A method, system and device for predicting the sound radiation performance of a rectangular plate with arbitrary holes

Abstract

The present invention relates to a field of acoustic technology, and in particular to a method, system, and device for predicting the sound radiation performance of a rectangular plate with arbitrary holes. The method for predicting the sound radiation performance of a rectangular plate with arbitrary holes comprises: establishing a numerical model of the rectangular plate with arbitrary holes, including a plate domain, a hole domain, and elastic boundary conditions; dividing the rectangular plate with arbitrary holes into units, and obtaining the vibration equation of the rectangular plate with arbitrary holes according to the Lagrangian functional of the rectangular plate with arbitrary holes; obtaining the vibration displacement and vibration velocity according to the vibration equation of the rectangular plate with arbitrary holes, and further using the Ruili sound radiation integral equation to obtain the radiation sound pressure of each unit on the plate; calculating the radiation sound power and radiation efficiency parameters of the entire rectangular plate with arbitrary holes based on the radiation sound pressure of each unit, and further obtaining the coupling equation of the system to realize the prediction of the sound radiation performance of the rectangular plate with arbitrary holes. The present invention improves the efficiency of predicting the sound radiation performance of the rectangular plate with arbitrary holes.

Description

Technical Field

[0001] The present invention relates to the field of acoustic technology, and in particular to a method, system and device for predicting the sound radiation performance of a rectangular plate with arbitrary holes. Background Art

[0002] At present, plate structures are widely used in the fields of engineering and science and are an important part of engineering design and construction. Among them, the vibration and acoustics research of plates with arbitrary holes is a common problem in engineering.

[0003] A plate with a random hole is a flat or thin plate with a number of holes. These holes can be of any shape. These plates are commonly used in a variety of applications in engineering and science, offering a wide range of functions and properties.

[0004] Perforated plates, as a special case of plate structures, have varying effects on their performance, and predicting their various properties requires significant time and effort during the design phase. Currently, the most commonly used prediction method utilizes finite element theory, dividing the numerical model into numerous units to achieve high accuracy. However, this approach struggles to ensure overall efficiency when solving for the acoustic radiation characteristics. Currently, there is no analytical method for solving the acoustic radiation characteristics of rectangular plates with arbitrary perforations. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problem of low efficiency in predicting the sound radiation characteristics of a rectangular plate with arbitrary holes in the prior art.

[0006] To solve the above technical problems, the present invention provides a method for predicting the sound radiation performance of a rectangular plate with arbitrary holes, comprising:

[0007] S1. Establish a numerical model of a rectangular plate with an arbitrary hole, including the plate domain, hole domain, and elastic boundary conditions;

[0008] S2. Divide the rectangular plate with arbitrary holes into units and obtain the vibration equation of the rectangular plate with arbitrary holes according to the Lagrangian functional of the rectangular plate with arbitrary holes;

[0009] S3. Obtain the vibration displacement and vibration velocity based on the vibration equation of the rectangular plate with arbitrary holes, and further obtain the radiation sound pressure of each unit on the plate using the Rayleigh sound radiation integral equation;

[0010] S4. Calculate the radiation sound power and radiation efficiency parameters of the entire rectangular plate with arbitrary holes based on the radiation sound pressure of each unit; substitute the radiation sound power and radiation efficiency parameters of the entire plate into the vibration equation to further obtain the coupling equation of the system, thereby realizing the prediction of the sound radiation performance of the rectangular plate with arbitrary holes.

[0011] In one embodiment of the present invention, in S2, the Lagrangian functional expression is:

[0012] L plate =U plate -T plate -W F

[0013] Among them U plate represents the potential energy of a rectangular plate with an arbitrary hole, T plate represents the kinetic energy of a rectangular plate with an arbitrary hole, W F Represents the work done by external force.

[0014] In one embodiment of the present invention, a rectangular plate with an arbitrary hole is divided into V×G units. The potential energy of the entire rectangular plate is calculated from the potential energy of each unit as follows:

[0015]

[0016] The expression for calculating the kinetic energy of the entire rectangular plate from the kinetic energy of each unit is:

[0017]

[0018] Where D is the bending stiffness of the rectangular plate with an arbitrary hole, D = Eh 3 / (12(1-μ 2 )); E represents the Young's modulus of the material, a represents the length of the rectangular plate with an arbitrary hole, b represents the width of the rectangular plate with an arbitrary hole, w represents the displacement of each point of the rectangular plate with an arbitrary hole during vibration, x represents the abscissa of the rectangular plate with an arbitrary hole, y represents the ordinate of the rectangular plate with an arbitrary hole, k x0 、k xa 、k y0 、k yb represents the transverse spring in the boundary spring of a rectangular plate with an arbitrary hole, K x0 , K xa , K y0 , K yb Represents the torsion spring in the boundary spring of a rectangular plate with an arbitrary hole;

[0019] ρ represents the material density, ω represents the frequency of the external force, h represents the thickness of the rectangular plate with an arbitrary hole, V and G are the number of units in the x and y directions, respectively, and U(v, g) and T(v, g) are the potential energy and kinetic energy of the unit cell (v, g), respectively;

[0020] Determine the cell (v, g). If the geometric center of (v, g) is located on the rectangular plate with an arbitrary hole, then R(v, g) = 1; otherwise, R(v, g) = 0.

[0021] Taking a simple harmonic point force of magnitude F and frequency f as the external force, the expression for the work done on a rectangular plate with an arbitrary hole is:

[0022] w F =∫∫ S Fwδ(x-x0)δ(y-y0)dxdy

[0023] Substituting the potential energy, kinetic energy expressions of each unit and the expression of the work done by the external force into the Lagrange functional and differentiating the coefficients in the Fourier series, the vibration equation of the rectangular plate structure with arbitrary holes is obtained:

[0024] {[K p_h ]-ω 2 [M p_h ]}{A}={F}

[0025] Among them, K p_h represents the stiffness matrix of a rectangular plate with an arbitrary hole, ω represents the frequency of the external force, M p_h represents the mass matrix of a rectangular plate with an arbitrary hole, A represents the Fourier coefficient matrix, and F represents the force matrix.

[0026] In one embodiment of the present invention, obtaining the radiation sound pressure of each unit on the panel using the Rayleigh sound radiation integral equation includes:

[0027] Assume that a rectangular plate with an arbitrary hole is placed in an infinite barrier, and the radiated sound pressure on the plate surface is P(x, y, t) = p(x, y)e iωt , where the expression of p(x, y) is:

[0028]

[0029] Where t represents time, x represents the horizontal coordinate of the rectangular plate with an arbitrary hole, y represents the vertical coordinate of the rectangular plate with an arbitrary hole, and i represents a complex number in mathematics. 2 = -1, ω represents the frequency of the external force, ρ0 represents the air density, (x′, y′) are the coordinates of the vibration point, u represents the vibration velocity of a point on the surface of the rectangular plate with an arbitrary hole, e is a natural constant, k = ω / c, where k is the wave number, c is the sound velocity of the medium being air, R is the linear distance between the vibration point and the sound pressure point, and S is the surface area of the rectangular plate with an arbitrary hole;

[0030] Divide the rectangular plate with arbitrary holes into V×G units, and the expression of the plate surface radiation sound pressure after the integral operation is converted into a cumulative operation is:

[0031]

[0032] Where P(v, g) is the sound pressure of the unit (v, g). The unit cell (v, g) is judged. If the geometric center of (v, g) is located on the rectangular plate with an arbitrary hole, then R(v, g) = 1, otherwise R(v, g) = 0.

[0033] In one embodiment of the present invention, the radiated sound power of a rectangular plate with an arbitrary hole is expressed as follows:

[0034]

[0035] Where Re is the real part, I(x, y) is the normal vector of the sound intensity of the rectangular plate with an arbitrary hole, expressed as:

[0036] I(x,y)=Re[u * (x, y)p(x, y)]

[0037] Where * represents complex conjugation.

[0038] In one embodiment of the present invention, the radiation efficiency parameter expression of a rectangular plate with arbitrary holes is:

[0039]

[0040] where R rad is the radiation impedance of the plate, which is expressed as:

[0041]

[0042] 2 > is the mean square velocity of the plate, and the expression is:

[0043] In one embodiment of the present invention, the radiation sound power and radiation efficiency parameters of the entire plate are substituted into the vibration equation of the rectangular plate structure with arbitrary holes, and the coupling equation of the system is further obtained as follows:

[0044]

[0045] Where κ is the coefficient of the Rayleigh integration process, Q is the matrix form containing each element in the Rayleigh integral, and P is the Fourier coefficient matrix form of the sound pressure.

[0046] In one embodiment of the present invention, when the fluid surrounding the rectangular plate with an arbitrary hole is a heavy fluid, the Lagrangian functional of the strongly coupled system is:

[0047] L plate =U plate -T plate -W F -W sound

[0048] Where W​sound The mechanical work done by the acoustic pressure on a rectangular plate with an arbitrary hole;

[0049] The equations for a strongly coupled system are:

[0050]

[0051] Where C is the coupling term of the acoustic field reacting to the rectangular plate with an arbitrary hole.

[0052] The present invention also provides a system for predicting the sound radiation performance of a rectangular plate with arbitrary holes, comprising:

[0053] Model building module, used to establish a numerical model of a rectangular plate with arbitrary holes, including the plate domain, hole domain, and elastic boundary conditions;

[0054] The unit division module is used to divide the rectangular plate with arbitrary holes into units and obtain the vibration equation of the rectangular plate with arbitrary holes based on the Lagrangian functional of the rectangular plate with arbitrary holes;

[0055] The data analysis module is used to obtain the vibration displacement and vibration velocity based on the vibration equation of the rectangular plate with arbitrary holes, and further use the Rayleigh sound radiation integral equation to obtain the radiation sound pressure of each unit on the plate; then, based on the radiation sound pressure of each unit, the radiation sound power and radiation efficiency parameters of the entire rectangular plate with arbitrary holes are calculated; the radiation sound power and radiation efficiency parameters of the entire plate are substituted into the vibration equation to further obtain the coupling equation of the system, thereby realizing the prediction of the sound radiation performance of the rectangular plate with arbitrary holes.

[0056] The present invention also provides a device for predicting the sound radiation performance of a rectangular plate with arbitrary holes, comprising:

[0057] memory for storing computer programs;

[0058] A processor is used to implement the steps of the above-mentioned method for predicting the sound radiation performance of a rectangular plate with arbitrary holes when executing the computer program.

[0059] The above technical solution of the present invention has the following advantages over the prior art:

[0060] The present invention discloses a method for predicting the sound radiation performance of a rectangular plate with arbitrary holes. When establishing a numerical model of the plate with holes, the hole is considered to be an extremely thin part of the plate, its mass density and Young's modulus are set to zero, and the plate is divided into identifiable discrete units, thereby deriving the forced vibration equation of the plate with holes. The modal superposition method is then used to obtain the vibration velocity at each position on the plate, and the discrete Rayleigh integral equation for sound radiation is then used to obtain the radiated sound pressure at each position on the plate, thereby obtaining the radiated sound power and radiation efficiency parameters. While ensuring the accuracy of the prediction of the sound radiation performance of the rectangular plate with arbitrary holes, the present invention uses fewer calculation parameters and dimensions, simplifies the calculation of the numerical model, and improves the efficiency of the prediction of the sound radiation performance of the rectangular plate with arbitrary holes. Moreover, when predicting the sound radiation performance, the numerical model of the rectangular plate with arbitrary holes provided by the present invention only requires inputting parameter values to obtain good prediction results, thus having a wider applicability and higher prediction efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

[0062] Figure 1 This is a flow chart of a method for predicting the sound radiation performance of a rectangular plate with arbitrary holes provided by the present invention;

[0063] Figure 2 1 is a schematic diagram of a numerical model provided by an embodiment of the present invention;

[0064] Figure 3 1 is a schematic diagram comparing the radiated sound power calculated using the method provided by the present invention and the result calculated using the finite element method in an embodiment of the present invention;

[0065] Figure 4 1 is a schematic diagram comparing the calculation results obtained by changing the sound pressure point according to the method provided by the present invention and the calculation results obtained by using the finite element method in an embodiment of the present invention;

[0066] Figure 5 1 is a schematic diagram comparing modes of the method provided by the present invention and the method using finite element method according to an embodiment of the present invention; Figures a and b are comparisons of the plate surface sound pressure distribution diagrams of a rectangular plate with a circular hole in the center at the first and second order frequencies, respectively; Figures c and d are comparisons of the plate surface sound pressure distribution diagrams of a rectangular plate with a square hole in the center at the first and second order frequencies, respectively;

[0067] Figure 6 It is a structural schematic diagram of a sound radiation performance prediction system of a rectangular plate with arbitrary holes provided by the present invention. DETAILED DESCRIPTION

[0068] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention. Specific embodiment 1

[0070] Reference Figure 1 As shown, the present invention provides a method for predicting the sound radiation performance of a rectangular plate with arbitrary holes, comprising:

[0071] S1. Establish a numerical model of a rectangular plate with an arbitrary hole, including the plate domain, hole domain, and elastic boundary conditions.

[0072] Reference Figure 2 As shown, the rectangular thin plate in the figure does not consider the rotational inertia of the plate and the lateral shear of the plate. The plate boundary is supported by lateral springs and torsion springs to establish an elastic mounting boundary.

[0073] The dimensions of the plate are: length x = a, width y = b, and thickness h. The boundary springs are the transverse springs k x0 、k xa 、k y0 、k yb and torsion spring K x0 , K xa , K y0 , K yb . Where k xa Take the example to introduce the meaning of variables, k xa Indicates the spring stiffness value at coordinate x=a in the x-direction.

[0074] S2. Divide the rectangular plate with arbitrary holes into units and obtain the vibration equation of the rectangular plate with arbitrary holes based on the Lagrangian functional of the rectangular plate with arbitrary holes.

[0075] Assume that there is a force F(x i ,y i ), then the Lagrangian functional of the rectangular plate with arbitrary holes is:

[0076] L plate =U plate -T plate -W F

[0077] Among them U plate represents the potential energy of a rectangular plate with an arbitrary hole, T plate represents the kinetic energy of a rectangular plate with an arbitrary hole, W F Represents the work done by external force.

[0078] The maximum potential energy expression of the rectangular plate with arbitrary holes is:

[0079]

[0080] The maximum kinetic energy expression of the rectangular plate with arbitrary holes is:

[0081]

[0082] Taking a simple harmonic point force of magnitude F and frequency f as the external force, the expression for the work done on a rectangular plate with an arbitrary hole is:

[0083] W F =∫∫ S Fwδ(x-x0)δ(y-y0)dxdy

[0084] Where D is the bending stiffness of the rectangular plate with an arbitrary hole, D = Eh 3 / (12(1-μ 2 )).

[0085] S represents the surface area of the rectangular plate with an arbitrary hole, w represents the displacement of each point of the rectangular plate with an arbitrary hole during vibration, x represents the abscissa of the rectangular plate with an arbitrary hole, y represents the ordinate of the rectangular plate with an arbitrary hole, μ represents the Poisson's ratio of the material, a represents the length of the rectangular plate with an arbitrary hole, b represents the width of the rectangular plate with an arbitrary hole, k x0 、k xa 、k y0 、k yb represents the transverse spring in the boundary spring of a rectangular plate with an arbitrary hole, K x0 , K xa , K y0 , K yb represents the torsion spring in the boundary spring of the rectangular plate with an arbitrary hole; ρ represents the material density, ω represents the frequency of the external force, h represents the thickness of the rectangular plate with an arbitrary hole, and E represents the Young's modulus of the material; δ represents the Dirac function, x0 represents the abscissa of the external force point on the rectangular plate with an arbitrary hole, and y0 represents the ordinate of the external force point on the rectangular plate with an arbitrary hole.

[0086] To simplify the integral operation, in the embodiment of the present invention, the rectangular plate with an arbitrary hole is divided into V×G units. The expression for calculating the potential energy of the entire rectangular plate from the potential energy of each unit is:

[0087]

[0088] The expression for calculating the kinetic energy of the entire rectangular plate from the kinetic energy of each unit is:

[0089]

[0090] Among them, V and G are the number of units in the x and y directions, respectively, and U(v, g) and T(v, g) are the potential energy and kinetic energy of the unit cell (v, g), respectively. The unit cell (v, g) is judged. If the geometric center of (v, g) is located on the rectangular plate with an arbitrary hole, then R(v, g) = 1, otherwise R(v, g) = 0.

[0091] Substituting the potential energy, kinetic energy, and work done by external forces obtained after the above division into the Lagrange functional and differentiating the coefficients in the Fourier series, the vibration equation of the rectangular plate with an arbitrary hole is obtained as follows:

[0092] {[K p_h ]-ω 2 [M p_h ]}{A}={F}

[0093] Among them, K p_h represents the stiffness matrix of a rectangular plate with an arbitrary hole, ω represents the frequency of the external force, M p_h represents the mass matrix of a rectangular plate with an arbitrary hole, A represents the Fourier coefficient matrix to be solved, and F represents the force matrix.

[0094] S3. The vibration displacement and vibration velocity are obtained according to the vibration equation of the rectangular plate with arbitrary holes, and the radiation sound pressure of each unit on the plate is further obtained using the Rayleigh sound radiation integral equation.

[0095] The embodiment of the present invention improves the Fourier series by adding additional terms to the traditional Fourier cosine function to handle the discontinuity of the original cosine function at the elastic constraint boundary. The displacement expression of the rectangular plate with an arbitrary hole at each point is obtained as follows:

[0096]

[0097] Among them, A mn 、 are the expansion coefficients of the Fourier series, M and N represent the number of expansion terms of the Fourier series, m and n represent the mth and nth expansion terms of the Fourier series respectively; λ am =mπ / a,λ bn =nπ / b; and is an auxiliary function, the expression is:

[0098]

[0099]

[0100]

[0101]

[0102] The normal vibration velocity expression of a point on the rectangular plate with an arbitrary hole is:

[0103] u(x, y) = iωw(x, y)

[0104] The Fourier series expression of the vibration velocity of the rectangular plate is:

[0105]

[0106] Which represents the complex number in mathematics, there are i 2 =-1;

[0107] and is the supplementary term of the Fourier series, obtained by the Rayleigh method, and obtained by the supplementary term and The Fourier cosine expansion of

[0108]

[0109] in and is the complement of the Fourier series.

[0110] Will and A mn Restated in matrix form: The elements in the A matrix are the unknown coefficients to be solved, and T is the change matrix of the process.

[0111] By solving the vibration equation of the rectangular plate with arbitrary holes, the Fourier coefficient matrix A is obtained, and substituting it into the vibration displacement expression and vibration velocity expression of the rectangular plate with arbitrary holes, the vibration displacement and vibration velocity of the rectangular plate with arbitrary holes can be obtained.

[0112] Assuming that a rectangular plate with an arbitrary hole is placed in an infinite barrier, the sound radiation characteristics are solved using the Rayleigh integral equation for sound radiation, and the radiation sound pressure on the plate surface is obtained as P(x, y, t) = p(x, y)e iωt , where the expression of p(x, y) is:

[0113]

[0114] Where t represents time, x represents the horizontal coordinate of the rectangular plate with an arbitrary hole, y represents the vertical coordinate of the rectangular plate with an arbitrary hole, and i represents a complex number in mathematics. 2= -1, ω represents the frequency of the external force, ρ0 represents the air density, (x′, y′) are the coordinates of the vibration point, u represents the vibration velocity of a point on the surface of the rectangular plate with an arbitrary hole, e is a natural constant, k = ω / c, where k is the wave number, c is the sound velocity of the medium being air, R is the linear distance between the vibration point and the sound pressure point, and S is the surface area of the rectangular plate with an arbitrary hole;

[0115] After the rectangular plate with an arbitrary hole is divided into V×G units, the expression of the plate surface radiation sound pressure after the integral operation is converted into a cumulative operation is:

[0116]

[0117] Where P(v, g) is the sound pressure of the unit (v, g). The unit cell (v, g) is judged. If the geometric center of (v, g) is located on the rectangular plate with an arbitrary hole, then R(v, g) = 1, otherwise R(v, g) = 0.

[0118] This step is characterized by discretizing the sound pressure, treating all sound pressures in the same unit as a single value, and then accumulating them to obtain the radiated sound pressure of the entire panel.

[0119] S4. The radiation sound power expression of the entire rectangular plate with arbitrary holes is calculated based on the radiation sound pressure of each unit:

[0120]

[0121] Where Re is the real part, I(x, y) is the normal vector of the sound intensity of the rectangular plate with an arbitrary hole, expressed as:

[0122] I(x,y)=Re[u * (x, y)p(x, y)]

[0123] Where * represents complex conjugation.

[0124] The radiation efficiency parameter expression of the entire rectangular plate with arbitrary holes is obtained as follows:

[0125]

[0126] where R rad is the radiation impedance of the plate, which is expressed as:

[0127]

[0128] 2 > is the mean square velocity of the plate, and the expression is:

[0129]

[0130] ​Substituting the radiation sound power and radiation efficiency parameters of the whole panel into the vibration equation obtained in S2, the coupling equation of the system is further obtained as follows:

[0131]

[0132] Where κ is the coefficient of the Rayleigh integration process, Q is the matrix form containing each element in the Rayleigh integral, and P is the Fourier coefficient matrix form of the sound pressure.

[0133] The radiation sound power and radiation efficiency parameters of the entire panel can be calculated through the coupling equation of the system.

[0134] The coupling equation of the system adopts a weak coupling structure. When the fluid is water or other heavy fluids, the additional mass of water acting on the plate structure will have a greater impact on the vibration of the plate. Therefore, strong coupling needs to be taken into account, that is, the mechanical work W done by the sound pressure on the plate needs to be considered. sound , then the Lagrangian functional at this time can be expressed as:

[0135] L plate =U plate -T plate -W F -W sound

[0136] The equations for a strongly coupled system are:

[0137]

[0138] Where C is the coupling term of the acoustic field reacting to the rectangular plate with an arbitrary hole.

[0139] By solving the equations for the strongly coupled system, we can obtain the vibration velocity, surface acoustic pressure, radiated acoustic power, and radiation efficiency of a rectangular plate with an arbitrary hole in the strongly coupled system. Therefore, this method is also applicable to strongly coupled systems. Specific embodiment two:

[0141] In order to verify the correctness of the method proposed in the present invention, in the embodiment of the present invention, the effectiveness of the method of the present invention is illustrated by comparing the prediction results of the sound radiation performance of a rectangular plate with arbitrary holes in the present invention with the prediction results of the finite element method.

[0142] In the implementation of the present invention, the circular hole plate is taken as an example. The parameters of the rectangular plate are: length a = 0.5m, width b = 0.6m, thickness h = 0.003m, Young's modulus E = 70.3GPa, density ρ = 2700kg / m 3 , Poisson's ratio μ = 0.3. The coordinates of the center of the circular hole are (0.2, 0.2), and the aperture r = 0.1m.

[0143] The air parameters are set as follows: speed of sound c0 = 343 m / s, air density ρ0 = 1.23 kg / m 3 , the coordinates of the point of action of the simple harmonic force F are (0.1, 0.5). Set the boundary conditions of the rectangular plate with a circular hole to be simply supported on all four sides, that is, make the linear spring stiffness of the four sides infinite, that is, k x0 、k xa 、k y0 、k yb Both are 10″N / m, K x0 , K xa , K y0 , K yb All are zero.

[0144] The results of calculating the sound power radiated from the rectangular plate with a circular hole are as follows: Figure 3 As shown, it can be clearly seen from the comparison that the method of the present invention is highly consistent with the finite element results in calculating the sound radiation performance of the rectangular plate with holes.

[0145] To ensure the applicability of this method, the opening is set to a square with a side length of 0.1m and the center coordinates are (0.4, 0.45), and the coordinates of the point of action of the simple harmonic force F are changed to (0.1, 0.1). The results of the rectangular plate with the opening are compared again under the action of the simple harmonic force at different positions. Figure 4 As shown, it can be seen that the results obtained by the method of the present invention are in good agreement with those obtained by the finite element method.

[0146] Reference Figure 5 As shown in the figure, the top image shows the panel surface sound pressure distribution using this method, while the bottom image shows the panel surface sound pressure distribution using the finite element method. Figures a and b compare the panel surface sound pressure distributions for a rectangular plate with a circular hole in the center at the first and second order frequencies, respectively; Figures c and d compare the panel surface sound pressure distributions for a rectangular plate with a square hole in the center at the first and second order frequencies, respectively. This comparison clearly shows that the panel surface sound pressure calculated using this method is highly consistent with the finite element results.

[0147] In summary, the method for predicting the sound radiation performance of a rectangular plate with arbitrary holes provided by the present invention is substantially consistent with the accuracy of the finite element method. Furthermore, while ensuring accuracy, the method of the present invention uses fewer computational parameters and dimensions than the finite element method, simplifying the computation of the numerical model and improving the efficiency of predicting the sound radiation performance of a rectangular plate with arbitrary holes. Furthermore, when predicting sound radiation performance, the numerical model of a rectangular plate with arbitrary holes provided by the present invention only requires inputting parameter values to obtain good prediction results, rather than requiring the finite element method to draw images and divide cells in different scenarios, and then remodeling based on the specific scenario. Therefore, the method has wider applicability and higher prediction efficiency. Specific embodiment three:

[0149] Reference Figure 6 As shown, an embodiment of the present invention provides a system for predicting the sound radiation performance of a rectangular plate with arbitrary holes, comprising:

[0150] Model building module, used to establish a numerical model of a rectangular plate with arbitrary holes, including the plate domain, hole domain, and elastic boundary conditions;

[0151] The unit division module is used to divide the rectangular plate with arbitrary holes into units and obtain the vibration equation of the rectangular plate with arbitrary holes based on the Lagrangian functional of the rectangular plate with arbitrary holes;

[0152] The data analysis module is used to obtain the vibration displacement and vibration velocity based on the vibration equation of the rectangular plate with arbitrary holes, and further use the Rayleigh sound radiation integral equation to obtain the radiation sound pressure of each unit on the plate; then, based on the radiation sound pressure of each unit, the radiation sound power and radiation efficiency parameters of the entire rectangular plate with arbitrary holes are calculated; the radiation sound power and radiation efficiency parameters of the entire plate are substituted into the vibration equation to further obtain the coupling equation of the system, thereby realizing the prediction of the sound radiation performance of the rectangular plate with arbitrary holes.

[0153] An embodiment of the present invention further provides a device for predicting the sound radiation performance of a rectangular plate with arbitrary holes, comprising:

[0154] memory for storing computer programs;

[0155] A processor is used to implement the steps of the above-mentioned method for predicting the sound radiation performance of a rectangular plate with arbitrary holes when executing the computer program.

[0156] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0157] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1A device that provides the functions specified in a block or multiple blocks.

[0158] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0159] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0160] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for predicting the sound radiation performance of a rectangular plate with arbitrary holes, characterized by: S1. Establish a numerical model of a rectangular plate with an arbitrary hole, including the plate domain, hole domain, and elastic boundary conditions; S2, divide the rectangular plate with arbitrary holes into units; The expression for calculating the potential energy of the entire rectangular plate from the potential energy of each unit is: ； The expression for calculating the kinetic energy of the entire rectangular plate from the kinetic energy of each unit is: ； in, is the bending stiffness of the rectangular plate with an arbitrary hole, ; is the Young's modulus of the material, is the length of the rectangular plate with an arbitrary hole, is the width of the rectangular plate with an arbitrary hole, is the displacement of each point on the rectangular plate with arbitrary holes during vibration, is the horizontal coordinate of the rectangular plate with an arbitrary hole, is the ordinate of the rectangular plate with an arbitrary hole, 、 、 、 is the transverse spring in the boundary spring of a rectangular plate with an arbitrary hole, 、 、 、 is the torsion spring in the boundary spring of a rectangular plate with an arbitrary hole; is the material density, is the frequency of the external force, is the thickness of the rectangular plate with arbitrary holes, 、 They are 、 The number of units in the direction, 、 Cells potential and kinetic energy; For cells To judge, if The geometric center of is located on a rectangular plate with an arbitrary hole, then , otherwise ; By size , the frequency is The simple harmonic point force is used as the external force, and the expression for the work done on the rectangular plate with an arbitrary hole is: ； Substitute the potential energy, kinetic energy expressions of each unit and the expression of work done by external force into the Lagrange functional ,in is the potential energy of a rectangular plate with an arbitrary hole, is the kinetic energy of a rectangular plate with an arbitrary hole, is the work done by the external force; and by differentiating the coefficients in the Fourier series, the vibration equation of the rectangular plate structure with arbitrary holes is obtained: ； in, is the stiffness matrix of the rectangular plate with arbitrary holes, is the mass matrix of a rectangular plate with an arbitrary hole, is the Fourier coefficient matrix, is the force matrix; S3. Obtain the vibration displacement and vibration velocity based on the vibration equation of the rectangular plate with arbitrary holes, and further obtain the radiation sound pressure of each unit on the plate using the Rayleigh sound radiation integral equation; S4. Calculate the radiation sound power and radiation efficiency parameters of the entire rectangular plate with arbitrary holes based on the radiation sound pressure of each unit; substitute the radiation sound power and radiation efficiency parameters of the entire plate into the vibration equation to further obtain the coupling equation of the system, thereby realizing the prediction of the sound radiation performance of the rectangular plate with arbitrary holes.

2. The method for predicting the sound radiation performance of a rectangular plate with arbitrary holes according to claim 1, characterized in that: The radiation sound pressure of each unit on the board is obtained by using the Rayleigh sound radiation integral equation: Assuming that a rectangular plate with an arbitrary hole is placed in an infinite barrier, the radiation sound pressure on the plate surface is ,in The expression is: ； in Indicates time, represents the horizontal coordinate of the rectangular plate with an arbitrary hole, represents the ordinate of a rectangular plate with an arbitrary hole, To represent complex numbers in mathematics, we have , represents the frequency of the external force, represents the air density, are the coordinates of the vibration point, represents the vibration velocity of a point on the surface of a rectangular plate with an arbitrary hole, is a natural constant, ,in is the wave number, is the speed of sound in air, is the linear distance between the vibration point and the sound pressure point, is the surface area of a rectangular plate with an arbitrary hole; Divide the rectangular plate with arbitrary holes into units units, the expression of the plate surface radiation sound pressure after the integral operation is converted into a cumulative operation is: ； in for The sound pressure of the unit, the unit To judge, if The geometric center of is located on a rectangular plate with an arbitrary hole, then , otherwise .

3. The method for predicting the sound radiation performance of a rectangular plate with arbitrary holes according to claim 2, characterized in that: The expression of the radiated sound power of the entire rectangular plate with an arbitrary hole is: ； in is the real part, is the normal vector of the sound intensity of a rectangular plate with an arbitrary hole, expressed as: ； in represents the complex conjugate.

4. The method for predicting the sound radiation performance of a rectangular plate with arbitrary holes according to claim 3, characterized in that: The radiation efficiency parameter expression of the entire rectangular plate with arbitrary holes is: ； in is the radiation impedance of the plate, which is expressed as: ； is the mean square velocity of the plate, which is expressed as: .

5. The method for predicting the sound radiation performance of a rectangular plate with arbitrary holes according to claim 4, characterized in that: Substituting the radiation sound power and radiation efficiency parameters of the whole plate into the vibration equation of the rectangular plate structure with arbitrary holes, the coupling equation of the system is further obtained as follows: ； in is the coefficient of the Rayleigh integration process, is the matrix form containing each element in the Rayleigh integral, is the Fourier coefficient matrix form of the sound pressure.

6. The method for predicting the sound radiation performance of a rectangular plate with arbitrary holes according to claim 5, characterized in that: When the fluid around the rectangular plate with an arbitrary hole is a heavy fluid, the Lagrangian functional of the strongly coupled system is: ； in The mechanical work done by the acoustic pressure on a rectangular plate with an arbitrary hole; The equations for a strongly coupled system are: ； in is the coupling term of the acoustic field reacting to the rectangular plate with an arbitrary hole.

7. A system for predicting the sound radiation performance of a rectangular plate with arbitrary holes, characterized in that: include: Model building module, used to establish a numerical model of a rectangular plate with arbitrary holes, including the plate domain, hole domain, and elastic boundary conditions; Unit division module, used to divide the rectangular plate with arbitrary holes into units; The expression for calculating the potential energy of the entire rectangular plate from the potential energy of each unit is: ； The expression for calculating the kinetic energy of the entire rectangular plate from the kinetic energy of each unit is: ； in, is the bending stiffness of the rectangular plate with an arbitrary hole, ; is the Young's modulus of the material, is the length of the rectangular plate with an arbitrary hole, is the width of the rectangular plate with an arbitrary hole, is the displacement of each point on the rectangular plate with arbitrary holes during vibration, is the horizontal coordinate of the rectangular plate with an arbitrary hole, is the ordinate of the rectangular plate with an arbitrary hole, 、 、 、 is the transverse spring in the boundary spring of a rectangular plate with an arbitrary hole, 、 、 、 is the torsion spring in the boundary spring of a rectangular plate with an arbitrary hole; is the material density, is the frequency of the external force, is the thickness of the rectangular plate with arbitrary holes, 、 They are 、 The number of units in the direction, 、 Cells potential and kinetic energy; For cells To judge, if The geometric center of is located on a rectangular plate with an arbitrary hole, then , otherwise ; By size , the frequency is The simple harmonic point force is used as the external force, and the expression for the work done on the rectangular plate with an arbitrary hole is: ； Substitute the potential energy, kinetic energy expressions of each unit and the expression of work done by external force into the Lagrange functional ,in is the potential energy of a rectangular plate with an arbitrary hole, is the kinetic energy of a rectangular plate with an arbitrary hole, is the work done by the external force; and by differentiating the coefficients in the Fourier series, the vibration equation of the rectangular plate structure with arbitrary holes is obtained: ； in, is the stiffness matrix of the rectangular plate with arbitrary holes, is the mass matrix of a rectangular plate with an arbitrary hole, is the Fourier coefficient matrix, is the force matrix; The data analysis module is used to obtain the vibration displacement and vibration velocity based on the vibration equation of the rectangular plate with arbitrary holes, and further use the Rayleigh sound radiation integral equation to obtain the radiation sound pressure of each unit on the plate; then, based on the radiation sound pressure of each unit, the radiation sound power and radiation efficiency parameters of the entire rectangular plate with arbitrary holes are calculated; the radiation sound power and radiation efficiency parameters of the entire plate are substituted into the vibration equation to further obtain the coupling equation of the system, thereby realizing the prediction of the sound radiation performance of the rectangular plate with arbitrary holes.

8. A device for predicting the sound radiation performance of a rectangular plate with arbitrary holes, characterized in that: include: memory for storing computer programs; A processor is configured to implement the steps of a method for predicting the sound radiation performance of a rectangular plate with arbitrary holes as described in any one of claims 1 to 6 when executing the computer program.

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