Methods for calculating acoustic radiation of infinitely long periodic structures, electronic devices, and storage media.

Abstract

This invention provides a method, electronic device, and storage medium for calculating the acoustic radiation of an infinitely long periodic structure, specifically including the following steps: (1) establishing a finite-length periodic acoustic element model based on commercial finite element software; (2) extracting and storing the acoustic stiffness matrix and acoustic excitation vector of the periodic acoustic element model; (3) applying periodic structure theory to calculate the acoustic radiation of the infinitely long periodic structure. This invention, by utilizing periodic structure theory, realizes the prediction of acoustic radiation from finite-length periodic elements to infinitely long-scale structures. Compared with existing acoustic radiation prediction technologies, this invention effectively balances computational efficiency with the reproducibility of the calculation model, exhibiting significant advantages.

Description

Technical Field

[0001] This invention belongs to the field of acoustic radiation prediction technology, specifically relating to a method for calculating acoustic radiation of an infinitely long periodic structure. Background Technology

[0002] Infinitely long periodic structures have wide applications in practical engineering. When such structures are subjected to external excitation and vibrate, they radiate noise, directly affecting the acoustic environment quality around the structure. In recent years, scholars both domestically and internationally have conducted extensive research on the acoustic radiation characteristics of vibrating structures. Currently, commonly used numerical methods for calculating acoustic radiation mainly include the acoustic boundary element method, the acoustic finite element method, and the statistical energy method. However, the two-dimensional acoustic boundary element method cannot fully consider the influence of vibration attenuation in the third dimension on acoustic radiation; the three-dimensional acoustic boundary element method suffers from large computational load and low efficiency; the traditional acoustic finite element method is mainly applicable to the acoustic radiation analysis of finite structures in a specific acoustic domain; and the statistical energy method relies on statistical assumptions, resulting in limited predictive effectiveness for low-frequency acoustic radiation. Therefore, using conventional acoustic radiation calculation methods to analyze the acoustic radiation behavior of infinitely long-scale vibrating structures often faces challenges such as heavy computational burden and oversimplification of models. Summary of the Invention

[0003] This invention provides a method for calculating the acoustic radiation of infinitely long periodic structures. This method is based on a periodic acoustic unit model of finite length and utilizes periodic structure theory to predict the acoustic radiation of structures on an infinitely long scale, taking into account both computational efficiency and the reproducibility of the computational model.

[0004] In a first aspect, the present invention provides a method for calculating the acoustic radiation of an infinitely long periodic structure, comprising the following steps:

[0005] S1. Establish a periodic acoustic unit model of finite length;

[0006] S2. Extract and store the acoustic stiffness matrix and acoustic excitation vector of the periodic acoustic unit model;

[0007] S3. Based on Floquet's theorem in periodic structure theory, use the acoustic stiffness matrix and acoustic excitation vector obtained in step S2 to calculate the acoustic radiation of an infinitely long periodic structure.

[0008] Based on the above scheme, in step S1, the periodic acoustic unit model is constructed based on finite element software and includes a structure, an air domain surrounding the structure, and a perfectly matched layer surrounding the air domain.

[0009] Based on the above scheme, the periodic acoustic unit model is a single cell of the infinitely long periodic structure, and its length is determined according to the physical period of the structure.

[0010] Based on the above scheme, for an infinitely long uniform structure, the length of the unit cell can take any value.

[0011] Based on the above scheme, step S1, specifically including the meshing of the periodic acoustic unit model, includes:

[0012] S11. Mesh the solid mechanics and pressure acoustics modules to ensure that at least 6 mesh units are divided within each elastic wave wavelength;

[0013] S12, Mesh nodes at the interface between the mutually matching structure and the air domain;

[0014] S13. Make the mesh division at the left and right boundaries of the periodic element completely consistent.

[0015] Based on the above scheme, step S2 specifically includes:

[0016] S21. Extract the node and degree of freedom information of the periodic acoustic unit model;

[0017] S22. Reorder all nodes and degrees of freedom in the model in the order of left boundary, interior, and right boundary, and establish a mapping relationship between the old and new degrees of freedom.

[0018] S23. At each calculation frequency, run the model and extract the corresponding acoustic stiffness matrix and acoustic excitation vector;

[0019] S24. Based on the mapping relationship, rearrange and store the extracted acoustic stiffness matrix and acoustic excitation vector.

[0020] Based on the above scheme, step S3 includes free wave propagation analysis, specifically including:

[0021] S31. The reduced acoustic stiffness matrix is ​​obtained by eliminating internal degrees of freedom;

[0022] S32. Establish periodic boundary conditions based on Floquet's theorem;

[0023] S33. Construct and solve the characteristic equation to obtain the sound wave propagation constant and the corresponding sound wave mode in the infinitely long acoustic domain.

[0024] Based on the above scheme, step S3 further includes sound wave propagation analysis under the influence of acoustic excitation, specifically including:

[0025] S34. Consider the air domain surrounding the infinitely long structure excited by an external point as two semi-infinite subsystems, on the left and right.

[0026] S35. Based on the acoustic modes obtained from free wave analysis, establish the acoustic pressure continuity equation and acoustic excitation balance equation at the connection interface.

[0027] S36. Solve for the generalized wave coordinates and calculate the sound pressure response at any point in the system using the principle of wave superposition.

[0028] In a second aspect, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory, wherein when the processor executes the computer program, it implements the steps of the method by running the program instructions.

[0029] Thirdly, a computer-readable storage medium is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, the steps of the method are implemented by running the program instructions.

[0030] The beneficial effects of this invention are:

[0031] This invention employs an acoustic finite element method modified by periodic structure theory, which effectively avoids the computational burden of large-scale three-dimensional models in the traditional acoustic finite element method. At the same time, it considers the sound radiation variation caused by vibration attenuation in the third-dimensional direction, which is neglected in the two-dimensional boundary element method. This breaks the limitations of the traditional acoustic finite element method in finite structures and finite acoustic domains, and balances computational efficiency and the reproducibility of the computational model. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0033] To make the objectives, advantages and features of the present invention more apparent, the present invention will be further described in detail below with reference to specific embodiments.

[0034] like Figure 1 As shown, a method for calculating the acoustic radiation of an infinitely long periodic structure mainly includes the following steps:

[0035] Step 1: Establish a finite-length periodic acoustic element model based on commercial finite element software.

[0036] In an infinitely long periodic structure, a periodic element (also called a unit cell) is the smallest repeating unit that can be infinitely replicated in space through translation operations to generate the entire structure. For infinitely long homogeneous structures, such as infinitely long beams with uniform cross-sections, they can still be considered as infinitely long periodic structures with periodic elements of arbitrary length. Since sound radiation caused by structural vibration is an external acoustic problem, when establishing a periodic acoustic element model using the acoustic finite element method, it is necessary to artificially truncate the infinite air domain surrounding the structure. To simulate the non-reflection phenomenon of sound waves in a finite computational domain, a perfectly matched layer (PML) needs to be introduced. Therefore, the periodic acoustic element model of the structure should include the structural entity, the cylindrical air domain surrounding the structure, and the PML surrounding the air domain.

[0037] This specific embodiment is based on the construction of a finite element model using COMSOL software. When meshing with COMSOL, the following three principles should be followed:

[0038] (1) Each elastic wave wavelength in the solid mechanics and pressure acoustics module should contain at least 6 nodes.

[0039] (2) At the interface between the structure and the air domain, the unit nodes of the solid mechanics module should match the unit nodes of the pressure acoustics module.

[0040] (3) The mesh division at the left and right boundaries of the periodic cell is completely consistent.

[0041] Based on the above principles, in another embodiment, the specific analysis steps based on other commercial finite element software are as follows:

[0042] S11. Mesh the solid mechanics and pressure acoustics modules to ensure that at least 6 mesh units are divided within each elastic wave wavelength;

[0043] S12, Mesh nodes at the interface between the mutually matching structure and the air domain;

[0044] S13. Make the mesh division at the left and right boundaries of the periodic element completely consistent.

[0045] Step 2: Extract and store the acoustic stiffness matrix and acoustic excitation vector of the periodic acoustic unit model.

[0046] Using COMSOL with MATLAB, this method utilizes MATLAB as a scripting interface to build and solve models, enabling the modification, running, and matrix extraction of periodic acoustic unit models. Specifically, the MATLAB program should implement the following functions:

[0047] (1) Open the periodic acoustic unit model and extract the node and degree of freedom information of the model.

[0048] (2) Reorder all nodes and degrees of freedom in the model according to the order of the left boundary of the periodic unit, the middle of the periodic unit and the right boundary of the periodic unit, and establish the mapping relationship between the old and new degrees of freedom.

[0049] (3) Run the periodic acoustic unit model at each calculation frequency and extract the acoustic stiffness matrix and acoustic excitation vector at each calculation frequency.

[0050] (4) The acoustic stiffness matrix and acoustic excitation vector are rearranged according to the mapping relationship between the old and new degrees of freedom.

[0051] In another embodiment, the specific analysis steps based on other commercial finite element software are as follows:

[0052] S21. Extract the node and degree of freedom information of the periodic acoustic unit model;

[0053] S22. Reorder all nodes and degrees of freedom in the model in the order of left boundary, interior, and right boundary, and establish a mapping relationship between the old and new degrees of freedom.

[0054] S23. At each calculation frequency, run the model and extract the corresponding acoustic stiffness matrix and acoustic excitation vector;

[0055] S24. Based on the mapping relationship, rearrange and store the extracted acoustic stiffness matrix and acoustic excitation vector.

[0056] Step 3: Calculate the acoustic radiation of an infinitely long periodic structure using periodic structure theory.

[0057] Based on the acoustic stiffness matrix and acoustic excitation vector of periodic elements, and utilizing Floquet's theorem in periodic structure theory, the acoustic radiation of infinitely long periodic structures is considered. The acoustic response calculation is extended from finite-length periodic elements to infinitely long structures. This post-processing is implemented using MATLAB programming and mainly includes two parts: free wave state and forced wave state. The algorithm principle is as follows:

[0058] In the field of acoustics, the finite element method is used to solve the Helmholtz equations. The finite element equations for the sound field in the air domain are then:

[0059] ;

[0060] in, and These are the acoustic stiffness matrix and the acoustic mass matrix, respectively. It is the acoustic excitation vector caused by the normal vibration velocity of the structural surface or the sound source. The desired sound pressure level.

[0061] Based on Floquet's theorem in periodic structure theory, the wave finite element method can be used to calculate the vibration of periodic structures. Since the acoustic finite element equations and the dynamic stiffness equations in structural finite elements are mathematically consistent—both are linear system equations—and both vibration and acoustic radiation responses can be described in the form of elastic waves, the finite element derivation approach for periodic structure vibration can be applied to the acoustic finite element method to calculate the acoustic radiation of periodic structures. The derivation process is as follows:

[0062] All nodes of the periodic acoustic unit can be divided into three parts based on their position: left boundary nodes, internal nodes, and right boundary nodes, each represented by a subscript. and This indicates that the nodes at both the left and right boundary points have a degree of freedom of 1. The acoustic finite element equations, expanded in matrix form, are:

[0063] ;

[0064] (1) Free wave propagation analysis

[0065] Under free wave propagation conditions, the acoustic unit is only subject to the acoustic boundary conditions at its left and right ends, i.e. The acoustic finite element equations and acoustic stiffness matrices after eliminating the internal degrees of freedom of the acoustic unit are as follows:

[0066] ;

[0067] ;

[0068] Floquet's theorem describes the propagation characteristics of waves in periodic systems. Applying it to the periodic acoustic domain, let the propagation constant of an elastic wave in an infinitely long structure be... The sound pressure and acoustic excitation at the left and right ends of the periodic unit have the following relationship:

[0069] ;

[0070] ;

[0071] Substituting equations (5) and (6) into equation (3), we can obtain the following about The linear characteristic equation:

[0072] ;

[0073] Simultaneously, the relationship between the sound pressure and acoustic excitation at the left and right boundary points of the reference unit can be obtained:

[0074] ;

[0075] ;

[0076] Solving this characteristic equation will determine the propagation constants of each sound wave under the free wave propagation state in the infinite acoustic domain. Harmony and acoustic modes In a free-wave state, the sound pressure of each degree of freedom is the superposition of all elastic wave responses. Therefore, the sound pressure and acoustic excitation at the left boundary of the periodic element are respectively:

[0077] ;

[0078] ;

[0079] Among them, the number of free waves propagating and The sound pressure of each elastic wave Harmonic Excitation The normalized form, Let be the generalized wave coordinates of each elastic wave at the left-hand interface of the periodic unit.

[0080] (2) Analysis of sound wave propagation under acoustic excitation

[0081] When the external point excitation of the structure is located at the connection of the periodic unit, the vibration and acoustic radiation coupling system can be regarded as two parts: a left semi-infinite subsystem and a right semi-infinite subsystem. The left and right semi-infinite subsystems are only subjected to external excitation at the right or left end. In the acoustic radiation part, the sound pressure is controlled only by the characteristic wave propagating in a single direction to the left or right, and can be treated according to the equations under the free wave propagation state. Taking the right semi-infinite subsystem as an example, let the contact interface between the left end of the right semi-infinite structure and the left subsystem be the 0th connection, and let the first periodic unit on the right be numbered 1. Combining equations (10) and (11), the sound pressure and acoustic excitation vector of the right subsystem at the 0th connection are respectively:

[0082] ;

[0083] ;

[0084] Among them, prefix This indicates that the response is controlled by the forward-propagating elastic wave in the right-hand subsystem. Similarly, the sound pressure and acoustic excitation vector at the 0th connection of the left-hand semi-infinite periodic subsystem are respectively:

[0085] ;

[0086] ;

[0087] Among them, prefix This indicates that the response is controlled by the negatively propagating elastic wave in the left subsystem. Since the sound pressure at the 0th connection point is equal for both the left and right subsystems, that is:

[0088] ;

[0089] Simultaneously, the sum of the acoustic excitations of the left and right semi-infinite subsystems at the 0th connection point equals the total acoustic excitation vector experienced by the system at that point. ,Right now:

[0090] ;

[0091] Combining equations (16) and (17) into a formula concerning... The system of equations, namely:

[0092] ;

[0093] Solving this system of equations yields the generalized wave coordinates at the ends of the semi-infinite structures on both sides:

[0094] ;

[0095] Therefore, the sound pressure at any point in the entire system can be determined, such as the sound pressure at the cross section of the external point excitation (the 0th connection) and the sound pressure on the right side. The sound pressures at the connection points of the periodic units are as follows:

[0096] ;

[0097] ;

[0098] In another embodiment, step three specifically involves:

[0099] S31. The reduced acoustic stiffness matrix is ​​obtained by eliminating internal degrees of freedom;

[0100] S32. Establish periodic boundary conditions based on Floquet's theorem;

[0101] S33. Construct and solve the characteristic equation to obtain the sound wave propagation constant and the corresponding sound wave mode in the infinitely long acoustic domain;

[0102] S34. Consider the air domain surrounding the infinitely long structure excited by an external point as two semi-infinite subsystems, on the left and right.

[0103] S35. Based on the acoustic modes obtained from free wave analysis, establish the acoustic pressure continuity equation and acoustic excitation balance equation at the connection interface.

[0104] S36. Solve for the generalized wave coordinates and calculate the sound pressure response at any point in the system using the principle of wave superposition.

[0105] The specific calculation method is shown in equations (1)-(21).

[0106] It should be noted that any process or method description in the embodiments can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a particular logical function or process, and the scope of the preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order according to the functions involved, as should be understood by those skilled in the art to which the embodiments of the invention pertain.

[0107] It should be noted that the logic and / or steps in the embodiments, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0108] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0109] Those skilled in the art will understand that all or part of the steps of the methods described in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0110] Furthermore, in the embodiments of the present invention, the functional modules can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0111] The storage media mentioned above can be read-only memory, disk, or optical disk, etc.

[0112] The above embodiments have provided a detailed description of the technical solution of the present invention. Obviously, the present invention is not limited to the described embodiments. Based on the embodiments of the present invention, those skilled in the art can make various modifications, but any modifications that are equivalent to or similar to the present invention fall within the scope of protection of the present invention.

[0113] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A method for calculating acoustic radiation from an infinitely long periodic structure, characterized in that, Includes the following steps: S1. Establish a periodic acoustic unit model of finite length. The periodic acoustic unit model is constructed based on finite element software and includes a structure, an air domain surrounding the structure, and a perfectly matched layer surrounding the air domain. The meshing of the periodic acoustic unit model specifically includes: S11. Mesh the solid mechanics and pressure acoustics modules to ensure that at least 6 mesh units are divided within each elastic wave wavelength; S12, Mesh nodes at the interface between the mutually matching structure and the air domain; S13. Make the mesh division at the left and right boundaries of the periodic element completely consistent; S2. Extract and store the acoustic stiffness matrix and acoustic excitation vector of the periodic acoustic unit model, specifically including: S21. Extract the node and degree of freedom information of the periodic acoustic unit model; S22. Reorder all nodes and degrees of freedom in the model in the order of left boundary, interior, and right boundary, and establish a mapping relationship between the old and new degrees of freedom. S23. At each calculation frequency, run the model and extract the corresponding acoustic stiffness matrix and acoustic excitation vector; S24. Based on the mapping relationship, rearrange and store the extracted acoustic stiffness matrix and acoustic excitation vector; S3. Based on Floquet's theorem in periodic structure theory, using the acoustic stiffness matrix and acoustic excitation vector obtained in step S2, calculate the acoustic radiation of an infinitely long periodic structure, specifically including: S31. The reduced acoustic stiffness matrix is ​​obtained by eliminating internal degrees of freedom; S32. Establish periodic boundary conditions based on Floquet's theorem; S33. Construct and solve the characteristic equation to obtain the sound wave propagation constant and the corresponding sound wave mode in the infinitely long acoustic domain; S34. Consider the air domain surrounding the infinitely long structure excited by an external point as two semi-infinite subsystems, on the left and right. S35. Based on the acoustic modes obtained from free wave analysis, establish the acoustic pressure continuity equation and acoustic excitation balance equation at the connection interface. S36. Solve for the generalized wave coordinates and calculate the sound pressure response at any point in the system using the principle of wave superposition.

2. The method according to claim 1, characterized in that, The periodic acoustic unit model is a single cell of the infinitely long periodic structure, and its length is determined according to the physical period of the structure.

3. The method according to claim 2, characterized in that, For an infinitely long uniform structure, the length of the unit cell can take any value.

4. An electronic device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 3 by running the instructions of the computer program.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, the steps of the method as described in any one of claims 1 to 3 are implemented by running the instructions of the computer program.

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