Method for calculating near field of structural acoustic radiation under turbulent boundary layer excitation

Abstract

The method for calculating the near field of structure sound radiation under the excitation of turbulent boundary layer comprises the following steps: 1. determining the geometric parameters and material parameters of the turbulent boundary layer, the geometric parameters and material parameters of the four-side simply supported plate, and establishing the structure sound system of the plate excited by the turbulent boundary layer; 2. based on the modal expansion method, obtaining the structure transfer function of the four-side simply supported plate model, and then performing rectangular discrete summation on the transfer function and the TBL excitation under the Corcos model to obtain the vibration response of the plate; 3. discretizing the spatial information of the modal shape in the structure modal transfer function and the spatial information of the Green function into a transfer function, and then performing rectangular discrete summation on the transfer function and the TBL excitation under the Corcos model to obtain the sound field response of the plate; and 4. given parameters, arranging an array within the range of one-half wavelength from the plate, i.e. the near field range, to obtain the vibration displacement response cloud diagram of the plate and the sound pressure response cloud diagram in the sound field in the system. The present application provides a near field model for the turbulent boundary layer noise, which can be quickly solved, and the calculation speed is improved.

Description

Technical Field

[0001] This invention belongs to the field of acoustics and vibration technology, specifically relating to a method for calculating the near-field acoustic radiation of a structure under turbulent boundary layer excitation. Background Technology

[0002] In practical engineering structures, turbulent boundary layer excitation (TBL) is widely present in aircraft and submarine compartments, automobile and high-speed rail windows, wind turbine blades, etc. Large-amplitude vibrations caused by turbulent boundary layer excitation can lead to structural acoustic fatigue failure or high sound pressure level sound radiation, causing environmental noise pollution.

[0003] Over the past decade, many scholars have conducted research on structural vibration and acoustic radiation under TBL excitation, making this a research hotspot in the field of structural acoustics. However, existing research mainly focuses on the far-field acoustic radiation of structures under TBL excitation, without in-depth study of the near-field problem of structural acoustic radiation, and no theoretical model of near-field radiation of structures under TBL excitation has been published. Summary of the Invention

[0004] This invention aims to overcome the aforementioned shortcomings of existing technologies and provide a method for calculating the near-field of structural acoustic radiation under turbulent boundary layer excitation. The purpose of this invention in calculating the near-field of structural acoustic radiation under turbulent boundary layer excitation is to provide a rapidly solvable near-field model for real-time control of turbulent boundary layer noise, based on the theoretical foundation of structural vibration acoustic systems and the transfer function method.

[0005] This invention proposes a method to measure the evanescent wave radiated by a structure within a half-wavelength range from the plate, thereby solving for the structure's vibration displacement response and reconstructing the three-dimensional spatial distribution of acoustic quantities in the sound field. This method, through non-contact measurement using microphones, reveals the vibration characteristics and generation mechanism of the structure, providing a theoretical basis for structural acoustic fatigue failure and structural noise generation mechanisms, and is of significant importance.

[0006] The specific method proposed in this invention is as follows: First, the turbulent boundary layer excitation is simplified to a CSD function in the wavenumber-frequency domain of wall pressure, using the classic Corcos model. Second, based on the structural transfer function of a simply supported plate in the wavenumber-frequency domain derived by the modal expansion method, the spatial-frequency domain structural vibration response of the plate under TBL excitation can be obtained by Fourier transforming the product of the excitation and the structural transfer function. Then, based on the acoustic pressure cross-power spectral density function derived from the Wiener-Khinchin relation, the cross-power spectral density function of the acoustic field can be obtained by integrating the product of the spatial-frequency domain structural vibration response and the Green's transfer function of the sound field from the point source method.

[0007] In actual theoretical calculations, due to Fourier transforms and integral operations, numerical solutions are generally obtained using computers. The discretization methods used mainly include rectangular discretization and modal expansion. However, both rectangular discretization and modal expansion involve a large number of mathematical operations, affecting computational efficiency. To improve efficiency, a common method in truncation is to define a cutoff term to restrict higher-order terms, because in the summation process, the contribution of lower-order terms is often greater than that of higher-order terms, thus discarding terms higher than the cutoff term for the summation calculation. However, two integral discretization and summation calculations lead to low computational efficiency. Therefore, this invention, for the structural acoustic system of a turbulent boundary layer-excited plate, discretizes the spatial discretization of the Green's function together with the mode shapes containing spatial information in the structural modal transfer function. Finally, only one discretization and summation of the transfer function containing both the structure and the sound field in the wavenumber domain is needed, thus enabling faster calculation of the near-field acoustic radiation of the plate vibration under turbulent boundary layer excitation. Compared to previous methods, the calculation speed for a single field point is improved by two orders of magnitude.

[0008] The technical solution to achieve the purpose of this invention is: a method for calculating the near-field acoustic radiation of a structure under turbulent boundary layer excitation, comprising the following steps:

[0009] Step 1: Determine the geometric and material parameters of the turbulent boundary layer, the geometric and material parameters of the simply supported plate, establish the structural acoustic system of the turbulent boundary layer excitation plate, and proceed to Step 2;

[0010] Step 2: Based on the modal expansion method, obtain the structural transfer function of the four-sided simply supported plate model, and then perform rectangular discretization and summation of the transfer function and TBL excitation under the Corcos model to obtain the vibration response of the plate, and proceed to step 3;

[0011] Step 3: Discretize the spatial discretization of the Green's function together with the mode shapes containing spatial information in the structural modal transfer function into a single transfer function. Then, perform rectangular discretization and summation of this transfer function with the TBL excitation under the Corcos model to obtain the acoustic field response of the plate. Proceed to Step 4.

[0012] Step 4: Given parameters, obtain the vibration displacement response contour map of the plate in the system and the sound pressure response contour map in the sound field.

[0013] This invention, based on the structural vibration acoustic system and the transfer function method, provides a near-field model for turbulent boundary layer noise that can be solved quickly, improving the calculation speed by two orders of magnitude compared to previous single-point calculations. It achieves rapid calculation of the near-field radiation of plate vibration under turbulent boundary layer excitation, thus providing a theoretical basis for subsequent use of near-field acoustic holography to measure structural surface vibrations, which is of great significance for realizing non-contact measurement of structures using near-field acoustic response.

[0014] Compared with the prior art, the significant advantages of this invention are:

[0015] (1) The near-field acoustic radiation results of the plate under turbulent boundary layer excitation were considered. Compared with the far-field acoustic radiation results, the results provide a theoretical basis for non-contact detection of structural fatigue.

[0016] (2) When using the transfer function method to analyze the system from excitation to response, the spatial information of the two transfer functions, structure and sound field, is combined to obtain a new transfer function, which allows for a faster model of the system's near field. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the implementation steps of the method of the present invention;

[0018] Figure 2 This is a schematic diagram of the vibration model of the plate under turbulent boundary layer excitation according to the present invention;

[0019] Figure 3 This is a schematic diagram of the near-field model of the plate under turbulent boundary layer excitation according to the present invention;

[0020] Figures 4a to 4d The above are the four-order vibration mode shapes of the plate front of the present invention, wherein... Figure 4a It is a (1,1) mode shape. Figure 4b It is a (2,1) mode shape. Figure 4c It is a (3,1) mode shape. Figure 4d It is a (2,2) mode shape;

[0021] Figure 5 This is a displacement response diagram of a point as a function of frequency according to the present invention;

[0022] Figures 6a to 6d This is a contour plot of the fourth-order sound pressure response in front of the plate according to the present invention, wherein... Figure 6a It is a (1,1) mode shape. Figure 6b It is a (2,1) mode shape. Figure 6c It is a (3,1) mode shape. Figure 6d It is a (2,2) mode shape;

[0023] Figures 7a-7c This is a contour plot of the structural acceleration response in the wavenumber domain of the present invention, wherein... Figure 7a It is a TBL excitation cloud map. Figure 7b It is a contour plot of the structural acceleration transfer function. Figure 7c It is a structural acceleration response contour map;

[0024] Figures 8a-8c The present invention provides a sound field response contour map in the wavenumber domain, wherein... Figure 8a It is a TBL excitation cloud map. Figure 8b It is a sound field transfer function contour plot. Figure 8c It is a sound pressure response contour map. Detailed Implementation

[0025] Example 1

[0026] Referring to the accompanying drawings, this invention proposes a method for calculating the near-field acoustic radiation of a structure under turbulent boundary layer excitation, comprising the following steps:

[0027] Step 1: Determine the geometric and material parameters of the turbulent boundary layer, the geometric and material parameters of the simply supported plate, establish the structural acoustic system of the turbulent boundary layer excitation plate, and proceed to Step 2;

[0028] like Figure 2 As shown, it is assumed that the TBL excitation is uniformly and stably applied to the plate surface, and the wall pressure caused by the TBL excitation is not affected by the plate vibration.

[0029] The cross-spectral density (CSD) function of wall pressure in the wavenumber frequency domain under TBL excitation can be expressed as:

[0030]

[0031] In equation (1), S pp (ω) represents the auto-spectral density (ASD) function; U represents the normalized CSD function, which can be calculated from the Corcos semi-empirical model; c ω represents the convection velocity; ω is the angular frequency.

[0032] The normalized CSD function of wall pressure can be represented by the Corcos model, and its expression in the wavenumber domain is:

[0033]

[0034] In equation (2), the exponential decay coefficient α of the normalized CSD function in the flow and span directions is... x and α y U is taken as 0.11 and 0.77 respectively. c =50m / s.

[0035] Step 2: Based on the modal expansion method, obtain the structural transfer function of the four-sided simply supported plate model, and then perform rectangular discretization and summation of the transfer function and TBL excitation under the Corcos model to obtain the vibration response of the plate, and proceed to step 3;

[0036] Let x represent the wall pressure fluctuation function at point x on the plate caused by TBL. The acceleration at point x is represented by the Duhamel integral.

[0037] This represents the acceleration transfer function.

[0038]

[0039] Autocorrelation function R of acceleration γγ (x,t):

[0040]

[0041] Substituting equation (3) into equation (4) and performing a time Fourier transform on the result, we obtain the acceleration power spectral density function:

[0042]

[0043] In equation (5), Let be the acceleration frequency response function. * indicates complex conjugate. The transformation relationship between the wall pressure spectrum in the spatial domain and the wavenumber domain is:

[0044]

[0045] Substituting equation (6) into equation (5), we get:

[0046]

[0047]

[0048] This is called the transfer function, representing the acceleration response at point x when the plate is excited by a unit plane wave with wave vector k. The double integral in equation (7) is approximated by truncating and sampling the wavenumber space, and using the rectangular method. γ Represents a discrete set of wavenumbers.

[0049]

[0050] Regarding the wavenumber cutoff in the k-direction:

[0051]

[0052] The transfer function is calculated using the modal expansion method, and the modal angular frequencies are obtained as follows:

[0053]

[0054] Modal shape:

[0055]

[0056] Modal quality:

[0057]

[0058] The transfer function at a point is given by the following equation:

[0059]

[0060] Modal forces:

[0061]

[0062]

[0063] The vibration response of the plate can be obtained from formulas (2), (9) and (14).

[0064] Step 3: Discretize the spatial discretization of the Green's function together with the mode shapes containing spatial information in the structural modal transfer function into a single transfer function. Then, perform rectangular discretization and summation of this transfer function with the TBL excitation under the Corcos model to obtain the acoustic field response of the plate. Proceed to Step 4.

[0065] like Figure 3 The thin plate shown is placed on an infinitely large baffle, with the origin of the coordinate system at the geometric center of the plate. We study its sound radiation to one side. x and L y Let be the lengths of the thin plate in the x and y directions, respectively. According to the Rayleigh integral formula in the time domain, the sound pressure radiated by the vibrating thin plate towards a point r in space at time t is:

[0066]

[0067] Where, ρ0 = 1.29 kg / m 3 Let S be the density of the fluid medium, and S be the position vector of any point on the thin plate, w(S;t)

[0068] Let be the lateral displacement of the thin plate, (") denotes the second derivative with respect to time t, and g(r,S;τ-t) is the time-domain Green's function.

[0069] According to the Wiener-Khinchin relation, the cross-power spectral density function of the sound pressure p(r;t) can be expressed as:

[0070]

[0071] Where ω is the angular frequency, * denotes complex conjugate, and S ww (S1,S2;ω) is the power spectral density function of the lateral displacement w of the thin plate.

[0072]

[0073] Here, G(r,S;ω) is the Green's function in the frequency domain; k0=ω / c0 is the sound wave number, c0=340m / s. Equation (19) shows that the cross power spectral density function of sound pressure can be transformed into the power spectral density function for solving the transverse displacement of the thin plate.

[0074] Equation (7) can be transformed into a displacement response, with the following relationship:

[0075] H γ (x,ω)=-ω 2 H w (x,ω) (20)

[0076] Combining the above equation, substituting equation (7) into equation (18), we get...

[0077]

[0078] Where H p (r,k,ω)=∫ S H w (S,k,ω)g(r,S;ω)dS is the sound pressure transfer function, as follows:

[0079]

[0080] The acoustic response of the plate can be obtained from formulas (2), (21) and (22).

[0081] Step 4: Given parameters, obtain the vibration displacement response contour map of the plate in the system and the sound pressure response contour map in the sound field.

[0082] Example 2

[0083] The invention will be further described below with reference to specific implementation examples. The invention proposes a method for calculating the near-field acoustic radiation of a structure under turbulent boundary layer excitation. The specific method is as follows:

[0084] Step 1: Determine the geometric and material parameters of the turbulent boundary layer, the geometric and material parameters of the simply supported plate, and establish the structural acoustic system of the turbulent boundary layer excitation plate;

[0085] The geometric and material parameters of the simply supported plate are shown in Table 1.

[0086] Table 1 Geometric and material parameters of a simply supported plate

[0087]

[0088]

[0089] Step 2: Based on the modal expansion method, obtain the structural transfer function of the four-sided simply supported plate model, and then perform rectangular discretization and summation of the transfer function and TBL excitation under the Corcos model to obtain the vibration response of the plate, and proceed to step 3;

[0090] Based on the modal expansion method and the rectangular discretization and summation method, the plate is discretized into 16×10⁻⁶ segments. The center point is taken as the calculation point, and the four vibration mode shapes of the plate and the displacement response diagram of the point as a function of frequency are obtained, as shown in Figure 4. Figure 5 As shown.

[0091] Step 3: Discretize the spatial discretization of the Green's function together with the mode shapes containing spatial information in the structural modal transfer function into a single transfer function. Then, perform rectangular discretization and summation of this transfer function with the TBL excitation under the Corcos model to obtain the acoustic field response of the plate. Proceed to Step 4.

[0092] Step 4: Given parameters, obtain the vibration displacement response contour map of the plate in the system and the sound pressure response contour map in the sound field.

[0093] The array surface was selected in accordance with the discrete partitioning of the plate, and the sound pressure response contour map at 0.01m was obtained, as shown in Figure 6. Figures 7 and 8 illustrate the influence of the structural transfer function and the sound field transfer function on TBL excitation in the wavenumber domain, and the near-field sound radiation results of the plate under surface turbulent boundary layer excitation. These results are of great significance for subsequent detection of structural vibration fatigue using near-field acoustic holography, i.e., non-contact measurement. Compared with far-field sound radiation results, this method can provide a detection method for structural fatigue.

[0094] The embodiments described in this specification are merely examples of implementations of the inventive concept. The scope of protection of this invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of this invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for calculating the near-field of structural acoustic radiation under the excitation of turbulent boundary layer, characterized in that: Comprising the following steps: Step 1: Determine the geometric parameters and material parameters of the turbulent boundary layer, the geometric parameters and material parameters of the simply supported plate, establish the structural acoustic system of the turbulent boundary layer excitation plate, and go to Step 2; Assume that the TBL excitation uniformly and stably fully acts on the plate surface, and the wall pressure caused by the TBL excitation is not affected by the plate vibration; The (Cross-spectral density, CSD) function of the wall pressure under the action of the TBL excitation in the wave number frequency domain can be expressed as: In formula (1), S pp (ω) represents an auto-spectral density (ASD) function; represents a normalized CSD function, which can be calculated by a Corcos semi-empirical model;U c represents a convection velocity; and ω is an angular frequency. The normalized CSD function of the wall pressure can be represented by the Corcos model, which is expressed in the wave number domain as In equation (2), α x and α y These are the exponential decay coefficients of the normalized CSD function in the flow and span directions, respectively; Step 2: Based on the modal expansion method, the structural transfer function of the simply supported plate model is obtained, and then the transfer function is summed with the TBL excitation under the Corcos model to obtain the vibration response of the plate, and go to Step 3; Pwall(x) = Pwall(x) + (Pwall(x) - Pwall(x)) = Pwall(x) + (Pwall(x) - Pwall(x)) = Pwall(x) + (Pwall(x) - Pwall(x)) = Pwall(x) + (Pwall(x) - Pwall(x represents an acceleration transfer function; Autocorrelation function R of the acceleration γγ (x,t): Substitute equation (3) into equation (4), and perform time Fourier transform on the result to obtain the acceleration power spectral density function: In formula (5), is the acceleration frequency response function; the superscript * denotes complex conjugation; and the conversion relationship between the wall pressure spectrum in the spatial domain and the wave number domain is Substitute equation (6) into equation (5) to obtain: denotes the acceleration response at point x when the panel is excited by a unit plane wave with wave vector k; the double integral in (7) is approximated by truncating and sampling the wave number space and using rectangular rules; ∏ γ denotes the discrete set of wave numbers; The wave number truncation in the k direction is: Use the modal expansion method to calculate the transfer function to obtain the modal angular frequency: Modal shape: Modal mass: The transfer function of a certain point is given by: Where the modal force is: The vibration response of the plate can be obtained from equations (2), (9) and (14); Step 3: Discretize the spatial information of the Green function and the modal shape of the structural modal transfer function into a transfer function, and then sum the transfer function with the TBL excitation under the Corcos model to obtain the acoustic field response of the plate, and go to Step 4; A thin plate is placed on an infinite baffle, the coordinate origin is taken at the geometric center of the plate, and the sound radiation problem to one side of the plate is studied;L x andL y are the lengths of the thin plate in the x and y directions, respectively; according to the time-domain Rayleigh integral formula, the sound pressure radiated by the vibration of the thin plate to a point r in space at time t is where p0= 1.29 kg / m 3 is the fluid medium density, S is the position vector of an arbitrary point on the sheet, and w(S; t) is the second-order derivative with respect to time t, and g(r, S; τ-t) is the time-domain Green function; According to the Wiener-Khinchin relationship, the cross-power spectral density function of the sound pressure p(r; t) can be expressed as: where ω is the circular frequency, * denotes complex conjugation, S ww (S1, S2; ω) is the power spectral density function of the transverse displacement w of the sheet Here G(r, S; ω) is the frequency-domain Green function; k0=ω / c0 is the acoustic wave number, c0=340 m / s; equation (19) shows that the cross-power spectral density function of the sound pressure can be converted into the power spectral density function of the transverse displacement of the thin plate; For equation (7), the displacement response can be converted as follows: H γ (x, ω) = -ω 2 H w (x, ω)(20) Substitute equation (7) into equation (18) to obtain where H p (r, k, ω) = ∫ S H w (S, k, ω) g(r, S; ω) dS is the sound pressure transfer function, given by The acoustic field response of the plate can be obtained from equations (2), (21) and (22); Step 4: Given parameters, obtain the vibration displacement response cloud map of the plate in the system and the sound pressure response cloud map in the acoustic field.

2. The method of calculating near-field structural acoustic radiation due to turbulent boundary layer excitation of claim 1, wherein: The turbulent boundary layer described in Step 1 is suitable for air medium light fluid, and the parameters of the plate change with the actual changes.

3. The method of claim 1, wherein: The discrete point condition described in Step 4 changes according to the actual arrangement of the array.

4. The method of claim 1, wherein: The normalized CSD function exponentially decays in streamwise and spanwise with decay coefficient a x and a y = 0.11 and 0.77, respectively, and U c = 50 m / s.

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