Turbulence-induced vibration and acoustic radiation control method and system for local resonance meta-plate

Abstract

The present invention belongs to the technical field of underwater super-plate vibration and acoustic radiation, and discloses a method for controlling turbulence-excited vibration and acoustic radiation of a lateral localized resonant super-plate under turbulent excitation. The present invention uses the equivalent continuum theory to equate a discrete lateral localized resonant super-plate to a continuum whose mass density or Young's modulus varies with frequency. The equivalent continuum theory is used to present the effects of the lateral localized resonant structure in the equivalent mass density of the base plate by equivalent means, and the mutual power spectrum density equation of the displacement response of the elastic structure under turbulent excitation is established based on random theory. The velocity mutual power spectrum density solution expression is obtained by using modal expansion, Rayleigh integral, and modal orthogonality, so as to study the vibration and acoustic radiation mechanism of the finite period underwater lateral localized resonant super-plate under turbulent excitation.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater super plate vibration and acoustic radiation, and in particular relates to a method for controlling turbulence-induced vibration and acoustic radiation of a lateral localized resonant super plate under turbulence excitation. Background Art

[0002] When underwater vehicles such as ships are running at high speeds, the structural vibration noise excited by the turbulent boundary layer becomes an important component of the noise inside such vehicles, which not only has a great impact on their stealth performance, but also has a great impact on the structural strength. When ships are at medium and high speeds, the flow-induced vibration noise is an important component of the sonar self-noise, which has an adverse effect on the normal operation of the sonar.

[0003] Through the above analysis, the problems and defects of the prior art are as follows:

[0004] When underwater vehicles such as ships are running at high speeds, the structural vibration noise excited by the turbulent boundary layer becomes an important component of the noise inside such vehicles, which not only has a great impact on their stealth performance, but also has a great impact on the structural strength. When ships are at medium and high speeds, the flow-induced vibration noise is an important component of the sonar self-noise, which has an adverse effect on the normal operation of the sonar. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a method for controlling turbulence-induced vibration and acoustic radiation of a lateral localized resonant super-plate under turbulence excitation.

[0006] The present invention is implemented as follows: a method for controlling turbulence-induced vibration and acoustic radiation of a lateral localized resonant super-plate under turbulence excitation comprises:

[0007] Step 1: Through the equivalent continuum theory, the discrete lateral localized resonant meta-plate is equivalent to a continuum whose mass density or Young's modulus varies with frequency;

[0008] Step 2: Based on the stochastic theory, the cross-power spectrum density equation of the displacement response of the elastic structure under turbulent excitation is established;

[0009] Step 3, using mode expansion, Rayleigh integral, and mode orthogonality, the velocity cross-power spectrum density solution expression is obtained;

[0010] Step 4: Study the vibration suppression mechanism of underwater lateral localized resonance meta-plate with finite period under turbulent excitation.

[0011] Furthermore, according to the random theory, the cross-power spectral density equation of the displacement response of the elastic structure under turbulent excitation is established:

[0012] S w (u,ξ,ω)=∫∫Spp (ξ′,ω)H w (u,u′,-ω)×H w (u+ξ,u′+ξ′,ω)du′dξ′ (1)

[0013] Where u = (x, y) represents the coordinates of a point on the structure, ξ = (ξ x ,ξ y ) represents the distance between two observation points, H w (u,u′,ω) represents the single frequency response of displacement, S pp (ξ,ω) represents the transverse spectral density of the pressure fluctuation on the wall of the turbulent boundary layer;

[0014] The simplified formula for the cross power spectral density is:

[0015]

[0016] Where Φ p (ω) represents the autospectral density, coefficient α x and α y Represents the longitudinal and transverse coherence loss respectively; for smooth walls, commonly used values ​​are: α x =0.116 and α y = 0.7; the average convection velocity of the turbulent boundary layer is expressed as U c express

[0017] U c =β c U ∞ ,β c =0.65 (3)

[0018] The autopower spectral density can be expressed as

[0019]

[0020] In the formula δ * is the displacement thickness of the boundary layer, α is a dimensionless quantity,

[0021] The fluctuating pressure generated by the turbulent boundary layer can be considered as an external force exciting the plate, and the governing equation describing the response of the plate to the excitation of the turbulent boundary layer in the surrounding fluid can be expressed as

[0022]

[0023] Where W(u,ω) represents the displacement function of the plate, D p and are the bending stiffness and equivalent surface density of the lateral local resonance plate, t is the time, P(u,ω) represents the turbulent boundary layer fluctuation pressure, P a(u,ω) represents the acoustic pressure generated by fluid-structure interaction.

[0024] Furthermore, the equivalent surface density of the super plate is derived from the following formula:

[0025]

[0026] In the formula Indicates the surface density of the substrate;

[0027] The single-frequency response of the plate displacement can be expressed as

[0028] H w (u,u′,ω)=W(u,ω)when P(u,ω)=δ(uu′) (7)

[0029] According to the mode expansion and inverse Fourier transform, the displacement function of the plate can be expressed as

[0030]

[0031] Where α mn (u) is the mode function, W mn (ω) is the mode expansion coefficient in the frequency domain, W(u,ω) is the frequency spectrum of the plate displacement at u;

[0032] For a simply supported plate, α mn (u) can be expressed as

[0033]

[0034] Where S p =L x L y Indicates the plate area, L x and L y represent the side lengths of the LLR plate along the x and y directions, respectively.

[0035] According to Rayleigh integral, the far-field sound pressure can be expressed as

[0036]

[0037] Substituting formulas (7) to (10) into formula (6), we can obtain:

[0038]

[0039] definition

[0040]

[0041] but

[0042]

[0043] set up

[0044]

[0045] but

[0046]

[0047] The single frequency response function of the board can be expressed as

[0048]

[0049] The relationship between the cross power spectral density of displacement and velocity is:

[0050] S v (u,ξ,ω)=ω 2 S w (u,ξ,ω) (17)

[0051] Substituting formula (16) and (17) into formula (1), we can obtain the solution expression of velocity cross power spectrum density:

[0052]

[0053] ξ can be set to (0,0) to obtain the velocity autospectral density at a point on the plate, which can be derived as

[0054]

[0055] The average panel response in terms of velocity can be expressed concisely as

[0056]

[0057] In order to improve the calculation efficiency, the mutual radiation impedance between vibration modes is omitted; on this basis, combined with orthogonality and simplified expressions,

[0058]

[0059]

[0060] A finite-size metaplate is constructed, which consists of 25 unit cells along the x-direction and 20 unit cells along the y-direction, with a side length of 0.02 m. It is assumed that there is a turbulent boundary layer excitation generated by a flow rate of 6 m / s.

[0061] The present invention provides a system for studying the vibration and acoustic radiation mechanism of a finite period underwater lateral local resonance superstructure plate under turbulent excitation, comprising:

[0062] An equivalent continuum module, configured to treat a discrete lateral local resonance meta-plate as an equivalent continuum whose mass density or Young's modulus varies with frequency;

[0063] Stochastic theory module, used to establish the cross-power spectral density equation for the displacement response of elastic structures under turbulent excitation;

[0064] The calculation module includes the functions of modal expansion, Rayleigh integration, and modal orthogonality to obtain the solution expression of velocity cross-power spectrum density;

[0065] The analysis module is used to study the vibration suppression mechanism of the meta-plate under turbulent excitation.

[0066] Furthermore, the random theory module is further configured to calculate the distance between two observation points, the single frequency response of the displacement and the transverse spectral density representing the pressure fluctuation on the wall of the turbulent boundary layer, and simplify the cross power spectral density according to the coherence loss coefficient and the average convection velocity.

[0067] Furthermore, the calculation module is further configured to calculate the equivalent surface density of the meta-plate, and obtain the single-frequency response of the plate displacement according to the modal function and the mode expansion coefficient in the frequency domain.

[0068] Furthermore, the analysis module is further configured to calculate the far-field sound pressure according to the Rayleigh integral, and simplify the relationship between the cross power spectrum density of the displacement and the velocity by defining relevant parameters, thereby deriving a solution expression for the cross power spectrum density of the velocity.

[0069] Furthermore, the system further includes a super-plate model configured with a plurality of unit cells, wherein the unit cells are arranged along the x-direction and the y-direction respectively to simulate the vibration response under the excitation of the turbulent boundary layer.

[0070] Furthermore, the system is configured to simulate the influence of turbulent boundary layer excitation generated by a flow rate of 6 m / s, and calculate the vibration and sound radiation characteristics of the superstructure plate under the excitation.

[0071] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0072] First, the present invention uses the equivalent continuum theory to equate the discrete lateral local resonance super-plate to a continuum whose mass density or Young's modulus varies with frequency. The equivalent continuum theory is used to present the effects of the lateral local resonance structure in the equivalent mass density of the base plate by equivalent means. According to the random theory, the mutual power spectrum density equation of the displacement response of the elastic structure under turbulent excitation is established. Using modal expansion, Rayleigh integral, and modal orthogonality, the solution expression of the velocity mutual power spectrum density is obtained, thereby studying the vibration and acoustic radiation mechanism of the underwater lateral local resonance super-plate with a finite period under turbulent excitation.

[0073] Second, the present invention, on the basis of solving the technical problems and technical defects in the prior art, realizes the effective control of the vibration and acoustic radiation of the lateral localized resonant meta-plate under turbulent excitation, and has significant technical progress and practical value.

[0074] Improved structural vibration control efficiency: Through the above method, the vibration of the lateral local resonance super-structure plate under turbulence excitation can be effectively controlled, the vibration response of the structure can be reduced, and the stability and service life of the structure can be improved.

[0075] Reducing sound radiation: By controlling structural vibration, the present invention also effectively reduces the sound radiation caused by structural vibration, which is of great significance for improving the concealment of underwater or aerial structures.

[0076] Broadening the application scope of metamaterials: The present invention utilizes the characteristics of metamaterials to provide a new approach for the application of metamaterials in the field of vibration and acoustic radiation control, thereby broadening their application scope.

[0077] An efficient analysis method is provided: by combining equivalent continuum theory, random theory and modal analysis technology, the present invention provides an efficient and accurate method for dynamic response analysis of complex structures under complex excitations.

[0078] Third, the expected benefits and commercial value after the technical solution of the present invention is as follows: Compared with the finite element method, the present invention realizes the band gap calculation of the metamaterial plate more efficiently and quickly, improves the calculation efficiency, and creates higher commercial value. The present invention is not limited to this structure, and the present invention has guiding significance for the research on the vibration and acoustic radiation excitation of underwater metamaterial plates under various turbulent excitations.

[0079] The technical solution of the present invention fills the technical gap in the industry at home and abroad: the present invention explains the research method of vibration and acoustic radiation excitation of underwater metamaterial plates under turbulent excitation, which has guiding significance for the research of vibration and acoustic radiation excitation of underwater metamaterial plates under various turbulent excitations.

[0080] The technical solution of the present invention overcomes technical prejudice: the present invention uses the equivalent continuum theory to present the effects of the lateral local resonance structure in the equivalent mass density of the base plate through equivalent means, and establishes the mutual power spectrum density equation of the displacement response of the elastic structure under turbulent excitation based on the random theory. The velocity mutual power spectrum density solution expression is obtained by using modal expansion, Rayleigh integral, and modal orthogonality, so as to study the vibration and acoustic radiation mechanism of the finite period underwater lateral local resonance super-structure plate under turbulent excitation. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1It is a flow chart of a method for controlling turbulence-induced vibration and acoustic radiation of a lateral localized resonant super-plate under turbulence excitation provided by an embodiment of the present invention.

[0082] Figure 2 This is an analogy conversion diagram of the lateral localized resonance meta-plate equivalent to the homogeneous plate provided by the embodiment of the present invention. (a) Front view of the meta-plate cell; (b) Bird's-eye view of the meta-plate cell; (c) Model diagram of the meta-plate; (d) Equivalent homogeneous plate.

[0083] Figure 3 It is a calculation model diagram of the acoustic vibration characteristics of the lateral localized resonant super-plate under turbulent excitation provided by an embodiment of the present invention.

[0084] Figure 4 It is an average power spectrum density diagram of the plate caused by a flow rate of 6 m / s in vacuum and underwater provided by an embodiment of the present invention.

[0085] Figure 5 1 is a self-spectral density distribution diagram of the vibration velocity of the underwater lateral localized resonance metamaterial plate provided by an embodiment of the present invention at different frequencies: (a) 63 Hz, (b) 185 Hz, (c) 331 Hz, and (d) 429 Hz.

[0086] Figure 6 Graphs showing the effect of flow velocity on the vibroacoustic performance of a meta-plate provided by an embodiment of the present invention: (a) autospectral density of the turbulent boundary layer fluctuation pressure at different flow velocities, and (b) power spectral density of the average plate velocity at different flow velocities.

[0087] Figure 7 1 is a diagram showing the influence of the geometric dimensions of the meta-plate provided in an embodiment of the present invention on the vibration response: (a) the plate is elongated along the flow direction, and (b) the plate is widened perpendicular to the flow direction. DETAILED DESCRIPTION

[0088] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0089] The present invention proposes a method for controlling the vibration and acoustic radiation of a lateral localized resonant meta-plate under turbulent excitation, and proposes an innovative solution to the structural vibration and noise problem of turbulent boundary layer excitation encountered by underwater vehicles at high speeds mentioned in the background technology. The claimed technical solution of the present invention solves the problems of the prior art and achieves significant technical progress through the following steps:

[0090] Solution:

[0091] Step 1: Application of Equivalent Continuum Theory

[0092] Through the equivalent continuum theory, the present invention simplifies the complex lateral localized resonant meta-plate into a continuum whose mass density or Young's modulus varies with frequency, thereby simplifying the analysis process of the complex structure and providing a theoretical basis for subsequent vibration control.

[0093] Step 2: Establish the cross power spectrum density equation of displacement response

[0094] Based on random theory, the cross-power spectral density equation of the displacement response of elastic structures under turbulent excitation is established, which provides a mathematical model for analyzing the dynamic response of structures under random turbulent excitation.

[0095] Step 3: Solve the velocity cross power spectrum density

[0096] Through the methods of modal expansion, Rayleigh integral and modal orthogonality, the solution expression of velocity cross-power spectrum density is obtained. This step provides an effective calculation tool for accurately calculating structural response.

[0097] Step 4: Study on the vibration suppression mechanism

[0098] The vibration suppression mechanism of a finite-period underwater lateral localized resonant meta-plate under turbulent excitation was studied in depth, and the effectiveness of the meta-plate in reducing the vibration and noise caused by turbulence was explored.

[0099] Technical effects and progress:

[0100] Vibration and noise control: The method proposed in the present invention can effectively control the structural vibration and noise of high-speed underwater vehicles, especially the vibration and noise generated by turbulent boundary layer excitation, thereby improving the stealth performance and structural strength of the vehicle.

[0101] Improved sonar performance: For military vessels such as ships, the present invention can significantly reduce flow-induced vibration noise, reduce sonar self-noise, and thus improve the detection performance and accuracy of sonar.

[0102] Technological innovation: This invention applies metamaterial technology to the vibration and noise control of underwater vehicles, demonstrating new applications of materials science in traditional fields and embodying significant technological innovation and progress.

[0103] The present invention aims at the vibration and noise problems faced by underwater vehicles when running at high speeds, and proposes an effective control method, which not only solves the defects of the prior art, but also provides a technical solution with practical application value and broad application prospects.

[0104] Two specific application examples of the embodiment of the present invention are:

[0105] Example 1: Vibration and acoustic radiation control of aircraft wing surface

[0106] Construction of the equivalent continuum model: First, through the equivalent continuum theory, the lateral localized resonant metamaterial covering the wing surface is equivalent to a frequency-dependent continuum, in which the mass density and Young's modulus vary with frequency. This step simplifies the complex metamaterial structure into an easy-to-handle continuum model for further analysis.

[0107] Vibration response analysis under turbulence excitation: Considering the turbulence excitation encountered during the flight of the aircraft, the cross-power spectral density equation of the displacement response of the wing surface under turbulence excitation is established using stochastic theory. This step quantifies the excitation effect of turbulence on the wing surface and provides a theoretical basis for vibration control.

[0108] Control of vibration and acoustic radiation: The velocity cross-power spectrum density is solved through modal expansion, Rayleigh integration and modal orthogonality technology to accurately calculate the vibration response of the wing surface. By optimizing the design of metamaterials, such as adjusting the parameters of local resonance units, the vibration of the wing surface can be effectively suppressed, thereby reducing the acoustic radiation caused by structural vibration.

[0109] Example 2: Vibration and noise control of underwater hull

[0110] Equivalence of continuum model: For underwater hulls, the lateral local resonance metamaterial attached to the hull surface is firstly equivalent to a continuum model with variable mass density and variable Young's modulus through equivalent continuum theory. This step simplifies the complex metastructure for further analysis.

[0111] Turbulence excitation analysis: underwater hulls are subject to turbulent excitation from the surrounding water flow during navigation. Using random theory, the cross-power spectral density equation of the displacement response of the hull surface under turbulent excitation is established to quantify the impact of turbulence on the hull.

[0112] Vibration suppression and noise reduction: modal analysis technology is used to calculate the velocity mutual power spectrum density of the hull surface to obtain the vibration response. By adjusting the design parameters of the superstructure (such as the size and distribution of the local resonance unit), its vibration control performance is optimized, thereby effectively reducing the noise generated by the hull due to structural vibration and improving the concealment and comfort of the hull.

[0113] In view of the problems existing in the prior art, the technical solution adopted by the present invention is:

[0114] Application of equivalent continuum theory: First, the present invention uses equivalent continuum theory to equate the discrete lateral localized resonant meta-plate to a continuum whose mass density or Young's modulus varies with frequency. This step solves the technical difficulty of simplifying complex discrete structures into a continuum model that is easier to analyze and process, thus providing a basis for subsequent analysis and control.

[0115] Application of random theory in displacement response analysis: Through random theory, the present invention establishes the cross-power spectrum density equation of the displacement response of the elastic structure under turbulent excitation. This step solves the problem of how to quantify the dynamic response of the elastic structure under turbulent excitation and provides a theoretical basis for vibration control.

[0116] Application of modal analysis technology: Using modal expansion, Rayleigh integral and modal orthogonality, the present invention obtains the solution expression of velocity cross power spectrum density. This step makes vibration analysis more accurate and efficient, and solves the problem of solving complex vibration problems.

[0117] Research on the vibration suppression mechanism under turbulent excitation: This paper studies the vibration suppression mechanism of a finite period underwater lateral localized resonant meta-plate under turbulent excitation. This step proposes a specific vibration suppression strategy for the vibration control problem in practical applications and solves the technical challenges in practical applications.

[0118] like Figure 1 As shown, the present invention provides a method for controlling turbulence-induced vibration and acoustic radiation of a lateral localized resonant meta-plate under turbulence excitation, comprising the following steps:

[0119] S101, through the equivalent continuum theory, the discrete lateral localized resonant meta-plate is equivalent to a continuum whose mass density or Young's modulus varies with frequency;

[0120] S102, based on stochastic theory, establish the cross-power spectral density equation of the displacement response of elastic structures under turbulent excitation;

[0121] S103, using mode expansion, Rayleigh integral, and mode orthogonality, the velocity cross-power spectrum density solution expression is obtained;

[0122] S104, the vibration suppression mechanism of underwater lateral localized resonant meta-plate with finite period under turbulent excitation is studied.

[0123] The present invention provides a cross-power spectrum density equation for establishing the displacement response of an elastic structure under turbulent excitation based on random theory:

[0124] S w (u,ξ,ω)=∫∫S pp (ξ′,ω)H w (u,u′,-ω)×H w (u+ξ,u′+ξ′,ω)du′dξ′ (23)

[0125] Where u = (x, y) represents the coordinates of a point on the structure, ξ = (ξ x ,ξ y ) represents the distance between two observation points, H w(u,u′,ω) represents the single frequency response of displacement, S pp (ξ,ω) represents the transverse spectral density of the pressure fluctuation on the wall of the turbulent boundary layer;

[0126] The simplified formula for the cross power spectral density is:

[0127]

[0128] Where Φ p (ω) represents the autospectral density, coefficient α x and α y Represents the longitudinal and transverse coherence loss respectively; for smooth walls, commonly used values ​​are: α x =0.116 and α y = 0.7; the average convection velocity of the turbulent boundary layer is expressed as U c express

[0129] U c =β c U ∞ ,β c =0.65 (25)

[0130] The autopower spectral density can be expressed as

[0131]

[0132] In the formula δ * is the displacement thickness of the boundary layer, α is a dimensionless quantity,

[0133] The fluctuating pressure generated by the turbulent boundary layer can be considered as an external force exciting the plate, and the governing equation describing the response of the plate to the excitation of the turbulent boundary layer in the surrounding fluid can be expressed as

[0134]

[0135] Where W(u,ω) represents the displacement function of the plate, D p and are the bending stiffness and equivalent surface density of the lateral local resonance plate, t is the time, P(u,ω) represents the turbulent boundary layer fluctuation pressure, P a (u,ω) represents the acoustic pressure generated by fluid-structure interaction.

[0136] The equivalent surface density of the super structure plate provided by the present invention is derived from the following formula:

[0137]

[0138] In the formula Indicates the surface density of the substrate;

[0139] The single frequency response of the plate displacement can be expressed as

[0140] H w (u,u′,ω)=W(u,ω)when P(u,ω)=δ(uu′) (29)

[0141] According to the mode expansion and inverse Fourier transform, the displacement function of the plate can be expressed as

[0142]

[0143] Where α mn (u) is the mode function, W mn (ω) is the mode expansion coefficient in the frequency domain, W(u,ω) is the frequency spectrum of the plate displacement at u;

[0144] For a simply supported plate, α mn (u) can be expressed as

[0145]

[0146] According to Rayleigh integral, the far-field sound pressure can be expressed as

[0147]

[0148] From this we can get,

[0149]

[0150] definition

[0151]

[0152] but

[0153]

[0154] set up

[0155]

[0156] but

[0157]

[0158] The single frequency response function of the board can be expressed as

[0159]

[0160] The relationship between the cross power spectral density of displacement and velocity is:

[0161] S v (u,ξ,ω)=ω 2 S w (u,ξ,ω) (39)

[0162] From this, the solution expression of velocity cross power spectrum density can be obtained as follows:

[0163]

[0164] The average panel response in terms of velocity can be expressed concisely as

[0165]

[0166] In order to improve the calculation efficiency, the mutual radiation impedance between vibration modes is omitted; on this basis, combined with orthogonality and simplified expressions,

[0167]

[0168]

[0169] A finite-size metaplate is constructed, which consists of 25 unit cells along the x-direction and 20 unit cells along the y-direction, with a side length of 0.02 m. It is assumed that there is a turbulent boundary layer excitation generated by a flow rate of 6 m / s.

[0170] When an underwater vehicle is on its way, it is affected by turbulence excitation. The purpose of the present invention is to use acoustic metamaterials to control the vibration and sound radiation of the underwater vehicle in a specific frequency band.

[0171] Extension: The present invention is applicable to various underwater structures in engineering.

[0172] Research on low-frequency vibration and acoustic radiation mechanism of underwater lateral local resonance metamaterial plate under turbulent excitation:

[0173] The discrete lateral local resonance meta-plate is equivalent to a continuum whose mass density or Young's modulus varies with frequency through the equivalent continuum theory. After obtaining the equivalent parameters of the lateral local resonance structure, it is attached to the homogeneous plate to form a lateral local resonance meta-plate. Then, the equivalent continuum theory is used to present the effects of the lateral local resonance structure in the equivalent mass density of the base plate through equivalent means. The equivalent process of the meta-plate is as follows: Figure 2 shown.

[0174] Establish as Figure 3 The acoustic-vibration coupling calculation model shown in the figure includes a fluid domain and a lateral localized resonant meta-plate under turbulent excitation. Based on random theory, the vibration characteristics and acoustic radiation characteristics of the lateral localized resonant meta-plate under turbulent excitation are studied, revealing the research mechanism of low-frequency vibration and acoustic radiation of the lateral localized resonant meta-plate with a finite period excited by underwater turbulence.

[0175] Consider a simply supported finite metaplate on an infinite rigid baffle. One side of the plate is immersed in a fluid with density ρ0 and sound velocity c0. The surface z < 0 is excited by the turbulent boundary layer due to the introduced flow. Assume that the far-field flow velocity is far U ∞ is less than the speed of sound, so its influence on the speed of sound is neglected. Due to the randomness of turbulent pulsating pressure and the temporal and spatial correlation between these excitation pressures, random acoustic problems are complex. According to random theory, the cross-power spectral density of the displacement response of an elastic structure under turbulent excitation can be expressed as:

[0176] S w (u,ξ,ω)=∫∫S pp (ξ′,ω)H w (u,u′,-ω)×H w (u+ξ,u′+ξ′,ω)du′dξ′(44)

[0177] Where u = (x, y) represents the coordinates of a point on the structure, ξ = (ξ x ,ξ y ) represents the distance between two observation points, H w (u,u′,ω) represents the single frequency response of displacement, S pp (ξ,ω) represents the transverse spectral density of the pressure fluctuations on the wall of the turbulent boundary layer.

[0178] The simplified formula for the cross power spectral density is:

[0179]

[0180] Where Φ p (ω) represents the autospectral density, coefficient α x and α y Represents the longitudinal and transverse coherence loss respectively. For smooth walls, commonly used values ​​are: α x =0.116 and α y = 0.7. The average convection velocity of the turbulent boundary layer is expressed as U c express

[0181] U c =β c U ∞ ,β c =0.65 (46)

[0182] The autopower spectral density can be expressed as

[0183]

[0184] In the formula δ * is the displacement thickness of the boundary layer, α is a dimensionless quantity,

[0185] The fluctuating pressure generated by the turbulent boundary layer can be considered as an external force exciting the plate, and the governing equation describing the response of the plate to the excitation of the turbulent boundary layer in the surrounding fluid can be expressed as

[0186]

[0187] Where W(u,ω) represents the displacement function of the plate, D p and are the bending stiffness and equivalent surface density of the lateral local resonance plate, t is the time, P(u,ω) represents the turbulent boundary layer fluctuation pressure, P a (u,ω) represents the acoustic pressure generated by fluid-structure interaction.

[0188] The equivalent surface density of the super plate is derived from the following formula:

[0189]

[0190] In the formula Indicates the surface density of the substrate.

[0191] The single frequency response of the plate displacement can be expressed as

[0192] H w (u,u′,ω)=W(u,ω)when P(u,ω)=δ(uu′) (50)

[0193] According to the mode expansion and inverse Fourier transform, the displacement function of the plate can be expressed as

[0194]

[0195] Where α mn (u) is the mode function, W mn (ω) is the mode expansion coefficient in the frequency domain, and W(u,ω) is the frequency spectrum of the plate displacement at location u.

[0196] For a simply supported plate, α mn (u) can be expressed as

[0197]

[0198] According to Rayleigh integral, the far-field sound pressure can be expressed as

[0199]

[0200] From this we can get,

[0201]

[0202] definition

[0203]

[0204] but

[0205]

[0206] set up

[0207]

[0208] but

[0209]

[0210] The single frequency response function of the board can be expressed as

[0211]

[0212] The relationship between the cross power spectral density of displacement and velocity is:

[0213] S v (u,ξ,ω)=ω 2 S w (u,ξ,ω) (60)

[0214] From this, the solution expression of velocity cross power spectrum density can be obtained as follows:

[0215]

[0216] The average panel response in terms of velocity can be expressed concisely as

[0217]

[0218] In order to improve the calculation efficiency, the mutual radiation impedance between vibration modes is omitted. On this basis, combined with orthogonality and simplified expressions,

[0219]

[0220]

[0221] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0222] Figure 5 , Figure 6 , Figure 7 Both of these demonstrate the effectiveness of underwater metamaterials in controlling vibration and acoustic radiation.

[0223] Construct a finite metaplate consisting of 25 units along the x-direction and 20 units along the y-direction, with a side length of 0.02 m. Assume that there is a turbulent boundary layer excitation generated by a flow rate of 6 m / s. Figure 5 The average power spectral density of the meta-plate under excitation is shown.

[0224] All three average velocity power spectral densities show a decreasing trend with increasing frequency. This behavior is attributed to the attenuation characteristics of the excitation spectrum. There are two response valleys corresponding to the band gaps. Obviously, the band gap in vacuum is much wider than that underwater. Under the turbulent boundary layer excitation condition, the band gap effect still exists. This shows that meta-plates have broad application prospects in underwater vehicles.

[0225] Several velocity power spectrum density distributions of the super-structure plate are selected to explain its wave suppression and vibration reduction mechanism. Figure 5In the figure, (a) and (b) show the vibration response at 63 Hz and 185 Hz, both frequencies below the band gap. These panels illustrate the natural vibration characteristics of modes (2, 1) and (3, 2). However, as shown in Figures (c) and (d), the attached resonators play an important role at 331 Hz and 429 Hz. Since these two frequencies fall within the band gap, the entire plate experiences a nearly quiet state. Obviously, the vibration peak amplitudes at 63 Hz and 185 Hz are 9 to 11 orders of magnitude larger than those at 331 Hz and 429 Hz. The periodic arrangement of the lateral local resonators produces translational inertia to balance the shear forces in the substrate, which is the reason for such a large difference in the vibration peaks.

[0226] Figure 6 The vibration response changes caused by flow velocity ranging from 4m / s to 8m / s are shown. Figure 6 In (a), the autospectral density of the turbulent boundary layer fluctuating pressure at different flow rates is given, which generally shows a decreasing trend with increasing frequency. As the flow rate increases, the magnitude of the turbulent boundary layer fluctuating pressure also increases with the increase in flow rate, which is due to the higher dynamic pressure at faster flow rates. At the same time, the vibration response follows a similar pattern to the excitation. It is worth noting that the band gap effect persists, indicating that changes in flow rate have minimal impact on the ability of the superstructure plate to attenuate waves.

[0227] Figure 7 Effect of the geometry of the meta-plate on the vibration response: (a) elongating the plate along the flow direction, (b) widening the plate perpendicular to the flow direction

[0228] The average plate velocity power spectral density curve changes with the plate geometry. This behavior can be attributed to the fact that the geometric parameters determine the natural vibration modes of the plate, which is the basic principle of the proposed method. In the lower frequency range, several high response peaks correspond to the excitation of natural modes, emitting sound into the surrounding environment. With increasing frequency, the average plate velocity tends to decrease due to the characteristics of the excitation. The band gap effect is almost unaffected and is closely related to the main plate and the surrounding water. Smaller plates tend to have lower overall vibration levels, especially at medium and high frequencies, which is mainly due to the relatively strong influence of boundary constraints.

[0229] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for controlling turbulence-induced vibration and acoustic radiation of a lateral localized resonant meta-plate under turbulence excitation, characterized in that: The following steps are involved: Step 1: Through the equivalent continuum theory, the discrete lateral localized resonant meta-plate is equivalent to a continuum whose mass density or Young's modulus varies with frequency; Step 2: Based on the stochastic theory, the cross-power spectrum density equation of the displacement response of the elastic structure under turbulent excitation is established; Step 3, using mode expansion, Rayleigh integral, and mode orthogonality, the velocity cross-power spectrum density solution expression is obtained; Step 4: Study the vibration suppression mechanism of the underwater lateral local resonance super-structure plate with a finite period under turbulent excitation; According to the random theory, the cross-power spectrum density equation of the displacement response of the elastic structure under turbulent excitation is established: S w (u,ξ,ω)=∫∫S pp (ξ′,ω)H w (u,u′,-ω)×H w (u+ξ,u′+ξ′,ω)du′dξ′ (65) Where u = (x, y) represents the coordinates of a point on the structure, ξ = (ξ x ,ξ y ) represents the distance between two observation points, H w (u,u′,ω) represents the single frequency response of displacement, S pp (ξ,ω) represents the transverse spectral density of the pressure fluctuation on the wall of the turbulent boundary layer; The simplified formula for the cross power spectral density is: Where Φ p (ω) represents the autospectral density, coefficient α x and α y Represents the longitudinal and transverse coherence loss respectively; for smooth walls, commonly used values ​​are: α x =0.116 and α y = 0.7; the average convection velocity of the turbulent boundary layer is expressed as U c express U c =b c U ∞ ,b c =0.65(67) The autopower spectral density can be expressed as In the formula δ * is the displacement thickness of the boundary layer, α is a dimensionless quantity, The fluctuating pressure generated by the turbulent boundary layer can be considered as an external force exciting the plate, and the governing equation describing the response of the plate to the excitation of the turbulent boundary layer in the surrounding fluid can be expressed as Where W(u,ω) represents the displacement function of the plate, D p and are the bending stiffness and equivalent surface density of the lateral local resonance plate, t is the time, P(u,ω) represents the turbulent boundary layer fluctuation pressure, P a (u,ω) represents the acoustic pressure generated by fluid-structure interaction.

2. The method for controlling turbulence-induced vibration and acoustic radiation of a lateral localized resonant super-plate under turbulence excitation as claimed in claim 1, characterized in that: The equivalent surface density of the super plate is derived from the following formula: In the formula Indicates the surface density of the substrate; The single-frequency response of the plate displacement can be expressed as H w (u, u′, ω) = W(u, ω) when P(u, ω) = δ(u - u′) (71) According to the mode expansion and inverse Fourier transform, the displacement function of the plate can be expressed as Where α mn (u) is the mode function, W mn (ω) is the mode expansion coefficient in the frequency domain, W(u,ω) is the frequency spectrum of the plate displacement at u; For a simply supported plate, α mn (u) can be expressed as According to Rayleigh integral, the far-field sound pressure can be expressed as From this we can get, definition but set up but The single frequency response function of the board can be expressed as The relationship between the cross power spectral density of displacement and velocity is: S v (u,ξ,ω)=ω 2 S w (u,ξ,ω) (81) From this, the solution expression of velocity cross power spectrum density can be obtained as follows: The average board response in terms of velocity can be expressed concisely as In order to improve the calculation efficiency, the mutual radiation impedance between vibration modes is omitted; on this basis, combined with orthogonality and simplified expressions, A finite-size metaplate is constructed, which consists of 25 unit cells along the x-direction and 20 unit cells along the y-direction, with a side length of 0.02 m. It is assumed that there is a turbulent boundary layer excitation generated by a flow rate of 6 m / s.

3. A system using the method for controlling turbulence-induced vibration and acoustic radiation of a lateral localized resonant meta-plate under turbulence excitation as described in any one of claims 1-2, characterized in that: include: An equivalent continuum module, configured to treat a discrete lateral local resonance meta-plate as an equivalent continuum whose mass density or Young's modulus varies with frequency; Stochastic theory module, used to establish the cross-power spectral density equation for the displacement response of elastic structures under turbulent excitation; The calculation module includes the functions of modal expansion, Rayleigh integration, and modal orthogonality to obtain the solution expression of velocity cross-power spectrum density; The analysis module is used to study the vibration suppression mechanism of the meta-plate under turbulent excitation.

4. The system according to claim 3, characterized in that The stochastic theory module is further configured to calculate the distance between two observation points, the single frequency response of the displacement and the transverse spectral density representing the pressure fluctuations on the wall of the turbulent boundary layer, and to simplify the cross power spectral density according to the coherence loss coefficient and the average convection velocity.

5. The system according to claim 3, characterized in that The calculation module is further configured to calculate the equivalent surface density of the meta-plate and obtain the single frequency response of the plate displacement according to the mode function and the mode expansion coefficient in the frequency domain.

6. The system according to claim 3, characterized in that The analysis module is further configured to calculate the far-field sound pressure according to the Rayleigh integral, and simplify the relationship between the cross power spectrum density of the displacement and the velocity by defining relevant parameters, thereby obtaining a solution expression for the cross power spectrum density of the velocity.

7. The system according to claim 3, characterized in that The system further includes a super plate model configured with a plurality of unit cells, wherein the unit cells are arranged along the x-direction and the y-direction respectively to simulate the vibration response under the excitation of the turbulent boundary layer.

8. The system according to claim 3, characterized in that The system is configured to simulate the influence of turbulent boundary layer excitation generated by a flow rate of 6 m / s, and calculate the vibration and acoustic radiation characteristics of the meta-plate under the excitation.

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