A design method for underwater pressure-resistant sound-absorbing covering layer with embedded tree-shaped acoustic black holes

Abstract

The invention discloses a design method of an underwater pressure-resistant sound-absorbing covering layer with an embedded tree-shaped acoustic black hole. Based on the local resonance principle and the acoustic black hole principle, an underwater pressure-resistant sound-absorbing covering layer with an embedded tree-shaped acoustic black hole is designed; the model of the hexagonal prism unit cell of the sound-absorbing unit is approximately simplified to a cylindrical model, and the cylindrical model is further simplified to a two-dimensional axisymmetric model; the material and geometric parameters of the sound-absorbing unit are optimized; the sound-absorbing unit sample is processed according to the optimization result, a hyperelastic constitutive model is established for the base material rubber used in the processing, and the sound absorption coefficient of the sound-absorbing unit under different hydrostatic pressures is simulated by finite element software. The underwater pressure-resistant sound-absorbing covering layer with an embedded tree-shaped acoustic black hole has good sound absorption performance under high hydrostatic pressure.

Description

Technical Field

[0001] The invention relates to the field of underwater sound absorption, and in particular to a design method for an underwater pressure-resistant sound-absorbing covering layer with embedded tree-shaped acoustic black holes. Background Art

[0002] Laying a sound-absorbing coating on the surface of the underwater vehicle shell is the main technical means to control the strength of underwater targets. The acoustic coating needs excellent sound absorption performance to meet the needs of underwater vehicle acoustic stealth. For every 100m increase in the underwater vehicle's dive, the hydrostatic pressure on its surface increases by about 1MPa. The underwater working environment requires that the sound-absorbing coating still has good sound absorption performance under high water pressure.

[0003] However, the existing underwater acoustic covering layers have poor sound absorption performance under relatively high hydrostatic pressure, and there is currently a lack of design methods for underwater sound-absorbing covering layers that can withstand high hydrostatic pressure. Summary of the invention

[0004] The purpose of the present invention is to provide a design method for an underwater pressure-resistant sound-absorbing covering layer with embedded tree-shaped acoustic black holes.

[0005] The technical solution to achieve the purpose of the present invention is: a method for designing an underwater pressure-resistant sound-absorbing covering layer with an embedded tree-shaped acoustic black hole, comprising the following steps:

[0006] (1) Based on the principle of local resonance and acoustic black hole, an underwater pressure-resistant sound-absorbing covering layer with an embedded tree-shaped acoustic black hole is designed. The covering layer is composed of hexagonal prism cells arranged in a honeycomb shape, and one cell is called a sound-absorbing unit.

[0007] (2) The model of the hexagonal prism unit cell of the sound absorption unit is approximately simplified into a cylindrical model, and then the cylindrical model is further simplified into a two-dimensional axisymmetric model;

[0008] (3) Optimize the material and geometric parameters of the sound absorbing unit;

[0009] (4) The sound absorbing unit samples are processed according to the optimization results, a hyperelastic constitutive model is established for the base material rubber used in the processing, and the sound absorption coefficient of the sound absorbing unit under different hydrostatic pressures is simulated using finite element software.

[0010] Furthermore, the hexagonal prism-shaped sound absorbing unit in step (1) is composed of a metal frame, a plurality of acoustic black hole-shaped scattering plates of different scales, a support column, a viscoelastic material matrix, and a back plate lined under the sound absorbing unit; the support column passes through the centers of the plurality of scattering plates to form a tree-shaped acoustic black hole structure, the tree-shaped acoustic black hole structure is embedded in the hexagonal prism-shaped viscoelastic material matrix, the support column (3) is located at the center of the sound absorbing unit, and the six sides of the viscoelastic material matrix are surrounded by the metal frame.

[0011] Furthermore, in step (3), the following parameters are optimized: support column radius r v , border thickness δ, acoustic black hole root thickness h t , the acoustic black hole length l ABH , cut-off thickness h0, Young's modulus E1 of the base material, loss factor η, density ρ1; specifically: in the finite element software, the Nelder-Mead algorithm is used to optimize the material and geometric parameters of the cover layer sound absorption unit in the specified frequency band [f1, f2] by two strategies, using the square of the sound pressure reflection coefficient |r p 2 and the square of the sound pressure transmission coefficient |t p 2 The maximum value J1=max(r p | 2 ,t p 2 ) and its average value As two objective functions, the total objective function is Among them, r p is the sound pressure reflection coefficient, t p is the sound pressure transmission coefficient, n f =(f2-f1) / Δf+1, Δf is the frequency interval, frequency f∈[f1,f2], q i is a weighting factor; the first optimization strategy comprehensively considers the average weighting of high and low frequencies in the [f1, f2] frequency band, taking q1 = q2 = 0.5; the second optimization strategy focuses on the sound absorption performance of low frequencies. in It's J i The average value in [f1,f2], with i=1,2,

[0012] Furthermore, in the step (4), stress-strain data of the rubber material are obtained by using a rubber compression test, substituted into the strain energy density function of the hyperelastic model, and the hyperelastic constitutive model parameters are fitted to establish a hyperelastic constitutive model of the rubber; the hyperelastic model is used to calculate the deformation of the sound-absorbing cover layer unit under hydrostatic pressure in finite element software; the deformed structure is re-gridged, and the dynamic mechanical parameters of the rubber matrix material under different hydrostatic pressures measured in the test: Young's modulus and loss factor are substituted to calculate the sound absorption coefficient of the sound-absorbing unit under different hydrostatic pressures.

[0013] Compared with the prior art, the present invention has the following significant advantages: (1) the sound-absorbing covering layer of the embedded tree-shaped acoustic black hole has good resistance to hydrostatic pressure; (2) the embedded tree-shaped acoustic black hole still has good sound absorption performance under a high hydrostatic pressure of 4.5 MPa. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1is a schematic diagram of the sound absorbing covering layer and the sound absorbing unit model; Figure 1 (a) is the arrangement of the unit cells of the sound absorbing layer and the covering layer. Figure 1 (b) is the water-sound absorbing unit structure-air model. Figure 1 (c) is the three-dimensional model of the sound absorption unit. Figure 1 (d) is a simplified three-dimensional cylindrical model of the sound absorption unit. Figure 1 (e) is a simplified two-dimensional axisymmetric model of the sound-absorbing unit and a schematic diagram of the acoustic black hole-shaped scattering plate structure.

[0015] Figure 2 It is a comparison of the sound absorption coefficient of a three-dimensional model (3D) and a two-dimensional axisymmetric model (2D axisymmetric).

[0016] Figure 3 It is the sound absorption coefficient of the covering layer sound absorption unit before and after optimization.

[0017] Figure 4 is the Young's modulus of butyl rubber under different static pressures.

[0018] Figure 5 is the loss factor of butyl rubber at different static pressures.

[0019] Figure 6 It is a comparison between COMSOL simulation and experimental results of the sound absorption coefficient of the sound absorption unit at 0.1MPa (normal pressure).

[0020] Figure 7 It is a comparison between COMSOL simulation and experimental results of the sound absorption coefficient of the sound absorption unit at 0.5MPa.

[0021] Figure 8 It is a comparison between COMSOL simulation and experimental results of the sound absorption coefficient of the sound absorption unit at 1.0MPa.

[0022] Fig. 9 It is a comparison between COMSOL simulation and experimental results of the sound absorption coefficient of the sound absorption unit at 2.0MPa.

[0023] Fig.10 It is a comparison between COMSOL simulation and experimental results of the sound absorption coefficient of the sound absorption unit at 3.0MPa.

[0024] Fig.11 It is the sound absorption coefficient of the sound absorbing unit under different static pressures (standing wave tube test). DETAILED DESCRIPTION

[0025] The technical scheme adopted by the present invention is: designing an underwater pressure-resistant sound-absorbing covering layer with an embedded tree-shaped acoustic black hole; determining the size parameters and material parameters of each part of the underwater pressure-resistant sound-absorbing covering layer unit with the embedded tree-shaped acoustic black hole; establishing a hyperelastic model of rubber material to simulate the sound absorption coefficient of the underwater pressure-resistant sound-absorbing covering layer unit with the embedded tree-shaped acoustic black hole under different hydrostatic pressures; placing the underwater pressure-resistant sound-absorbing covering layer unit with the embedded tree-shaped acoustic black hole in a standing wave tube to test its sound absorption coefficient under different hydrostatic pressures, and the sound absorption coefficient can be compared and verified with the simulation result.

[0026] The specific process includes the following steps:

[0027] (1) Based on the principle of local resonance and acoustic black hole, an underwater pressure-resistant sound-absorbing covering layer with an embedded tree-shaped acoustic black hole is designed. The covering layer is composed of hexagonal prism units, and one unit cell is called a sound-absorbing unit.

[0028] (2) The three-dimensional hexagonal prism model of the sound absorption unit is approximately simplified into a cylindrical model, and then the three-dimensional cylindrical model is simplified into a two-dimensional axisymmetric model;

[0029] (3) Optimize the material and geometric parameters of the sound absorbing unit;

[0030] (4) The sound absorbing unit samples are processed according to the optimization results, and a hyperelastic constitutive model is established for the base material rubber used in the processing. The sound absorption coefficient of the sound absorbing unit under different hydrostatic pressures is simulated by finite element software. The sound absorption coefficient of the sound absorbing unit of the designed covering layer is tested by a standing wave tube test.

[0031] The hexagonal prism-shaped sound-absorbing unit in step (1) is composed of a metal frame 1, a plurality of acoustic black hole-shaped scattering plates 2 of different scales, a support column 3, a viscoelastic material matrix 4, and a back plate lining the bottom of the sound-absorbing unit. The support column 3 passes through the center of the plurality of scattering plates 2 to form a tree-shaped acoustic black hole structure, and the tree-shaped acoustic black hole structure is embedded in the hexagonal prism-shaped viscoelastic material matrix 4. The support column 3 is located at the center of the sound-absorbing unit, and the six sides of the viscoelastic material matrix 4 are surrounded by a metal frame 1 of uniform thickness. The structural schematic diagram of the sound-absorbing covering layer and the sound-absorbing unit is shown in FIG. Figure 1 shown.

[0032] In step (3), the following parameters are optimized: support column radius r v , border thickness δ, acoustic black hole root thickness h t , the acoustic black hole length l ABH , cut-off thickness h0, Young's modulus E1 of the base material, loss factor η, density ρ1; specifically: in the finite element software, the Nelder-Mead algorithm is used to optimize the material and geometric parameters of the cover layer sound absorption unit in the specified frequency band [f1, f2] by two strategies, using the square of the sound pressure reflection coefficient r p2 and the square of the sound pressure transmission coefficient t p 2 The maximum value J1=max(r p | 2 ,t p 2 ) and its average value As two objective functions, the total objective function is Among them, r p is the sound pressure reflection coefficient, t p is the sound pressure transmission coefficient, n f =(f2-f1) / Δf+1, Δf is the frequency interval, frequency f∈[f1,f2], q i is a weighting factor. The first optimization strategy comprehensively considers the average weighting of high and low frequencies in the frequency band [f1, f2], taking q1 = q2 = 0.5; the second optimization strategy focuses on the sound absorption performance of low frequencies. in It's J i The average value in [f1,f2], with i=1,2,

[0033] In the step (4), the stress-strain data of the rubber material is obtained by using a rubber compression test, and the data is substituted into the strain energy density function of the hyperelastic model to fit the hyperelastic constitutive model parameters and establish a hyperelastic constitutive model of the rubber; the hyperelastic model is used to calculate the deformation of the sound-absorbing cover layer unit under hydrostatic pressure in COMSOL finite element software; the deformed structure is re-gridged, and the dynamic mechanical parameters of the rubber matrix material under different hydrostatic pressures measured in the test are substituted: Young's modulus and loss factor, and the sound absorption coefficient of the sound-absorbing structure under different hydrostatic pressures is calculated.

[0034] The geometric parameters of the sound-absorbing covering layer unit parameters involved in the above process include: the hexagon side length L, the equivalent radius R of the sound-absorbing unit c , substrate layer thickness h1, backplane thickness h2, number of scattering plates I, support column radius r v , border thickness δ, acoustic black hole index m, root thickness h t , length l ABH , cut-off thickness h0; material parameters include: Young's modulus E1, loss factor η, density ρ1, Poisson's ratio ν1 of matrix material - rubber, Young's modulus E2, density ρ2, Poisson's ratio ν2 of the material of back plate, support column, frame and scattering plate - steel.

[0035] The following simulation experiment is used to further illustrate the invention in conjunction with the accompanying drawings.

[0036] The schematic diagram of the structure of the underwater pressure-resistant sound-absorbing covering layer with embedded tree-shaped acoustic black holes designed by the present invention is as follows: Figure 1shown.

[0037] Simplify the 3D model of the sound-absorbing cover layer's sound-absorbing unit into a 2D axisymmetric model:

[0038] The base material of the underwater pressure-resistant sound-absorbing covering layer with embedded tree-shaped acoustic black holes is rubber, and the materials of the back plate, support column, frame and acoustic black hole scattering plate are steel. The three-dimensional hexagonal prism model of the sound-absorbing unit of the underwater pressure-resistant sound-absorbing covering layer with embedded tree-shaped acoustic black holes is simplified to a two-dimensional axisymmetric model. Taking the sound-absorbing unit with 6 identical acoustic black hole-shaped scattering plates uniformly embedded as an example, r v =3mm, δ=2mm, the root thickness of the acoustic black hole structure h t =5mm, exponent m=2, cutoff thickness h0=0.5mm, acoustic black hole length l ABH =45mm, and the other parameters are shown in Table 1. The results of calculating the sound absorption coefficient using the three-dimensional model and the two-dimensional axisymmetric model are as follows Figure 2 When the loss factor η of the rubber is ≥ 0.35, the first sound absorption peak of the axisymmetric model and the hexagonal prism model almost overlap, and the difference between the remaining sound absorption peaks is very small, moving toward low frequencies, but it can still characterize the trend of the sound absorption coefficient curve of the sound absorbing structure within 200Hz-5000Hz, thereby determining the lower limit of the optimization range of the loss factor of the base material of the sound absorbing unit.

[0039] Table 1 Geometric parameters and material parameters

[0040]

[0041] Optimize the material and geometric parameters of the sound-absorbing elements of the sound-absorbing cover layer:

[0042] Based on the verified two-dimensional axisymmetric model, the sound absorption unit proposed in the previous article is optimized using the Nelder-Mead algorithm in COMSOL finite element software to achieve the best sound absorption performance. The optimization tolerance is 0.01, and the maximum number of model calculations is 1000. The optimization parameters are: support column radius r v , border thickness δ, acoustic black hole root thickness h t , the acoustic black hole length l ABH , cut-off thickness h0, Young's modulus E1 of matrix material, loss factor η, density ρ1.

[0043] The square of the sound pressure reflection coefficient | r p 2 and the square of the sound pressure transmission coefficient |t p 2 The maximum value J1=max(r p 2 ,t p 2) and its average value As two objective functions, the total objective function is Among them, r p is the sound pressure reflection coefficient, t p is the sound pressure transmission coefficient, n f =(f2-f1) / Δf+1, Δf is the frequency interval, frequency f∈[f1,f2], q i is a weighting factor. The first optimization strategy (hereinafter referred to as optimization 1) comprehensively considers the average weighting of high and low frequencies in the frequency band [f1, f2], and takes q1 = q2 = 0.5. The second optimization strategy (hereinafter referred to as (optimization 2) focuses on the sound absorption performance of low frequencies. in It's J i The average value in [f1,f2], with i=1,2, The first and second optimization strategies are referred to as optimization 1 and optimization 2, respectively. Except for the optimization parameters, the other parameters refer to Table 1. The parameters before and after optimization are shown in Table 2, and the sound absorption coefficients before and after optimization are shown in Table 2. Figure 3 As shown. The optimization constraint is 13mm≤r v +l ABH δ≤58mm.

[0044] Table 2 Parameters of sound absorption unit before and after optimization

[0045]

[0046] According to the optimization results, a cylindrical sound-absorbing unit sample is processed. The density of butyl rubber used in the sample is ρ1=1250kg / m 3 , Poisson's ratio v1 = 0.45. The hyperelastic constitutive model of butyl rubber was established, and the dynamic mechanical parameters of butyl rubber under different static pressures were obtained: Young's modulus and loss factor were as follows: Figure 4 and Figure 5 As shown in Table 3, based on these two, COSOL is used to simulate the sound absorption coefficient of the sound absorption unit sample under different static pressures. Some geometric parameters of the sound absorption unit sample are shown in Table 3, and the remaining parameters are shown in Table 1.

[0047] Table 3 Internal geometric parameters of the sound absorption unit

[0048]

[0049] The above design results are also verified by the standing wave tube test. The comparison between COMSOL simulation results and standing wave tube test results is shown in Figure 6-Figure 11 The results show that the simulation model is consistent with the test results, which verifies the accuracy of the simulation model in predicting the sound absorption performance of the sound absorption unit of the cover layer. The underwater pressure-resistant sound-absorbing cover layer with embedded tree-shaped acoustic black holes designed in this paper has a good sound absorption effect under static pressure.

Claims

1. A design method for an underwater pressure-resistant sound-absorbing covering layer with an embedded tree-shaped acoustic black hole, characterized in that: The following steps are involved: (1) Based on the principle of local resonance and acoustic black hole, an underwater pressure-resistant sound-absorbing covering layer with an embedded tree-shaped acoustic black hole is designed. The sound-absorbing covering layer is composed of hexagonal prism cells arranged in a honeycomb shape, and one cell is called a sound-absorbing unit. (2) The model of the hexagonal prism unit cell of the sound absorption unit is approximately simplified into a cylindrical model, and then the cylindrical model is further simplified into a two-dimensional axisymmetric model; (3) Optimize the material and geometric parameters of the sound absorbing unit; The following parameters are optimized: support column radius r v , border thickness δ, acoustic black hole root thickness h t , the acoustic black hole length l ABH , cut-off thickness h0, Young's modulus E1 of the base material, loss factor η, density ρ1; specifically: in the finite element software, the Nelder-Mead algorithm is used to optimize the material and geometric parameters of the cover layer sound absorption unit in the specified frequency band [f1, f2] by two strategies, using the square of the sound pressure reflection coefficient |r p | 2 and the square of the sound pressure transmission coefficient |t p | 2 The maximum value J1=max(|r p | 2 ,|t p | 2 ) and its average value As two objective functions, the total objective function is Among them, r p is the sound pressure reflection coefficient, t p is the sound pressure transmission coefficient, n f =(f2-f1) / Δf+1, Δf is the frequency interval, frequency f∈[f1,f2], q i is the weighting factor; The first optimization strategy comprehensively considers the average weighting of high and low frequencies in the frequency band [f1, f2], taking q1 = q2 = 0.5; the second optimization strategy focuses on the sound absorption performance of low frequencies. in It's J i The average value in [f1,f2], with i=1,2, (4) The sound absorbing unit samples are processed according to the optimization results, a hyperelastic constitutive model is established for the base material rubber used in the processing, and the sound absorption coefficient of the sound absorbing unit under different hydrostatic pressures is simulated using finite element software.

2. The design method of an underwater pressure-resistant sound-absorbing covering layer with an embedded tree-shaped acoustic black hole according to claim 1 is characterized in that: In step (1), the hexagonal prism-shaped sound absorbing unit is composed of a metal frame (1), a plurality of acoustic black hole-shaped scattering plates (2) of different scales, a support column (3), a viscoelastic material matrix (4), and a back plate lined below the sound absorbing unit; the support column (3) passes through the centers of the plurality of scattering plates (2) to form a tree-shaped acoustic black hole structure, the tree-shaped acoustic black hole structure is embedded in the hexagonal prism-shaped viscoelastic material matrix (4), the support column (3) is located at the center of the sound absorbing unit, and the six sides of the viscoelastic material matrix (4) are surrounded by the metal frame (1).

3. The design method of underwater pressure-resistant sound-absorbing covering layer with embedded tree-shaped acoustic black holes according to claim 1 is characterized in that: In the step (4), the stress-strain data of the rubber material is obtained by using a rubber compression test, and the data is substituted into the strain energy density function of the hyperelastic model to fit the hyperelastic constitutive model parameters and establish a hyperelastic constitutive model of the rubber; the hyperelastic model is used to calculate the deformation of the sound-absorbing cover layer unit under hydrostatic pressure in finite element software; the deformed structure is re-gridged, and the dynamic mechanical parameters of the rubber matrix material under different hydrostatic pressures measured in the test are substituted: Young's modulus and loss factor, and the sound absorption coefficient of the sound-absorbing unit under different hydrostatic pressures is calculated.

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