Customizable broadband ventilation and sound insulation superstructure based on dual-mode fano resonance and design method

Abstract

The invention relates to the technical field of noise control, and relates to a customizable broadband ventilation and sound insulation superstructure based on dual-mode fano resonance. The ventilation and sound insulation superstructure is formed by alternately arranging three layers of structures; the first layer and the third layer are structural layers and are formed by arranging rectangular pipelines with different section areas in an S shape; the second middle layer is an air layer to ensure air circulation; the structural layer comprises two hollow cavities, and the two cavities are connected through a throat pipe; the throat pipes are also arranged on the inlet sides and the outlet sides of the two cavities; sound energy is propagated along the thickness direction of the structure, one part reaches the transmission end through the structure layer, and the other part reaches the transmission end through the air layer; the two parts of sound energy are opposite in sound pressure phase and similar in amplitude at two resonant frequency points, and dual-mode fano resonance is formed. By adjusting the structural parameters of the structural layer, the working frequency band and the working bandwidth can be flexibly adjusted, and therefore the effect of customizable broadband sound insulation is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of noise control, and in particular to a customizable broadband ventilation and sound insulation superstructure based on dual-mode Fano resonance. Background Art

[0002] Noise pollution is one of the major pollutions in human life, and efficient noise control structures have become a major demand of the current industry. With the increase in demand, ventilation and sound-absorbing metamaterials have attracted the attention of many researchers, which can ensure air circulation while ensuring sound insulation and noise reduction. However, ensuring high ventilation rate, high efficiency, high bandwidth and small thickness at the same time is still a major problem in metamaterials. In addition, the working frequency bands required for noise treatment in different working occasions are different, so acoustic metamaterials that can flexibly customize the working frequency band and bandwidth have high application value. However, it is difficult for current metamaterials to meet the needs of flexible customization of working bandwidth, and it is difficult to meet the needs of simultaneously ensuring wide-band sound insulation and greater ventilation performance. Summary of the invention

[0003] The purpose of the present invention is to address the problems existing in the background technology and propose a design method for a customizable broadband ventilation and sound insulation superstructure based on dual-mode Fano resonance; the superstructure can achieve customizable broadband ventilation and sound insulation within 1 / 3-1 octave layer, which can be used in scenes such as electrical appliances that need ventilation, industrial exhaust ducts and large industrial machines.

[0004] The technical solution of the present invention:

[0005] A first aspect of the present invention provides a customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance, wherein the ventilated sound insulation superstructure is composed of three layers of structures arranged alternately;

[0006] The first and third layers are structural layers, which are composed of rectangular pipes with different cross-sectional areas arranged in an "S" shape; the second layer in the middle is the air layer to ensure air circulation;

[0007] The structural layer includes two hollow cavities, which are connected by a throat; throats are also provided at the inlet and outlet sides of the two cavities;

[0008] The width and height of the two middle chambers are the same; the inlet and outlet throat geometry parameters are also the same;

[0009] The sound energy propagates along the thickness direction of the structure, with part of it passing through the structural layer to reach the transmission end, and part of it passing through the air layer to reach the transmission end; the two parts of the sound energy have opposite sound pressure phases and similar amplitudes at the two resonant frequency points, forming a dual-mode Fano resonance, which is used for broadband sound insulation between the two mode frequency points.

[0010] Preferably, the first and third structural layers have the same geometric dimensions; the length and width of the middle throat pipe and the throat pipes at both ends of the same layer are different; the boundary wall thickness of different rectangular units in the structural layer is the same; and all ventilation and sound insulation sections are rectangular pipe interfaces.

[0011] Preferably, the geometric parameters of the structural layer affect the resonant frequency points of the dual-mode Fano resonance, the low-frequency resonance point is a dipole resonance mode, and the high-frequency resonance point is a monopole resonance mode. The high-frequency resonance point and the low-frequency resonance point tend to low frequency as L increases, and the increase in L will cause the overall working frequency band to shift to low frequency. h has an impact on the high-frequency Fano resonance point, and the high-frequency resonance frequency point moves to low frequency as h increases. The low-frequency Fano resonance point is not affected by the parameter h, so reducing the length of the middle narrow channel h can widen the bandwidth. Both Fano resonance frequency points show a trend of moving to high frequency as d1 increases. The low-frequency resonance point and the high-frequency resonance point of the dual-mode Fano resonance show a trend of moving to low frequency and high frequency as d2 increases. Different parameters have different effects on the monopole mode frequency point, the dipole mode frequency point and the working bandwidth; therefore, the geometric parameters of the structural layer can be determined according to the required working bandwidth and frequency band to achieve the needs of customizable broadband ventilation and sound insulation.

[0012] Preferably, the width and length of the middle throat of the structural layer only affect the monopole mode, and the bandwidth can be flexibly adjusted within 1 / 3-1 octave layer by adjusting the length of the middle throat.

[0013] Preferably, the width B of the structural layer has no effect on the working frequency band. The sound pressure reflection coefficient and the sound pressure transmission coefficient of the structural layer are calculated using the transfer matrix method. The structural layer has a total of seven layers, and its transfer matrix is:

[0014]

[0015] in and are the incident sound pressure and the reflected sound pressure, M i is the transfer matrix of the i-th layer of medium. Then the sound pressure reflection coefficient and sound pressure transmission coefficient of the unit equivalent model can be calculated:

[0016]

[0017] Since the 7th layer is an air waveguide layer with infinite width, there is no reflected sound pressure in the 7th layer, that is, The transfer matrix M1-M6 of the intermediate structure is:

[0018]

[0019]

[0020] where yi is the thickness of the i-th layer structure. y2=y6=L,y3=y5=L-2t,y4=2h. ij is the impedance ratio of the jth layer to the ith layer of media. The impedance ratio of each layer of media is the inverse ratio of the area of ​​the equivalent rectangular tube cross section. That is, R ij =S i / S j ,S i is the cross-sectional area of ​​the i-th layer of the medium. Since the overall thickness of the structure is B, the ratio of the cross-sectional areas is the ratio of the widths of the rectangles, R ij =d i / d j It has nothing to do with the width B of the structure; the height H of the air layer has no effect on the range of the working frequency band, but the ventilation rate H / (L+2H) is inversely proportional to the sound insulation effect. Therefore, the height of the air layer can be adjusted to adapt to the noise reduction needs of environments at different heights. However, when the ventilation rate is greater than 40%, the sound insulation will be lower than 10dB. Therefore, the ventilation rate should be adjusted while meeting the required sound insulation.

[0021] Preferably, the acoustic impedance Z of the structural layer eff and speed C eff It is expressed as:

[0022]

[0023] Where d is the total thickness of the structure, and m is the number of branches of the arccosine function, which is taken as 0 here; The sign of R should ensure that the real part of Zeff is positive, that is, the real part of the equivalent relative impedance is positive; r and t are the sound pressure transmission coefficient and sound pressure reflection coefficient of the structural layer respectively; c0=343m / s is the speed of sound in air.

[0024] The second aspect of the present invention provides a design method for a customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance, comprising the following specific steps:

[0025] S1. Design broadband ventilation sound insulation superstructure as a three-layer structure, the upper and lower layers are structural layers, the height is L; the middle layer is an air layer to ensure air circulation, the height is H;

[0026] S2. Use the transfer matrix method to calculate the total transfer matrix of the ventilation sound insulation structure and calculate the sound intensity transmission coefficient at different frequency points;

[0027] S3. Place ventilation and sound insulation superstructures with different structural parameters in series to achieve the superposition of the bandwidths of the two superstructures.

[0028] Preferably, in step S2, the sound intensity transmission coefficient at different frequency points is expressed by the following formula:

[0029]

[0030] Where T mn is the element in the mth row and nth column of TP; is the acoustic characteristic impedance of the waveguide layers in regions 1 and 3, S total is the total cross-sectional area of ​​the ventilation and sound insulation structure, S total =(H+2L)B.

[0031] Preferably, when continuous broadband sound insulation noise control is required, the working bandwidths of the two super structures are connected first to achieve superposition of the working bandwidths; when there is a gap between the working bandwidths of the two super structures, the function of controllable filtering can be achieved.

[0032] Preferably, when multiple units are connected in series, the narrow passages at a certain distance between the units will form FP resonance; connecting four units in series and utilizing the resonant coupling of Fano resonance and FP resonance can achieve the ultra-wideband ventilation and sound insulation requirements of 400Hz-2450Hz.

[0033] Compared with the prior art, the present invention has the following beneficial technical effects:

[0034] 1. The operating frequency band of the customizable broadband ventilation and sound insulation superstructure in the present invention is independent of the width dimension of the structure, and can meet the requirements of ventilation and sound insulation of different widths;

[0035] 2. The customizable broadband ventilation and sound insulation superstructure of the present invention can flexibly customize the working frequency band, and customize the bandwidth by adjusting the high-frequency working frequency point while ensuring that the starting working frequency remains unchanged;

[0036] 3. The height H of the ventilation layer of the customizable broadband ventilation and sound insulation structure of the present invention has no effect on the working frequency band of the structure, so it can be applied to the requirements of different height ventilation and sound insulation working occasions;

[0037] 4. By placing the structures with different parameters in series in the present invention in front and behind, the effect of superposition of the working frequency bands of the two ventilation and sound insulation superstructures can be achieved;

[0038] 5. Through the resonant coupling of Fano resonance and FP resonance, the noise reduction requirements of ultra-wideband ventilation and sound insulation can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a schematic diagram of the overall structure of the present invention;

[0040] Figure 2 is a cross-sectional view of the structure of the present invention, including structural parameters of the structural layers;

[0041] Figure 3It is a structural schematic diagram of two ventilation and sound insulation superstructures with different geometric parameters placed in series in front and behind of the present invention;

[0042] Figure 4 It is a schematic diagram of the structure of four units connected in series, which can achieve wide-bandwidth noise control requirements through the resonance coupling of Fano resonance and FP.

[0043] Figure numerals: 1. upper structural layer; 2. air layer; 3. lower structural layer; 4. first throat; 5. cavity; 6. second throat; 7. low-frequency working unit in series; 8. high-frequency working unit in series; 9. first series unit; 10. FP resonance tube; 11. second series unit; 12. third series unit; 13. fourth series unit. DETAILED DESCRIPTION

[0044] Example 1

[0045] like Figure 1-2 As shown, the customizable ventilated broadband sound insulation structure of the present invention is composed of three layers, the first layer and the third layer are respectively an upper structure layer 1 and a lower structure layer 3, and the second layer is an air layer 2. The sound propagation direction and the air flow direction are as shown in FIG. Figure 2 As shown by the arrow in the middle, the sound energy passing through the structural layer and the sound energy passing through the air layer interact with each other to form a dual-mode Fano resonance, thereby achieving a sound insulation effect;

[0046] The height of the upper structure layer 1 and the lower structure layer 3 is L=35 mm, and the height of the air layer 2 is H=30 mm. In order to calculate the working frequency band of the customizable broadband ventilation sound insulation structure of the present invention by using the transfer matrix method, the equivalent impedance and equivalent sound velocity of the structural layer should be calculated first.

[0047] Calculation method of equivalent impedance and equivalent acoustic resistance of structural layer:

[0048]

[0049] Where d is the total thickness of the structure, and m is the number of branches of the arccosine function, which is taken as 0 here; The sign of R should be chosen to ensure that Z eff The real part of is positive, that is, the real part of the equivalent relative impedance is positive; r and t are the sound pressure transmission coefficient and sound pressure reflection coefficient of the structural layer respectively; c0 = 343 m / s is the speed of sound in air;

[0050] After obtaining the equivalent impedance and equivalent sound velocity of the structural layer, the total transfer matrix of the ventilation and sound insulation structure of the present invention can be calculated using the transfer matrix calculation method of the three-layer structure in parallel;

[0051] The total transfer matrix is ​​calculated as:

[0052]

[0053] k i is the wave number of the i-th layer, ω is the angular frequency, h i is the thickness of the i-th layer structure, Z i is the equivalent relative impedance of the i-th layer.

[0054] After obtaining the transfer matrix of each layer, the admittance Y of the i-th layer is further calculated. i :

[0055]

[0056] where t i,mn is the transfer matrix T of the i-th layer structure i The total transfer matrix of the customizable broadband ventilation and sound insulation structure in the present invention can be expressed as:

[0057]

[0058] where y i,mn is the matrix Y i After obtaining the total transfer matrix of the ventilation structure, its sound intensity transmission coefficient T and sound transmission loss (STL) can be calculated:

[0059]

[0060] Where T mn is the matrix T p The mth row and nth column element of can be used to calculate the sound intensity transmission coefficient T and the sound insulation STL to obtain the working bandwidth of the structure.

[0061] In addition, for the broadband ventilation sound insulation structure of the present invention, the working bandwidth can be adjusted by adjusting the length h of the throat in the middle of the structural layer; when h changes from 6.5mm to 32mm, the working frequency band changes from 1 / 3 to 1 octave layer. The working bandwidth is proportional to the length of h;

[0062] If two broadband ventilation sound insulation structures are connected in series, the superposition of working frequency bands can be achieved; Figure 3 The result of connecting structure 7 and structure 8 in series is shown in Table 1 (unit: mm):

[0063] Table 1 Superstructure geometric parameters

[0064]

[0065] Substitute the structural parameters of the two structures into M iThe reflection coefficient and transmission coefficient can be obtained, and the equivalent impedance and equivalent sound velocity of the structural layer can be obtained by the equivalent medium method mentioned above.

[0066]

[0067] Finally, the transfer matrix method is used to solve the operating frequency bands of the two structures.

[0068]

[0069] Through the solution, it is found that the working frequency band of structure 7 is 630Hz-900 Hz, and the working frequency band of structure 8 is 880Hz-1160Hz; after connecting structure 7 and structure 8 in series, the working frequency band of the ventilation sound insulation structure is 630Hz-1160 Hz.

[0070] In order to achieve the noise control demand with a wider bandwidth, four units with continuous working frequency bands are connected in series, and an FP resonance pipe with a distance of 8mm is formed between every two units. Through the resonant coupling of the Fano resonance of the four units and the narrow FP resonance in the middle, the wide bandwidth noise control demand of 400Hz-2450Hz is achieved.

[0071] The embodiments of the present invention are described in detail above in conjunction with the accompanying drawings, but the functions of the present invention are not limited thereto. Various changes can be derived within the knowledge of technicians in the relevant technical field without departing from the purpose of the present invention; for example, connecting more units in series can achieve a broadband ventilation sound insulation effect with a wider working frequency band, and adapt to different noise control requirements by modifying the geometric shape of the dual-mode Fano resonance.

Claims

1. A customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance, characterized in that: The ventilation and sound insulation superstructure is composed of three layers of structures arranged alternately; The first and third layers are structural layers, which are composed of rectangular pipes with different cross-sectional areas arranged in an "S" shape; the second layer in the middle is the air layer to ensure air circulation; The structural layer includes two hollow cavities, which are connected by a throat; throats are also provided at the inlet and outlet sides of the two cavities; The width and height of the two middle chambers are the same; the inlet and outlet throat geometry parameters are also the same; The sound energy propagates along the thickness direction of the structure, with part of it passing through the structural layer to reach the transmission end, and part of it passing through the air layer to reach the transmission end; the two parts of the sound energy have opposite sound pressure phases and similar amplitudes at the two resonant frequency points, forming a dual-mode Fano resonance, which is used for broadband sound insulation between the two mode frequency points.

2. The customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance according to claim 1, characterized in that: The first and third structural layers have the same geometric dimensions; the length and width of the middle throat and the throats at both ends of the same layer are different; the boundary wall thickness of different rectangular units in the structural layer is the same; and all ventilation and sound insulation sections are rectangular pipe interfaces.

3. The customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance according to claim 1, characterized in that: The geometric parameters of the structural layer affect the resonant frequency point of the dual-mode Fano resonance. Different parameters have different effects on the monopole mode frequency point, dipole mode frequency point and working bandwidth. The geometric parameters of the structural layer are determined according to the required working bandwidth and frequency band. Specifically, the parameter h only affects the upper boundary of the working bandwidth, and the parameters L, D, d1, and d2 have an impact on the upper and lower boundaries of the entire frequency band. The lower boundary of the working frequency band is determined by adjusting the parameters, and the upper boundary of the working frequency band is determined by adjusting h, thereby customizing the noise reduction requirements of the bandwidth.

4. The customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance according to claim 3, characterized in that: The width and length of the throat in the middle of the structural layer only affect the monopole mode. By adjusting the length of the throat in the middle, the bandwidth can be flexibly adjusted within 1 / 3-1 octave layer.

5. The customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance according to claim 1, characterized in that: The sound pressure reflection coefficient and sound pressure transmission coefficient of the structural layer are calculated using the transfer matrix method; The structural layer has a total of seven layers, and its transfer matrix is: in and are the incident sound pressure and the reflected sound pressure, M i is the transfer matrix of the i-th layer of medium; the sound pressure reflection coefficient and sound pressure transmission coefficient of the unit equivalent model are calculated: The impedance ratio of each layer of the medium is inversely proportional to the area of ​​the equivalent rectangular tube cross section. ij =S i / S j ,S i is the cross-sectional area of ​​the i-th layer of medium.

6. The customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance according to claim 1, characterized in that: The acoustic impedance Z of the structural layer eff and speed C eff It is expressed as: Where d is the total thickness of the structure, and m is the number of branches of the arccosine function, which is taken as 0 here; The sign of R should ensure that the real part of Zeff is positive, that is, the real part of the equivalent relative impedance is positive; r and t are the sound pressure transmission coefficient and sound pressure reflection coefficient of the structural layer respectively; c0=343m / s is the speed of sound in air.

7. A design method for a customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance, comprising the following specific steps: S1. Design broadband ventilation sound insulation superstructure as a three-layer structure, the upper and lower layers are structural layers, the height is L; the middle layer is an air layer to ensure air circulation, the height is H; S2. Use the transfer matrix method to calculate the total transfer matrix of the ventilation sound insulation structure and calculate the sound intensity transmission coefficient at different frequency points; S3. Place ventilation and sound insulation superstructures with different structural parameters in series to achieve the superposition of the bandwidths of the two superstructures.

8. The design method of a customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance according to claim 7, characterized in that: In step S2, the sound intensity transmission coefficient at different frequency points is expressed by the following formula: Where T mn is the element in the mth row and nth column of TP; is the acoustic characteristic impedance of the waveguide layers in regions 1 and 3, S total is the total cross-sectional area of ​​the ventilation and sound insulation structure, S total =(H+2L)B.

9. The design method of a customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance according to claim 7, characterized in that: When continuous broadband sound insulation noise control is required, the working bandwidths of the two super structures are connected in the first place to achieve the superposition of the working bandwidths; when there is a gap between the working bandwidths of the two super structures, the function of controllable filtering can be achieved.

10. The design method of a customizable broadband ventilated sound insulation superstructure based on dual-mode Fano resonance according to claim 7, characterized in that: When multiple units are connected in series, the narrow passages at a certain distance between the units will form FP resonance; by connecting four units in series and utilizing the resonant coupling of Fano resonance and FP resonance, the ultra-wideband ventilation and sound insulation requirements of 400Hz-2450Hz can be met.

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