A method for predicting noise of multi-plate spliced ​​structures under flow excitation

Abstract

This paper provides a method for predicting noise in multi-panel spliced ​​structures under flow excitation. This method addresses the drawback that existing acoustic-vibration coupling models for multi-panel spliced ​​structures typically use classical boundary conditions, which is inconsistent with practical engineering practices. This method employs modal analysis, based on the principles of structural mechanics, vibration differential equations, wave theory, and the acoustic Lagrange equations. It constructs a plate-plate coupling substructure model (i.e., a panel-cavity coupling model) under stiffness constraints. It also establishes a unified panel-cavity coordinate transformation model, combined with multiple fluid excitation models, to form a full-process acoustic-vibration coupling analysis paradigm for fluid-structure-acoustic fields.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural noise prediction methods, and in particular relates to a method for predicting structural noise of a multi-plate splicing structure under flow excitation. Background Art

[0002] The key to improving noise control effectiveness lies in the ability to predict noise efficiently and accurately. Therefore, an efficient prediction method that is closer to actual conditions is needed.

[0003] The cabin structure of various types of transportation vehicles, such as aircraft, can be simplified into a coupling of multiple spliced ​​panels and acoustic cavities, where the connections between the panels are mostly elastic. However, existing acoustic-vibration coupling models for panels and cavities typically set the boundary conditions to classical boundary conditions (e.g., simply supported, clamped, and free), which do not fully conform to actual engineering situations. Therefore, it is necessary to introduce elastic boundary conditions to construct a more realistic coupling model. Furthermore, in order to construct a unified model for the entire process from fluid excitation, structural vibration response, and radiated acoustic field analysis, considering that the excitation source also has a significant impact on the noise response, it is necessary to construct a generalized form in the model that can adapt to different fluid excitation sources, such as low-Mach number turbulent boundary layer excitation and high-Mach speed shock wave excitation. Therefore, for multi-panel spliced ​​structures, how to consider the boundary and connection elastic constraints and establish an acoustic-vibration prediction method for fluid-structure-acoustic cavity coupling has become an urgent problem that needs to be solved. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem that the boundary conditions in the existing acoustic-vibration coupling model of multi-plate splicing structures are usually set as classical boundary conditions, which is inconsistent with actual engineering. Instead, a method for predicting the noise of multi-plate splicing structures under flow excitation is provided.

[0005] To achieve the above objectives, the technical solutions provided by the present invention are:

[0006] A method for predicting noise of a multi-plate spliced ​​structure under flow excitation is special in that it includes the following steps:

[0007] S1: Analyze the outer boundary stiffness and internal constraints or connection characteristics of the actual panel structure, clarify the material parameters of each part of the panel structure (these constraint stiffness can be obtained through preliminary experiments, numerical simulations, or querying structure and material parameter tables), divide the panel structure into multiple substructures based on the internal constraints or connection characteristics, and form a multi-substructure spliced ​​panel model. The outer boundary stiffness of the entire panel structure and the constraints or connection characteristics between the internal substructures are described, which will be used to construct the boundary equations and vibration control equations of the panel structure.

[0008] For a specific panel structure, it is necessary to analyze the outer boundary stiffness and internal characteristics of the entire structure, determine the boundary conditions of the outer boundary of the panel and the stiffness constraints inside, clarify the areas with different material parameters, and divide the panel structure into substructures to form a multi-substructure spliced ​​panel model.

[0009] There are no specific restrictions on the division of substructures. It can be done only based on the internal stiffness constraints of the wall panels. This is mainly because after analysis (preliminary experiments or numerical simulation analysis or product structure and material parameter table), internal constraints or connection features can be quantitatively described as boundary conditions using constraint stiffness. Therefore, it can be said that division can be done only based on internal stiffness constraints. After the division is completed, the boundary conditions of each substructure need to be clarified. In this application, the boundary conditions are composed of displacement constraint stiffness and rotation constraint stiffness.

[0010] S2: Apply modal analysis to the model obtained in S1. Based on the basic principles of structural mechanics and vibration control differential equations, construct the coordinate systems of each substructure and establish the boundary equations and vibration control equations corresponding to the model obtained in S1.

[0011] Specifically, based on the equilibrium conditions of forces and moments, as well as the continuity of displacements and rotations, the boundary equations are derived. Then, based on the vibration control differential equations, the vibration control equations are derived. During this process, attention should be paid to whether coordinate transformation is required between the substructure coordinate systems.

[0012] S3: Simplify the cavity structure connected to the wall panel into a rectangular acoustic cavity with arbitrary impedance boundary conditions (the present invention establishes a model for rectangular acoustic cavities, so the acoustic cavities mentioned in the article should all be rectangular, and in the model, the side where the plate is located is regarded as the upper surface of the acoustic cavity, and the corresponding side is the bottom surface of the acoustic cavity), construct an acoustic cavity coordinate system, and establish an acoustic response equation group of the acoustic cavity based on wave theory and acoustic Lagrangian function, that is, construct an acoustic cavity model; couple the acoustic cavity with the plate structure, and perform necessary coordinate transformation with the substructure coordinate system (the coordinates of the same point in the two coordinate systems are different, so coordinate transformation is required when deriving the coupling terms in the equation; since the coordinate systems constructed by this method are all simple rectangular coordinate systems, the coordinate transformation method is also a simple addition and subtraction, so those skilled in the art can perform coordinate transformation as long as they find the relative orientation of the coordinate system), couple the acoustic cavity with the plate structure, combine the acoustic response equation group with the boundary equations and vibration control equations obtained in S2 and add coupling terms to establish a plate-cavity coupling equation, which can also be called a "wall panel-cavity coupling model";

[0013] (1) Applying the modal analysis method, the Fourier series expression of the sound pressure is substituted into the acoustic Lagrangian function to obtain the acoustic characteristic equations of the impedance boundary acoustic cavity, and the equations are written in matrix form;

[0014] (2) Add the plate-cavity coupling term to the acoustic characteristic equations and the vibration control equations to obtain the total coupling equation. Pay attention to the coordinate transformation of the substructure coordinate system and the acoustic cavity coordinate system to ensure the correctness of each element.

[0015] S4: Establish multiple different excitation models, select the correct model corresponding to the excitation source according to the actual working conditions, and substitute it into the plate-cavity coupling equation obtained in S3 to obtain the excitation vector or the power spectrum density matrix representing the excitation for solution calculation;

[0016] The different excitations are uniform acoustic pressure excitation, turbulent flow excitation, and flow excitation with shock wave interference;

[0017] S5: Apply the excitation source corresponding to the working condition to the wall panel structure. The response calculation formula is derived through the panel-cavity coupling equation obtained in S3 to obtain the system transfer matrix. The transfer matrix is ​​subdivided into a vibration transfer matrix and an acoustic transfer matrix. Matrix operations are performed with the excitation vector obtained in S4 or the power spectral density matrix representing the excitation to calculate the vibration and acoustic response results, analyze the structural vibration characteristics and the acoustic performance of the acoustic cavity, and predict the noise of the multi-panel splicing structure.

[0018] Furthermore, S1 is specifically:

[0019] S1.1 Analyze and describe the various characteristics of the wall panel structure:

[0020] Determine the constraints on the outer boundary of the panel structure and provide the correct displacement constraint stiffness and rotation constraint stiffness to jointly describe the outer boundary stiffness. The correct constraint stiffness can be obtained through preliminary experiments or numerical simulation analysis or the product's structural and material parameter table.

[0021] Analyze the constraints or connection features inside the panel structure and give the correct displacement constraint stiffness and rotation constraint stiffness at the corresponding positions to describe these constraints or connection features;

[0022] Analyze and organize to clarify the material parameters of different parts of the wall panel structure;

[0023] S1.2 Divide the wall panel structure into substructures:

[0024] Based on the analysis and description of the various characteristics of the wall panel structure in S1.1, it is divided into a multi-panel splicing structure formed by coupling multiple substructures, as follows:

[0025] S1.2.1 Preliminarily divide the panel structure according to the existing internal constraints and connection characteristics, and at the same time divide the parts of different materials to preliminarily determine the necessary factual boundaries;

[0026] S1.2.2 Extend the determined fact boundary to the outer boundary of the panel to obtain the subdivision boundary, thus completing the subdivision. The number and splicing form of the subdivided substructures are related to the panel characteristics obtained by analysis and are not subject to special restrictions.

[0027] S1.2.3 Select appropriate constraint stiffness on the extended partition boundary so that it does not affect the original force and vibration propagation of the wall panel, forming a multi-substructure spliced ​​plate model.

[0028] Furthermore, S2 is specifically:

[0029] According to the model obtained in S1, a two-dimensional coordinate system of each substructure is constructed with any vertex of the substructure as the origin. The boundary equations of each substructure are established based on the equilibrium conditions of force and bending moment in structural mechanics and the continuity of displacement and rotation, as follows:

[0030]

[0031] The above two equations are the force equation and bending moment equation at the boundary respectively;

[0032] Among them, i represents the substructure index, l is the edge index (for example, when l is 1, it represents the first edge. The specific numbering method of edges can be referred to Figure 5 ), x and y are the coordinates of the point in the substructure coordinate system. Due to the different internal constraints or connection characteristics of different panel structures, the adjacent splicing forms of the substructures after division are not unique and are not limited to a certain substructure connection form. Therefore, the number of transverse shear force or bending moment terms contained in each equation also changes with different models, which shows that this method has universal adaptability.

[0033] Taking four sides as an example, the k in the boundary equation is i1 ~k i4 , K i1 ~K i4 are the displacement constraint stiffness and rotation constraint stiffness at each boundary, and the two substructures have equal constraint stiffness at adjacent boundaries;

[0034] Different combinations of the two constraint stiffness values ​​can represent any different boundary conditions including classical boundary conditions. For example, setting k to a large value (such as 1×10 10 N / m), and then set K to a very small value (such as 1×10 -2 Nm / rad), it can represent the simply supported boundary condition;

[0035] In order to introduce the influence of loss factor, the complex stiffness is used in the boundary conditions, that is, k(1+iη) is used instead of k, and K(1+iμ) is used instead of K;

[0036] w i(x,y) is the Fourier series expansion of the displacement function of the sub-plate (here, the sub-plate is a rectangular plate with 4 sides):

[0037]

[0038] in, is the Fourier coefficient; a, b are the length and width of the substructure; m, n are the mode numbers of the plate in the x and y directions respectively;

[0039] The supplementary function in the Fourier series expansion is:

[0040]

[0041] in, To supplement the function coefficients, the specific assignments are as follows:

[0042]

[0043] Substitute the displacement function into equation (1) and eliminate cosλ on both sides. im xcosλ in y, we get the position-independent boundary equations, which are recorded as:

[0044] [HQ]*C p =0 (2)

[0045] Among them, C p =[ap] T , is the Fourier coefficient vector, the elements of a are A imn , the elements of p are

[0046] The boundary equations derived above are independent of the position coordinates x and y, and take into account the elastic boundary conditions of the wall panels and the rigid connections between the substructures;

[0047] Under elastic boundary conditions, the vibration control differential equations of each substructure are as follows:

[0048]

[0049] Among them, F i Refers to the stimulus received by each sub-board, and the specific form is determined by different stimulus forms; is the bending stiffness of the plate, E i is the Young's modulus of the plate, h i is the thickness of the plate, ν i is the Poisson's ratio of the plate; x, y are the coordinates of the point in the substructure coordinate system;

[0050] Substitute the plate displacement function into equation (3) and multiply both sides of the equation by cosλ after expansion. im xcosλ in y and integrate to eliminate the position effect, and obtain the vibration control equations that are independent of the position coordinates:

[0051] [KB]*C p -ω 2 [MT]*C p =0orF (4)

[0052] The above is a set of linear vibration equations without considering damping;

[0053] If the damping effect is considered, the following equations are obtained by adding Rayleigh damping to the equation:

[0054] [KB]*C p +jωC*C p -ω 2 [MT]*C p =0orF (5)

[0055] Where C = α[K B] + β[M T], j is an imaginary unit, and α and β are the stiffness factor and quality factor of Rayleigh damping, respectively.

[0056] Furthermore, S3 is specifically:

[0057] First, a three-dimensional acoustic cavity coordinate system is constructed with any vertex of the acoustic cavity bottom surface (i.e., the acoustic cavity wall surface opposite to the wall panel) as the origin, and the sound pressure function in the acoustic cavity is written as the following Fourier series expansion form:

[0058]

[0059] in, L x ,L y ,L z are the length, width and height of the vocal cavity, x, y, z are the coordinates of the point in the vocal cavity coordinate system; A mxmymz ,a mxmy ,b mxmy ,c mxmz ,d mxmz ,e mymz ,f mymz is the Fourier coefficient; m x ,m y ,m z are the modes of the acoustic cavity in the length, width and height directions respectively;

[0060] The supplementary function expression in the sound pressure function expansion is as follows:

[0061]

[0062] The expression of the acoustic Lagrangian function of the acoustic cavity with arbitrary impedance boundary conditions is:

[0063] L=VTW wall -W Q

[0064] Among them, V is the total acoustic potential energy of the acoustic cavity, T is the total kinetic energy, and W is the total acoustic potential energy. wall is the work done on the impedance boundary, W Q is the work done by the sound source in the acoustic cavity; from this, the acoustic response equations of the acoustic cavity under arbitrary impedance boundary conditions can be derived as follows:

[0065] (K C +ωZ C +ω 2 M C )*C C =Q0 (6)

[0066] C C The elements of are the coefficients in the Fourier series expansion of the sound pressure; at the same time, if there is no sound source in the sound cavity, the right side of the equation is 0;

[0067] The acoustic cavity is coupled with the multi-substructure splicing plate, and the coupling equations are derived:

[0068]

[0069] Where ρ0 is the air density in the acoustic cavity; K p 、M p It is a coupling matrix. When deriving it, it is necessary to pay attention to the coordinate transformation between the acoustic cavity coordinate system and the substructure coordinate system. Since the constructed substructure coordinate system is a two-dimensional coordinate system and the acoustic cavity coordinate system is a three-dimensional coordinate system, the coordinate transformation is only for the x, y coordinates of the point.

[0070] When performing coordinate transformation, it is necessary to clarify the relative position of the acoustic cavity and the wall panel structure, measure the relative position of the origin of the acoustic cavity coordinate system and the origin of each substructure coordinate system, and superimpose the coordinate value of any point in the substructure coordinate system with the coordinate value of the origin of the substructure coordinate system in the acoustic cavity coordinate system to complete the transformation.

[0071] Arrange and combine the above equations (7) and write them into matrix form to obtain:

[0072]

[0073] in:

[0074]

[0075] C0=-ω 2 ρ0*Μ pD=K C +ωZ C +ω 2 M C

[0076] Among them, O is a zero matrix, which is used to make up the number of matrix items and meet the matrix operation conditions.

[0077] Furthermore, in S4, the excitation source has various forms. This method can be used to calculate the acoustic vibration response characteristics under different excitations, including uniform sound pressure excitation, turbulent excitation, and flow excitation under shock wave interference.

[0078] A simpler excitation form, such as uniform sound pressure excitation, can be directly derived from the plate vibration control equations (4) or (5) (which one to use depends on whether damping is considered), and the sound pressure amplitude is multiplied by cosλ im xcosλ in By integrating y again, we can get the excitation elements corresponding to each substructure, and then write it into an excitation vector for acoustic performance analysis;

[0079] Complex flow excitation requires the use of complex models for derivation. For example, turbulent excitation requires the Corcos model to describe the stationary random process, and the power spectral density function is introduced to obtain the power spectral density matrix of turbulent excitation; the power spectral density function of turbulent excitation is as follows:

[0080]

[0081] Among them, ξ x =xx ' ,ξ y =yy ' is the spatial separation function, α x ,α y is the empirical coefficient, U c is the turbulent boundary layer convection velocity, S ref (ω) is the reference power spectral density;

[0082] The power spectrum density matrix is ​​also used to characterize the flow excitation caused by shock wave interference. However, there is currently insufficient research on shock wave interference flow. In practical applications, the shock wave timing signal can be obtained through experiments or numerical simulations, and the corresponding power spectrum density can be calculated through a program to derive the corresponding power spectrum density matrix.

[0083] Furthermore, S5 is specifically:

[0084] Apply excitation to the panel structure and select different formulas to analyze the acoustic performance according to different forms of excitation;

[0085] For simple excitation forms, the excitation source can be directly used in the calculation in the form of an excitation vector, which can be substituted into the response calculation formula Y(ω)=H(ω)F(ω), where F(ω) refers to the excitation vector.

[0086] Transfer matrix H(ω)=X(ω)H S (ω), H S (ω) consists of two parts: the plate vibration response transfer matrix H w (ω) and the sound pressure response transfer matrix H p (ω):

[0087] H w (ω)=A -1 +A -1 *B0*(D-C0*A -1 *B0) -1 *C0*A -1

[0088] H p (ω)=-(D-C0*A -1 *B0) -1 *C0*A -1

[0089] X(ω) contains the expression vectors of the panel displacement and the sound pressure response, which are: w 、X p ;In practical applications, the vibration response and sound pressure response can be calculated separately;

[0090] When faced with complex excitation forms such as turbulent excitation, it is necessary to apply the auto-power spectral density function to convert to the power spectral density domain for calculation; the auto-power spectral density function is as follows:

[0091]

[0092] Among them, P tbl (ω) is the load vector of turbulence excitation; the system response power spectrum density matrix S YY (ω) contains the displacement response S ww (ω) and the sound pressure response S pp (ω) Two parts:

[0093]

[0094] By applying the corresponding response power spectrum density matrix and the response expression vector to perform operations, the displacement power spectrum density or sound pressure power spectrum density at a certain point can be obtained:

[0095]

[0096]

[0097] Principle of the present invention:

[0098] The present invention is aimed at multi-panel splicing structures. To address the noise problem of multi-panel splicing structures, the modal analysis method is adopted. Based on the principles of structural mechanics, vibration differential equations, wave theory, and acoustic Lagrange equations, a plate-plate coupling substructure model under stiffness constraints (i.e., a wall panel-cavity coupling model) is constructed, a unified wall panel-cavity coordinate transformation mode is established, and a full-process acoustic-vibration coupling analysis paradigm of fluid-structure-acoustic field is formed by combining multiple fluid excitation models. Furthermore, a prediction method for the acoustic-vibration characteristics of multi-panel splicing structures under flow excitation is proposed to solve the acoustic analysis problem of multi-panel splicing structures and provide a solution to the cabin noise problem. The method can be applied to the noise problems of various multi-panel splicing structures, and has the advantages of a model close to the actual situation and a complete and direct calculation process.

[0099] The advantages of the present invention are:

[0100] 1. In the method of the present invention, elastic boundary conditions that are closer to reality are adopted for the boundary conditions of the wall panel structure: the elastic boundary conditions are to jointly characterize the boundary conditions of the plate using displacement constraint stiffness and rotation constraint stiffness. Through different stiffness combinations, any elastic boundary conditions can be realized, including but not limited to the three classic boundary conditions of simply supported, free, and clamped. At the same time, the loss factor is introduced in the form of complex stiffness to characterize the influence of material damping.

[0101] 2. In the method of the present invention, the connection parts between the substructures adopt the same rigidity connection as the outer boundary conditions of the wall panel, and the specific constraint rigidity is obtained by the specific analysis of the model. At the adjacent boundaries of each divided substructure, equal constraint rigidity is set according to the internal characteristics of the wall panel, and complex rigidity is also introduced to add the influence of loss factor. In this way, the coupling effect between multiple substructures is taken into account in the calculation, and the coupled structure is no longer split into independent substructures and then superimposed on each other. That is, through the rigidity connection, the bending moment and force of each substructure can be transmitted to each other and are no longer regarded as several independent superimposed structures in the calculation.

[0102] 3. The method of the present invention is direct and can directly calculate and analyze the acoustic performance of the coupling model based on the excitation. It is only necessary to derive the transfer matrix through the above process, and then directly calculate the acoustic response results through the excitation terms. In the old method, it is usually necessary to first calculate the vibration response of the substructure based on the excitation terms, and then calculate the acoustic response results in the cavity through the vibration response. That is, the method of the present invention only needs to derive the coupling equations and system transfer matrix that conform to the specific model through steps S1 to S3, and can directly calculate the acoustic response in the cavity based on the correct excitation source, without the need to use the vibration response of the substructure as an intermediate result for calculating the acoustic response of the acoustic cavity. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 : Flowchart of the calculation method of the present invention;

[0104] Figure 2 :Schematic diagram of substructure division example;

[0105] Figure 3 : Schematic diagram of the multi-board splicing structure and the acoustic cavity coordinate system transformation;

[0106] Figure 4 : Schematic diagram of the coupling model of the embodiment;

[0107] Figure 5 : Schematic diagram of the wall panel model of the embodiment;

[0108] Figure 6 :Calculation result diagram of embodiment;

[0109] Figure 7 : Physical parameter table of embodiment. DETAILED DESCRIPTION

[0110] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments:

[0111] The present invention aims at the noise analysis and prediction problem of multi-plate splicing structure, divides the splicing plate structure into multiple substructures, and characterizes its boundary stiffness and connection stiffness. Based on structural mechanics and wave theory, a plate and acoustic cavity model is established, and the substructure coordinate system and the cavity coordinate system are mapped and transformed to obtain a wall panel-cavity coupling model suitable for the multi-plate splicing structure, and characterize the acoustic vibration characteristics of the wall panel-cavity structure; based on the basic models of different excitations, a unified excitation model characterization mode is established and integrated with the coupling model, thereby proposing a universal prediction method for the acoustic vibration coupling characteristics of the structure under flow excitation, realizing the full-process flow-solid-acoustic analysis from flow excitation to structural vibration to acoustic radiation, and solving the acoustic analysis problem of the multi-plate splicing structure. The specific steps are as follows: Figure 1 As shown below:

[0112] S1: Analyze the outer boundary stiffness and internal constraints or connection characteristics of the panel structure, clarify the material parameters of each part of the panel structure, divide the panel structure into multiple substructures based on the internal constraints or connection characteristics, and form a multi-substructure spliced ​​panel model. The outer boundary stiffness of the entire panel structure and the constraints or connection characteristics between the internal substructures are described, which will be used to construct the boundary equations and vibration control equations of the panel structure.

[0113] S2: Apply modal analysis to the model obtained in S1. Based on the basic principles of structural mechanics and vibration control differential equations, construct the coordinate systems of each substructure and establish the boundary equations and vibration control equations corresponding to the model obtained in S1.

[0114] S3: Simplify the cavity structure connected to the plate into a rectangular acoustic cavity, construct the acoustic cavity coordinate system, and establish the acoustic response equations of the acoustic cavity based on wave theory and acoustic Lagrangian function to obtain the acoustic model of the acoustic cavity; couple the acoustic cavity with the plate structure, perform necessary coordinate transformations with the substructure coordinate system, and combine the acoustic response equations with the boundary equations and vibration control equations obtained in S2, adding coupling terms to establish the plate-cavity coupling equations;

[0115] S4: Establish multiple different excitation models, select the correct model corresponding to the excitation source according to the actual working conditions, and substitute it into the plate-cavity coupling equation obtained in S3 to obtain the excitation vector or the power spectrum density matrix representing the excitation for solution calculation;

[0116] The different excitations are uniform acoustic pressure excitation, turbulent flow excitation, and flow excitation with shock wave interference;

[0117] S5: Apply the excitation source corresponding to the working condition to the wall panel structure. The response calculation formula is derived through the panel-cavity coupling equation obtained in S3 to obtain the system transfer matrix. The transfer matrix is ​​subdivided into a vibration transfer matrix and an acoustic transfer matrix. Matrix operations are performed with the excitation vector obtained in S4 or the power spectral density matrix representing the excitation to calculate the vibration and acoustic response results, analyze the structural vibration characteristics and the acoustic performance of the acoustic cavity, and predict the noise of the multi-panel splicing structure.

[0118] In practical application, the entire work can be divided into two parts:

[0119] The first part is to analyze the structural characteristics of the wall panel, divide the model, and give the appropriate constraint stiffness (step S1);

[0120] The second part is to build a coupling model, apply an excitation source and analyze the acoustic characteristics (steps S2 to S5).

[0121] The following will be combined Figure 2 , the wall panel structure analysis and division work in step S1 is explained in detail:

[0122] There may be several stiffness constraints inside any panel structure, such as Figure 2 As shown in (a) and (b), the wall panel is substructured using these stiffness constraints as the actual boundaries, and the actual boundaries are extended to the outer boundaries of the wall panel, which are recorded as the partitioning boundaries.

[0123] The partition boundary and the actual boundary divide the entire wall into several substructures. The specific division form is not fixed and is determined by the internal stiffness constraint. Figure 2 (a) is divided into 2×2, or Figure 2 In (b), it is divided into 2×4, and can also be divided into 3×3 and other forms. The sizes of each substructure do not have to be exactly the same.

[0124] For some special structures, such as the panel structure consisting of windows and surrounding bulkheads, some substructures are made of different materials than others and require special consideration. In extreme cases, the material properties of some substructures are close to the acoustic impedance boundary, so these substructures can be simplified and excluded from the panel structure model.

[0125] The following combination Figure 3 Explain the coordinate system transformation:

[0126] The distance between the two adjacent right-angled sides (outer boundaries) of the wall structure and the corresponding right-angled sides of the upper surface of the sound cavity is x z ,y z , the side length of the divided substructure is Figure 3 The distance in the x direction between the origin O1 of the substructure coordinate system and the origin O of the acoustic cavity coordinate system is x z +a1, distance y in the y direction z +b1+b2. Therefore, when the coordinates of any point (x1, y1) in the substructure coordinate system are transformed to the acoustic cavity coordinate system, the new coordinates are (x1+x z +a1,y1+y z The coordinate transformations of the remaining substructures and any other arbitrary models can be deduced in this way.

[0127] The following combines a completed model and Figures 3 to 6 Steps S2 to S5 are described in detail:

[0128] The model as a whole Figure 4 , where the wall panel structure is composed of nine substructures spliced ​​together in a 3×3 form (e.g. Figure 5 , while from Figure 5 The numbering can also be seen in the figure). The physical parameters of each substructure are exactly the same. The displacement constraint stiffness and rotation constraint stiffness at the adjacent boundaries of the substructure are both set to 1×10 -2 N / m, 1×10 -2 Nm / rad, indicating that the substructures are connected in the form of free boundaries; the constraint stiffness of the outer boundary of the wall panel is set to 1×10 10 N / m, 1×10 -2 Nm / rad, represents the simply supported boundary condition, so the wall panel can be regarded as a large simply supported plate.

[0129] The length and width of the acoustic cavity in this model are completely consistent with the total length and width of the wall panel, that is, the upper wall of the acoustic cavity is completely coupled with the wall panel. At the same time, each wall of the acoustic cavity is set as a rigid wall boundary (i.e., 1×10 8 i).

[0130] In this implementation case, a 120dB uniform sound pressure excitation is applied to the upper surface of the wall panel, and two points at different heights are determined just below the center of the wall panel in the cavity. The sound pressure response at these points and the excitation sound pressure are calculated to obtain the sound insulation value as the calculation result of this implementation case (such as Figure 6 ). The specific location of the point is shown in Figure 3 .

[0131] The plate boundary equations in S2 include the following:

[0132] According to the physical parameters of the model (such as Figure 7 ) and elastic boundary conditions to establish the boundary equations of each substructure. At the same time, the influence of the loss factor is introduced, and the complex stiffness is used in the boundary conditions, that is, k is replaced by k(1+iη) and K(1+iμ) is replaced by K.

[0133] The structures of the matrices H, Q, K, M, B, and T in the derived plate boundary equations and plate vibration control equations are shown below:

[0134]

[0135]

[0136] By bringing parameters such as sound velocity, air density, acoustic cavity size, and impedance boundary value into the acoustic Lagrangian function, we can derive the acoustic response equations and coupling equations.

[0137] Acoustic system matrix K in S3 C 、Z C 、M C As shown below:

[0138]

[0139] Coupling matrix K p 、M P The elements in involve the coordinate transformation from the substructure coordinate system to the acoustic cavity coordinate system. The structures of the two coupling matrices are as follows:

[0140]

[0141]

[0142] M P =[M R M Z ]

[0143]

[0144]

[0145] The excitation vector P corresponding to the uniform sound pressure excitation mentioned in S4 is as follows:

[0146] P=[P1 P2 … P9] T

[0147] S5 includes the following:

[0148] Since the uniform sound pressure excitation of this model can be directly calculated in the form of an excitation vector, the response calculation formula is: Y(ω)=H(ω)P(ω). Where P(ω) is the sound pressure excitation, corresponding to the column vector P, and the transfer matrix H(ω)=X(ω)H S (ω), and H S (ω) consists of two parts: H w (ω) and H p (ω).

[0149] H w (ω)=A -1 +A -1 *B0*(D-C0*A -1 *B0) -1 *C0*A -1

[0150] H p (ω)=-(D-C0*A -1 *B0) -1 *C0*A -1

[0151] X(ω) contains the expression vectors of the panel displacement and the sound pressure response, which are: w 、X p .

[0152] The sound pressure response calculation formula is:

[0153] P res (ω)=X p *H p (ω)*P

[0154] The sound insulation calculation formula is:

[0155] TL=-20log 10 (P res (ω) / p0)

[0156] After calculating the sound insulation at the corresponding point, the sound insulation-frequency graph is drawn. Figure 6 , the noise of multi-board splicing structure can be predicted.

[0157] In summary, the proposed method employs elastic boundary conditions and rigid connections to construct multi-panel structures, making the model more realistic and the calculation results more reliable. Furthermore, the method constructs a complete fluid-structure-acoustic coupling model and a comprehensive and straightforward calculation process. Therefore, this method can facilitate noise research in multi-panel structures.

[0158] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present invention, and these modifications or replacements should all be included in the scope of protection of the present invention.

Claims

1. A method for predicting noise of multi-plate splicing structures under flow excitation, characterized in that: The following steps are involved: S1: Analyze the external boundary stiffness and internal constraints or connection characteristics of the actual panel structure, clarify the material parameters of each part of the panel structure, divide the panel structure into multiple substructures based on the internal constraints or connection characteristics, and form a multi-substructure spliced ​​panel model. The external boundary stiffness of the entire panel structure and the constraints or connection characteristics between the internal substructures are described, which are subsequently used to construct the boundary equations and vibration control equations of the panel structure. S2: Apply modal analysis to the model obtained in S1. Based on the basic principles of structural mechanics and vibration control differential equations, construct the coordinate systems of each substructure and establish the boundary equations and vibration control equations corresponding to the model obtained in S1. S3: Simplify the cavity structure connected to the wall panel into a rectangular acoustic cavity with arbitrary impedance boundary conditions, construct the acoustic cavity coordinate system, and establish the acoustic response equations of the acoustic cavity based on wave theory and acoustic Lagrangian function; couple the acoustic cavity with the plate structure, perform coordinate transformation with the substructure coordinate system, and combine the acoustic response equations with the boundary equations and vibration control equations obtained in S2 and add coupling terms to establish the plate-cavity coupling equations; S4: Establish multiple different excitation models, select the correct model corresponding to the excitation source according to the actual working conditions, and substitute it into the plate-cavity coupling equation obtained in S3 to obtain the excitation vector or the power spectrum density matrix representing the excitation for solution calculation; The different excitations are uniform acoustic pressure excitation, turbulent flow excitation, and flow excitation with shock wave interference; S5: Apply the excitation source corresponding to the working condition to the wall panel structure. The response calculation formula is derived through the panel-cavity coupling equation obtained in S3 to obtain the system transfer matrix. The transfer matrix is ​​subdivided into a vibration transfer matrix and an acoustic transfer matrix. Matrix operations are performed with the excitation vector obtained in S4 or the power spectral density matrix representing the excitation to calculate the vibration and acoustic response results, analyze the structural vibration characteristics and the acoustic performance of the acoustic cavity, and predict the noise of the multi-panel splicing structure.

2. The method for predicting noise of multi-plate splicing structures under flow excitation according to claim 1 is characterized in that: S1 is specifically: S1.1 Analyze and describe the various characteristics of the wall panel structure: Determine the constraints on the outer boundary of the panel structure and give the correct displacement constraint stiffness and rotation constraint stiffness to jointly describe the outer boundary stiffness; Analyze the constraints or connection features inside the panel structure and give the correct displacement constraint stiffness and rotation constraint stiffness at the corresponding positions to describe these constraints or connection features; Analyze and organize to clarify the material parameters of different parts of the wall panel structure; S1.2 Divide the wall panel structure into substructures: Based on the analysis and description of the various characteristics of the wall panel structure in S1.1, it is divided into a multi-panel splicing structure formed by coupling multiple substructures, as follows: S1.2.1 Preliminarily divide the panel structure according to the internal constraints and connection characteristics, and at the same time separate the parts of different materials to preliminarily determine the actual boundaries; S1.2.2 Extend the determined factual boundary to the outer boundary of the wall panel to obtain the demarcation boundary and complete the demarcation work; S1.2.3 Select the constraint stiffness on the extended partition boundary so that it does not affect the original force and vibration propagation of the wall panel, forming a multi-substructure spliced ​​plate model.

3. The method for predicting noise of multi-plate splicing structures under flow excitation according to claim 2 is characterized in that: S2 is specifically: According to the model obtained in S1, a two-dimensional coordinate system of each substructure is constructed with any vertex of the substructure as the origin. The boundary equations of each substructure are established based on the equilibrium conditions of force and bending moment in structural mechanics and the continuity of displacement and rotation, as follows: Where i represents the substructure index, l is the edge index, and x and y are the coordinates of the point in the substructure coordinate system; w i (x,y) is the Fourier series expansion of the sub-plate displacement function: in, A imn , is the Fourier coefficient; a, b are the length and width of the substructure; m, n are the mode numbers of the plate in the x and y directions respectively; The supplementary function in the Fourier series expansion is: in, To supplement the function coefficients, the specific assignments are as follows: Substitute the displacement function into equation (1) and eliminate cosλ on both sides. im xcosλ in y, we get the position-independent boundary equations, which are recorded as: [H-Q]*C p =0 (2) Among them, C p =[ap] T , is the Fourier coefficient vector, the elements of a are A imn , the elements of p are Under elastic boundary conditions, the vibration control differential equations of each substructure are as follows: D i ▽ 4 w i (x,y)-p i h i oh 2 w i (x,y)=0orF i (3) Among them, F i Refers to the stimulus received by each sub-board, and the specific form is determined by different stimulus forms; is the bending stiffness of the plate, E i is the Young's modulus of the plate, h i is the thickness of the plate, ν i is the Poisson's ratio of the plate, x, y are the horizontal and vertical coordinates of the point in the substructure coordinate system; Substitute the plate displacement function into equation (3) and multiply both sides of the equation by cosλ after expansion. im xcosλ in y and integrate to eliminate the position effect, and obtain the vibration control equations that are independent of the position coordinates: [K B]*C p -ω 2 [M T]*C p =0orF (4) The above is a set of linear vibration equations without considering damping; If the damping effect is considered, the following equations are obtained by adding Rayleigh damping to the equation: [K B]*C p +jωC*C p -ω 2 [M T]*C p =0orF (5) Where C = α[KB] + β[MT], j is an imaginary unit, and α and β are the stiffness factor and quality factor of Rayleigh damping, respectively.

4. The method for predicting noise of multi-plate splicing structures under flow excitation according to claim 3 is characterized in that: S3 specifically: First, a three-dimensional acoustic cavity coordinate system is constructed with any vertex of the acoustic cavity bottom surface as the origin, and the sound pressure function in the acoustic cavity is written as the following Fourier series expansion form: in, L x ,L y ,L z are the length, width and height of the vocal cavity, x, y, z are the coordinates of the point in the vocal cavity coordinate system; A mxmymz ,a mxmy ,b mxmy ,c mxmz ,d mxmz ,e mymz ,f mymz is the Fourier coefficient; m x ,m y ,m z are the modes of the acoustic cavity in the length, width and height directions respectively; The supplementary function expression in the sound pressure function expansion is as follows: The expression of the acoustic Lagrangian function of the acoustic cavity with arbitrary impedance boundary conditions is: L=V-T-W wall -W Q Among them, V is the total acoustic potential energy of the acoustic cavity, T is the total kinetic energy, and W is the total acoustic potential energy. wall is the work done on the impedance boundary, W Q is the work done by the sound source in the acoustic cavity; from this, the acoustic response equations of the acoustic cavity under arbitrary impedance boundary conditions can be derived as follows: (K C +ωZ C +oh 2 M C )*C C =Q0 (6) C C The elements of are the coefficients in the Fourier series expansion of the sound pressure; at the same time, if there is no sound source in the sound cavity, the right side of the equation is 0; The acoustic cavity is coupled with the multi-substructure splicing plate, and the coupling equations are derived: Where ρ0 is the air density in the acoustic cavity; K p 、M p For the coupling matrix, it is necessary to pay attention to the coordinate transformation between the acoustic cavity coordinate system and the substructure coordinate system when deriving it; Arrange and combine the above equations (7) and write them into matrix form to obtain: in: A1=[K B]+jωC-ω 2 [M T] C0=-ω 2 p0*M p D=K C +ωZ C +oh 2 M C Among them, O is a zero matrix, which is used to make up the number of matrix items and meet the matrix operation conditions.

5. The method for predicting noise of a multi-plate splicing structure under flow excitation according to claim 4 is characterized in that: In S4, for uniform sound pressure excitation, the vibration control equations (4) or (5) of each substructure are derived together to obtain the sound pressure amplitude multiplied by cosλ im xcosλ in y is then integrated to obtain the excitation elements corresponding to each substructure, which are then written as excitation vectors for acoustic performance analysis; For turbulent excitation, the Corcos model is used to describe the stationary random process, and the power spectral density function is introduced to obtain the power spectral density matrix of turbulent excitation; the power spectral density function of turbulent excitation is as follows: Among them, ξ x =x-x',ξ y =y-y' is the spatial separation function, α x ,α y is the empirical coefficient, U c is the turbulent boundary layer convection velocity, S ref (ω) is the reference power spectral density.

6. The method for predicting noise of multi-plate splicing structures under flow excitation according to claim 5 is characterized in that: S5 is specifically: Apply excitation to the panel structure and select different formulas to analyze the acoustic performance according to different forms of excitation; For simple excitation forms, the excitation source is directly involved in the calculation in the form of an excitation vector, which is substituted into the response calculation formula Y(ω)=H(ω)F(ω), where F(ω) refers to the excitation vector. Transfer matrix H(ω)=X(ω)H S (ω), H S (ω) consists of two parts: the plate vibration response transfer matrix H w (ω) and the sound pressure response transfer matrix H p (ω): H w (ω)=A -1 +A -1 *B0*(D-C0*A -1 *B0) -1 *C0*A -1 H p (ω)=-(D-C0*A -1 *B0) -1 *C0*A -1 X(ω) contains the expression vectors of the panel displacement and the sound pressure response, which are: w 、X p ;In practical applications, the vibration response and sound pressure response are calculated separately; In the face of complex excitation forms, the power spectrum density function is converted to the power spectrum density domain for calculation; the power spectrum density function is as follows: Among them, P tbl (ω) is the load vector of turbulence excitation; the system response power spectrum density matrix S YY (ω) contains the displacement response S ww (ω) and the sound pressure response S pp (ω) Two parts: By applying the corresponding response power spectrum density matrix and the response expression vector to perform operations, the displacement power spectrum density or sound pressure power spectrum density at a certain point can be obtained:

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