field_i(x, y, z; t) all satisfy the following wave equation:

when the incident sound pressure is p (x, y, z; t), the total sound pressure of the incident side sound field can be expressed by the following formula:

the sound pressure of the sound field in the cavity i can be expressed by formula (19):

the sound pressure of the sound field in the cavity II can be represented by formula (20):

the transmission-side sound field sound pressure can be represented by equation (21):

in the formula, I is the sound pressure amplitude of the incident sound wave; a. the_mn、C_mn、E_mnThe mode amplitudes of an incident side sound field, a sound field in the cavity I and a negative wave in the cavity II are respectively; b is_mn、D_mn、F_mnThe mode amplitudes of a sound field in the cavity I, a sound field in the cavity II and a forward wave in a transmission sound field are respectively; k is a radical of_z,mnThe wavenumber component in the z-direction for the spatial harmonics can be represented by equation (22):

at the fluid-solid coupling interface, the normal velocities of the particles on each panel and the fluid particles adjacent to the particles satisfy the continuity condition, see formula (23):

where ρ is₀Is the air density; v. of₂、v₃The normal speeds of the flexible plate and the lower panel are respectively; when the hole spacing is much smaller than the acoustic wavelength,which can be considered as the spatial average of the normal velocity of the air in the upper panel and the holes, can be represented by equation (24):

in the formula, v₁The upper panel normal speed; v. of_hThe average velocity of air particles in the holes; sigma is the perforation rate of the upper panel, and the effective perforation rate of the upper panel is that the reinforcing ribs have certain wall thickness, and the actual volume of the cavity at the back of the hole is reduced

Average velocity v of air particles in small holes_hThe acoustic impedance of the small hole and the pressure difference between the upper and lower ends of the upper plate are related to each other by equation (25):

in the formula, Z_RAnd Z_IRespectively, the acoustic resistance and the acoustic reactance of the pinhole, i.e. the specific acoustic impedance thereof being Z₀＝Z_R+Z_I. According to an approximate model of the microperforated panel sound absorbing structure proposed by mazaro 29495, the specific acoustic impedance of a single orifice can be represented by the formula (26):

wherein eta is₀Is the viscosity coefficient of air;d_pis the diameter of the small hole of the upper panel.

The normal velocity of the upper panel surface can be found finally, see equation (27):

wherein ζ is 1-Z_I/Z，Z＝Z₀/σ。

Combined upper type, can be solved to obtain A_mn、B_mn、C_mn、D_mn、E_mn、F_mn。

According to the principle of virtual work, in the periodic unit of one system, the sum of virtual work done by external force on any virtual displacement is zero, and for any given virtual displacement, see formula (28), the virtual work contributed by each panel in the periodic unit of one system can be represented by formulas (29) to (31):

wherein alpha is_m＝k_x+2mπ/l_x，β_n＝k_y+2nπ/l_y。

Wherein the content of the first and second substances,is δ w_iConjugation of (1).

The imaginary work contributed by the ribs in the x-direction of the upper and lower frames can be expressed by equations (32) to (34):

the virtual work contributed by the ribs in the y-direction of the upper and lower frames can be expressed by equations (35) to (37):

the imaginary work contributed by the additional mass can be represented by equation (38) and equation (39):

δΠ_m1＝δΠ_m3＝0 (38)

wherein m is_aThe mass is a mass block, and a and b are coordinates of the mass block in the x and y directions.

Therefore, the total virtual work in one cycle of the system can be represented by the following formula:

δΠ_pi+δП_xi+δП_yi+δП_mi＝0，i＝(1,2,3) (40)

substituting equations (28) to (39) into equation (40), and separating the variable α according to the arbitrary property of the virtual displacement_1,kl、α_2,kl、α_3,klThe following equations (41) to (43):

where γ is i ω ρ₀/Z。

Because the above equation is expressed in a series form, the above equation set needs to be truncated on the premise of ensuring the convergence of the result, i.e. the value ranges of the summation indexes m and n are limited to-k < m < k, -l < n < l, and then the above equation set can be rewritten into a matrix equation form, see formula (44):

wherein K is 2K +1 and L is 2L + 1.

The displacement coefficient alpha of each panel can be obtained by solving the matrix equation_i,klFurther, the sound pressure coefficient A can be determined_mn、B_mn、C_mn、D_mn、E_mn、F_mn. The transmission coefficient of the acoustic power can be calculated by equation (45):

angle of incidence with sound wavesWith respect to θ, the transmission coefficient of sound power under the action of a scattered sound field (e.g., reverberant sound in a reverberant room) can be defined as the transmission coefficient at all pitch anglesAnd a weighted average of the transmission coefficients at an azimuth angle θ, the azimuth angle θ not contributing to the calculation result in consideration of the symmetry of the periodic unit, the transmission coefficient of the structure under the scattered acoustic field being represented by the formula (46):

whereinAt extreme pitch, i.e. when the pitch is above this upper limit, a silent wave is incident on the panel, which is typical under laboratory conditionsTaking the angle of 70-85 degrees.

The Transmission Loss (TL) of the structure can be calculated according to equation (47):

in order to verify the accuracy of the model, COMSOL Multiphysics 5.5 is adopted to perform simulation verification on the calculation result of the acoustic transmission theoretical model. The structural parameters of the device are as follows, the length and the width of each periodic unit are both 30 mm; the thicknesses of the upper panel, the flexible plate and the lower panel are respectively 1mm, 0.188mm and 3 mm; the height of the upper frame and the lower frame is 5mm, and the wall thickness is 1 mm; in a periodic unit, a small hole with the diameter of 1.6mm is arranged in the center of the upper panel, and a cylindrical mass block is adhered in the center of the flexible panel; the mass block has a diameter of 4mm, a height of 3.1mm and an average mass of 0.3 g; the upper panel, the upper frame, the lower frame and the lower panel are all made of acrylic; the flexible board is made of polyester resin; the mass block is made of iron. The specific material parameters are as follows, acrylic [ density rho is 1190 kg/m%³(ii) a Young's modulus E ═ 3.2 Gpa; poisson ratio v is 0.35; loss factor eta of 0.01](ii) a Terylene resin [ density rho 1450kg/m ═³(ii) a Young's modulus E ═ 6.5 Gpa; poisson ratio v is 0.39; loss factor eta is 0.1](ii) a Iron [ Density rho 7800kg/m³(ii) a Young modulus E ═ 206 Gpa; poisson ratio v ═ 0.3]。

The comparison of the theoretical calculation and the simulation calculation result is shown in fig. 3. As can be seen from FIG. 3, the consistency between the calculation result of the theoretical model and the simulation result is good, which indicates that the theoretical model is accurate and reliable. Meanwhile, as can be seen from fig. 3, the device has two sound insulation peaks in the middle and low frequency bands, so that the low-frequency sound insulation performance of the existing sandwich plate structure can be further improved.

In order to further verify the accuracy of the theoretical model, an experimental sample is specially manufactured for experimental verification. As shown in FIG. 4, the sample consisted of 1024 (32X 32) unit cells, with an overall size of 1142mm X1142 mm. In order to ensure the structure has enough rigidity, a stainless steel outer frame is adoptedFixing, and simultaneously inserting two stainless steel pipes as main keels into the structure, namely the actual sample is formed by combining 4 substructures (16 multiplied by 16 unit cells). In order to reduce the processing difficulty, the wall thickness t of the X-direction and Y-direction partition plates of the upper frame and the lower frame of the sample_x、t_yAre changed into 4mm, and the height d of the upper frame and the lower frame is simultaneously changed₁、d₂All are changed into 10mm, and the aperture d of the upper panel perforation_pAnd 2mm is changed, a stainless steel cylindrical iron block (the average mass is 0.42g +/-0.01 g) with the diameter of 5mm and the height of 2.8mm is selected as the mass block, and all other parameters are the same as those of the simulation model. The sound insulation of the experimental samples was measured according to ISO140-3:1995 using the double reverberation chamber method, and the theoretical calculation and experimental results are compared in FIG. 5. As can be seen from FIG. 5, the experimental result and the theoretical calculation result have basically the same trend, and the accuracy of the theoretical model is further verified.

In order to ensure that the sound insulation quantity of the device obtains peak values at the frequencies of 3 th harmonic (300Hz) and 4 th harmonic (400Hz) (namely, the sound insulation target is taken), the surface density of the device is less than 7.2kg/m²And the thickness of the device is less than 20mm, and the device structure parameter combination is quickly calculated and determined by using the device special acoustic transmission theoretical model established by the invention through the following steps.

Step 1: and (5) initializing operation. With periodic unit 8 side length l, perforation aperture d of perforated top panel 1_pThickness h₁Thickness h of flexible board 4₂Thickness h of lower panel 7₃Wall thickness t of the partition plate in the x and y directions of the upper and lower frames_x、t_yHeight d of upper frame 3₁Height d of lower frame 6₂Mass m of the mass 5_aWait for 10 structural parameters as variables to be optimized, in areal density (less than 7.2 kg/m)²) And thickness (less than 20mm) of the structural parameter combinations x of 50 kinds of satisfaction_iFormed primary set S₁(x₁,x₂,x₃,……,x_N)。

Step 2: calculating a primary set S₁In each structural parameter combination x_iIs the objective function f (x)_i) Objective function f (x)_i) Can be determined by the following formula:

f(x_i)＝a₁×TL(f₁)+a₂×TL(f₂)

in the formula, TL (f)₁) And TL (f)₂) Respectively, are the combination x with the ith parameter_iThe sound insulation quantity of the device at the frequencies of 300Hz and 400Hz is directly calculated by the device-specific sound transmission theoretical model established by the invention. a is₁And a₂If the peak of the device corresponds to a frequency of 300Hz (or 400Hz) in order to be both a penalty function, then a₁(or a)₂) Take 1, otherwise take 0.1. The method for judging whether the frequency f is the frequency corresponding to the sound insulation peak of the device is that if TL (f)>TL (f + Deltaf) and TL (f)>TL (f-delta f), the frequency f is the frequency corresponding to the sound insulation peak of the device, wherein TL (f) is the sound insulation quantity of the device at the frequency f, and delta f is 0.1Hz and is the minimum frequency interval.

And step 3: in the first generation set S₁(or kth generation set S_k) Randomly selecting 2 structural parameter combinations x_aAnd x_bEach structural parameter combination x_i(x_aOr x_b) Probability of being selectedX is to be_aAnd x_bEach structural parameter in (1) is interchanged with a probability of 50%, and if the interchange determination of a single structural parameter is performed and the determination result is called 1 interchange operation, x containing 9 structural parameters is subjected to_iTotally 9 interchange operations are required to be executed, and two new structure parameter combinations x 'are finally generated after the interchange is finished'_aAnd x'_bRespectively judging the combination x 'of the structural parameters'_aAnd x'_bWhether the constraint conditions of quality and thickness in the step one are met or not, and if the constraint conditions are met, the second generation set S is used as the second generation set S₂(or k +1 th generation set S_k+1) An element of (1); repeating the above operations until the second generation set S₂(or k +1 th generation set S_k+1) The number of elements in reaches N. The implementation method related to the probability judgment comprises the steps of generating a random number of 0-1, if the random number is smaller than a preset probability (such as 50%), executing a judgment result, and otherwise, not executing the judgment.

And 4, step 4: respectively collecting the second generation with 5% probabilityS₂(or k +1 th generation set S_k+1) Each structural parameter combination x'_iAnd performing mutation operation, namely randomly selecting 2 structural parameters in the structural parameter combination and replacing the 2 structural parameters with any value meeting the constraint condition.

And 5: computing a second generation set S₂(or k +1 th generation set S_k+1) Of every structural parameter combination x'_iTarget function f (x'_i) Simultaneously using the primary set S₁(or kth generation set S_k) Middle corresponding objective function value f (x)_i) Substitution of the largest element (combination of structural parameters) for the second-generation set S₂(or k +1 th generation set S_k+1) Middle value corresponds to objective function value f (x'_i) Minimum element to ensure the corresponding objective function value f (x) in each iteration_i) The largest elements are not lost.

Step 6: the step 3-5 is called one iteration, and the set S generated by two iterations is generated₁(or kth generation set S_k) And S₂(or k +1 th generation set S_k+1) In, if set S₁(or kth generation set S_k) The mean value of the objective function f (x') corresponding to all the elements in the set S₂(or k +1 th generation set S_k+1) If the difference of the average values of the target functions f (x') corresponding to all the elements in the set is less than 0.01 or the iteration times reach 1000, stopping the iteration and outputting a set S_k+1The structural parameter combination x ' with the maximum objective function value f (x '), namely x ' is the optimal structural parameter combination, otherwise, the step 3 is skipped.

After a plurality of iterations, the iterations stop, and the optimal structural parameter composition obtained by calculation is as follows: the side length of the periodic unit is 31mm, the perforation aperture of the upper panel is 1.1mm, the thickness of the upper panel is 1mm, the thickness of the flexible plate is 0.155mm, the thickness of the lower panel is 3mm, the wall thickness of the upper frame and the lower frame is 2mm, the height of the upper frame is 8mm, the height of the lower frame is 8mm, and the mass of the mass block is 0.3 g. The sound insulation curve of a device with this combination of structural parameters is shown in fig. 6. As can be seen from FIG. 6, the device has obvious sound insulation peaks at 300Hz and 400Hz, and the sound insulation quantity at the two sound insulation peaks exceeds 35dB, so that the modulated noise at 300Hz and 400Hz of the ultra-high voltage converter transformer can be effectively reduced.