Acoustic vibration simulation prediction method, storage medium and device based on spatial spectrum unit

Abstract

The present invention relates to an acoustic vibration simulation prediction method, storage medium, and device based on spatial spectrum units. The method comprises: dividing the object to be predicted into units, dividing large structures into spatial spectrum units, and dividing the remaining fine structures into finite elements, and modeling the object to be predicted based on the unit division results; setting boundary conditions, excitations, response points, and couplings between units according to the actual conditions of the object to be predicted, and adding them to the constructed model; calculating the system matrix in the vibration equation of the current model system; solving the system vibration equation according to actual needs to obtain a solution result, wherein the solution result includes natural frequency and system response, etc.; and visualizing the constructed model based on the solution result. Compared with the existing technology, the present invention has the advantages of arbitrary unit shape, high computational efficiency, and the ability to directly consider the influence of sound radiation on structural vibration in the system equation without the need for post-processing or iteration.

Description

Technical Field

[0001] The present invention belongs to the technical field of acoustic vibration analysis, and in particular relates to an acoustic vibration simulation prediction method based on a spatial spectrum unit, a storage medium, and a device. Background Art

[0002] Numerical simulation and prediction of acoustics and vibration are widely used in various industrial fields critical to national economy and people's livelihoods, such as construction, bridges, ships, trains, aerospace, and medical devices. Currently, the most widely used numerical simulation method in this field is the finite element method (FEM). For certain high-frequency cases, the statistical energy method (SEM) is used, while for radiation and propagation in large spaces, the boundary element method (BEM) is used. Each of these methods has its own advantages and disadvantages.

[0003] The finite element method (FEM) is a simple theory with a mature model, making it the most widely used. However, FEM requires a certain number of nodes within each wavelength to ensure the accuracy of the results. This means that when calculating the high-frequency conditions of large models using the FEM matrix, the model size is so large that extremely powerful computing resources are required. Even in low-frequency situations, if the model is large, such as an entire ship in the shipbuilding industry, FEM is somewhat unable to cope. As an alternative, the statistical energy method can, to some extent, compensate for the shortcomings of the FEM method in high-frequency calculations. However, the statistical energy method is mainly based on the theory of acoustic vibration propagation, which greatly simplifies the theory. The results are difficult to verify experimentally and are more of a statistical indicator.

[0004] Furthermore, finite elements are not adept at handling sound radiation and propagation within large spaces, as they require the entire space to be meshed. For these conditions, the boundary element method (BEM) can achieve similar accuracy to the finite element method using a smaller number of elements, thus replacing the finite element method to a certain extent. However, due to the theoretical basis of the boundary element method itself, its system matrix is ​​often not a symmetric square matrix, and the Green's function may not converge or take an extremely long time to compute in some cases. Furthermore, the boundary element method cannot effectively handle some conditions, such as corners and inflection points. However, the boundary element method has an irreplaceable advantage: it only needs to consider the boundaries, regardless of the size of the space. This is something that the finite element method cannot achieve. Therefore, the boundary element method is a more suitable alternative method to compensate for the shortcomings of the finite element method in predicting sound radiation and propagation within large spaces.

[0005] Furthermore, the values ​​within finite element and boundary element cells are interpolated from nodal values, which means that the values ​​at any point are affected to some extent by the interpolation function, introducing errors. The spectral element method is also a method for solving acoustic partial differential equations. It does not require the very fine cell division required by the finite element method to ensure the number of cells within each wavelength, thus significantly reducing the number of cells. The unknown quantities in the spectral element method are the coefficients of the spectrum. Therefore, once these coefficients are determined, the value at any point within the cell is fixed, not an error. These are the powerful advantages of the spectral element. However, the disadvantage of the spectral element is that the theory is relatively complex, and developing analytical solutions for each cell type and its associated couplings is time-consuming and laborious. If numerical solutions are used instead of analytical solutions, the computational complexity increases exponentially. Precisely because of the complexity of the theoretical derivation, spectral elements were previously shaped like regular rectangles, right triangles, and so on. Although some have modified the elements using shape function methods similar to those used in finite elements, this approach loses the advantage of the spectral element, which is not limited by the number of cells within a wavelength. If the spectral element is divided into the same size as the finite element cell, it is not as efficient as the finite element due to the complexity of its system matrix. Therefore, spectral elements are inferior to finite elements in processing fine structural details. Furthermore, models for the added mass and radiation efficiency caused by the associated acoustic and vibration radiation of spectral elements have not been systematically developed before, which has limited the application of spectral elements in the field of acoustic and vibration prediction. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide an acoustic vibration simulation prediction method, storage medium and device based on spatial spectrum units that can break through the shape limitations of spectrum units, has high computational efficiency, and can directly consider the influence of sound radiation on structural vibration in the system equation without the need for post-processing or iteration.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A method for simulating and predicting acoustic vibration based on a spatial spectrum unit comprises the following steps:

[0009] Performing unit division on the object to be predicted, dividing large structures into spatial spectrum units and other fine structures into finite elements, wherein the large structures include beams, plates, shells or pipes, and modeling the object to be predicted based on the unit division results;

[0010] According to the actual situation of the object to be predicted, boundary conditions, excitation, response points and coupling between units are set and added to the constructed model;

[0011] Calculate the coefficient matrix of each spectral unit in the current model, and assemble the coefficient matrix to obtain the system matrix in the system vibration equation;

[0012] Solving the system vibration equation according to actual needs to obtain a solution result, wherein the solution result includes a natural frequency and a system response;

[0013] The constructed model is visualized based on the solution results.

[0014] Furthermore, when setting the coupling between the units, the elastic member is used as a coupling member, and the coupling includes point coupling, surface coupling or line coupling.

[0015] Furthermore, the coefficient matrix of the spectrum unit is calculated as follows:

[0016] Based on the use of Fourier series to obtain vibration solutions;

[0017] Obtaining kinetic energy, potential energy, and external work based on the vibration solution;

[0018] The coefficient matrix is ​​derived by using the Rayleigh-Ritz method and Hamilton equation, considering the steady state of the system.

[0019] Furthermore, if the material and properties of the element vary with position, a numerical integration method is used to calculate the coefficient matrix.

[0020] Furthermore, if there is coupling between units, the effect of the coupling stiffness is added to the potential energy term.

[0021] Furthermore, the method further comprises:

[0022] Construct a radiation model that divides each unit into multiple regions. Each region is considered a sound source. Based on the vibration amplitude of the unit in that region, the contribution of that sound source to the sound pressure at a certain point in the model is derived. The contributions of all sound sources are superimposed to obtain the total sound pressure at that point.

[0023] The total sound pressure at each point on the element is taken into account when calculating the coefficient matrix of each element.

[0024] Furthermore, when high accuracy is required and computing resources are sufficient, boundary elements can be used as a substitute or supplement to the above radiation model.

[0025] Furthermore, the sound source is a point sound source or a dipole sound source.

[0026] Furthermore, when calculating the coefficient matrix of each unit, the total sound pressure at each point on the unit is considered to be:

[0027] The total sound pressure is regarded as an external force added to the system, the external work generated by the external force is obtained, and a coefficient matrix is ​​calculated based on the superposition of the external work.

[0028] The present invention also provides a computer-readable storage medium comprising one or more programs for execution by one or more processors of an electronic device, wherein the one or more programs include instructions for executing the acoustic vibration simulation prediction method based on spectral units as described above.

[0029] The present invention also provides an electronic device, comprising one or more processors, a memory, and one or more programs stored in the memory, wherein the one or more programs include instructions for executing the acoustic vibration simulation prediction method based on spectral units as described above.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] 1. The present invention provides analytical solutions for a variety of spectral units and related coupling units, including beams, plates of arbitrary shapes (including reinforced plates, which may have cavities), shells of arbitrary shapes (including reinforced shells, which may have cavities), and pipes of arbitrary cross-section shapes (including fluid-filled pipes). The previous process of structural discretization and recoupling is integrated into the integral process of obtaining the system matrix, thereby breaking through the previous restrictions of spectral units on unit shapes, reducing the errors and calculation amount caused by unnecessary unit coupling, and greatly improving the applicability and computational efficiency of spectral units. By replacing finite elements with spectral elements, the matrix degrees of freedom can be reduced exponentially under the condition of the same prediction accuracy, thereby improving computational efficiency and greatly increasing the upper frequency limit of the model. At the same time, a numerical method corresponding to the analytical method is provided to deal with the problem of material and unit properties changing with position.

[0032] 2. The present invention provides an acoustic vibration radiation model applicable to spectral elements and a solution to the problems of added mass and radiation efficiency caused by radiation impedance. The influence of acoustic radiation on structural vibration can be directly considered in the system equations without the need for post-processing or iteration. This makes it possible to use spectral elements to solve problems such as attached water, which is extremely important in the shipbuilding industry, and track radiation efficiency, which is required in the train industry, thereby expanding the application of the spectral element method in related important fields.

[0033] 3. The present invention couples spectral elements with finite elements and boundary elements, using finite elements to process small structural details and boundary elements as a supplement to the radiation model to process sound radiation and propagation in large spaces, so that each method can complement each other and simulate and predict acoustic vibrations and related radiation problems in the full frequency domain. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a schematic diagram of the process of the present invention;

[0035] Figure 2 2. The plan view and cross-sectional view of the steel spring floating plate track in the embodiment;

[0036] Figure 3is the vertical displacement amplitude curve of the response point in the embodiment. DETAILED DESCRIPTION

[0037] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0038] like Figure 1 As shown, the present invention provides an acoustic vibration simulation prediction method based on a spatial spectrum unit, comprising the following steps:

[0039] 1) Performing unit division on the object to be predicted: dividing large structures into spectral elements and other small structures into finite elements. The large structures include beams, plates of arbitrary shapes (including reinforced plates, which may have cavities), shells of arbitrary shapes (including reinforced shells, which may have cavities), and pipes of arbitrary cross-section shapes (including fluid-filled pipes). Modeling the object to be predicted based on the unit division results;

[0040] 2) Determine whether a radiation model is needed. If so, select a radiation model based on the problem's requirements for sound radiation and sound field prediction, combined with accuracy and speed considerations, and then proceed to the next step. If not, proceed directly to the next step.

[0041] 3) Set boundary conditions, excitations, response points, and couplings between units according to the actual conditions of the object to be predicted, and add them to the constructed model;

[0042] 4) Calculate the coefficient matrix of each unit in the current model, and assemble the coefficient matrices of each unit to obtain the system matrix in the system vibration equation;

[0043] 5) Solve the system vibration equation according to the problem requirements to obtain the natural frequency, system response and other radiation parameters;

[0044] 6) Visualizing the constructed model based on the solution results.

[0045] The specific innovations of the above method are as follows:

[0046] 1) Analytical solutions are given for a variety of spectral elements, including beams, plates of arbitrary shapes (including stiffened plates and cavities), shells of arbitrary shapes (including stiffened shells and cavities), and pipes of arbitrary cross-section shapes (including fluid-filled pipes), as well as related coupled elements. Numerical methods corresponding to the analytical methods are also presented to deal with the problem of position-dependent variations in material and element properties.

[0047] The analytical solution is derived from theory and is a formula that can directly calculate the required equation results based on the given parameters. In this method, the derivation of the analytical solution of each unit is as follows: the Fourier series form of the unit vibration solution is given, and the expressions of the unit kinetic energy, potential energy, and external work are derived from the form of the solution; these are then substituted into the Hamilton equation, and the matrix form of the unit vibration equation is obtained using the Rayleigh-Ritz method. This process involves many integrals to obtain the matrix in the vibration equation, and the analytical solution must be obtained for each integral to obtain the analytical solution form of the final system matrix. The previous process of structural discretization and recoupling is also integrated into the integral process of obtaining the system matrix, thus breaking through the previous spectral unit's restrictions on unit shape, reducing the error and computational complexity caused by unnecessary unit coupling, and greatly improving the applicability and computational efficiency of the spectral unit.

[0048] Here, we take the one-dimensional beam element considering only the vertical deflection as an example to give the method of deriving the analytical solution. Other types of spectral elements and other degrees of freedom directions can be obtained by following the same idea, so we will not go into details one by one.

[0049] Using the concept of Fourier series, the solution to the vibration of a one-dimensional beam in the deflection direction is given as:

[0050]

[0051] Where w is the deflection, m is the order of the Fourier series in the x-direction, M is the maximum order of the Fourier series expansion, a is the coefficient of the Fourier series, p is the smoothing auxiliary function, and L is the length of the beam. The choice of p can be arbitrary, but it must ensure that the solution is high-order continuous on the boundary.

[0052] Using solution (1), we can get the kinetic energy, potential energy, and external work of the unit

[0053]

[0054]

[0055]

[0056] Where V is potential energy, T is kinetic energy, W is external work, D is bending stiffness, t is time variable, ρ is density, S is beam cross-sectional area, and f is external force in the considered deflection direction.

[0057] Using the Rayleigh-Ritz method and Hamilton equation, we know that in a stable state, the system must satisfy

[0058] δ(T–V+W)=0 (5)

[0059] Using (1)-(5), substituting (1)-(4) into (5), we can derive the matrix form of the system vibration equation of the unit as follows:

[0060] (K-ω 2 M)A=F (6)

[0061] Among them, K, M, and F are the stiffness matrix, mass matrix, and force matrix respectively, ω is the circular frequency, and A is a vector composed of the system's Fourier series expansion coefficients and smoothing function coefficients, which is also the unknown number to be solved in the problem.

[0062] For each beam element, the coefficient matrix of the element can be obtained. Similarly, the coefficient matrix of other types of elements can be obtained. These elements include but are not limited to Euler beams, Timoshenko beams, plates of arbitrary shapes (including reinforced plates, which may have cavities), shells of arbitrary shapes (including reinforced shells, which may have cavities), hollow pipes of arbitrary cross-section shapes, and fluid-filled pipes of arbitrary cross-section shapes. Here, if the material and unit properties of the element vary with position, such as variable-section beams and non-uniform density plates, the integrals in formulas (2) to (5) can use numerical integration methods to consider the specific parameter characteristics of each integration point. If numerical integration is used, the integral interval will be divided into multiple small intervals, and the parameter value in each small interval is considered to be a constant. The final integral result can be obtained by superimposing the contributions of all small intervals.

[0063] Elements can be coupled together using a spring-like component. The stiffness of the spring determines the strength of the coupling. Depending on the element type, the coupling can be point, line, or surface. The effect of the coupling stiffness must be added to the potential energy term in the equation to affect the overall stiffness matrix of the system.

[0064] After the coefficient matrices and coupling matrices of all elements are obtained, the matrix form of the vibration equation of the entire system can be assembled using the coefficient matrices of each element. The total system equation is the same as (6), except that the matrix has taken into account the influence of all elements.

[0065] If coupling of finite elements and boundary elements is not required, the equation can be solved directly. If finite elements and boundary elements are used, the system matrix must be solved after adding the relevant coupling terms.

[0066] 2) Provide an acoustic vibration radiation model based on spectral units

[0067] If the impact of acoustic radiation on system vibration needs to be considered, a radiation model is selected based on the problem's requirements for acoustic radiation and sound field prediction, combined with accuracy and speed considerations. Available models include boundary elements (BEM) or a fast acoustic radiation model based on spectral elements. Because BEM significantly reduces the model's computational efficiency, the spectral-based radiation model is the system's default model. BEM can be used as an alternative or supplement to this model when high accuracy is required and computational resources are available. Regardless of which model is used, the impact of acoustic radiation on structural vibration can be directly accounted for in the system equations, without the need for post-processing or iteration.

[0068] The present invention designs a fast acoustic vibration radiation model that can be applied to spectral units. The specific idea of ​​this model is to regard each unit as a sound source, and deduce the contribution of the sound source to the sound pressure at a certain point in the model based on the magnitude of the vibration amplitude of the unit. Depending on the specific situation, the sound source can be regarded as a point sound source on an infinite baffle, such as for a plate or shell type spectral unit (7), or a dipole point sound source, such as for a beam or tube type spectral unit (8).

[0069]

[0070]

[0071] Where p is the sound pressure at a point, ρ0 is the medium density, w is the displacement at the sound source, r is the distance from the point to the sound source, ω is the circular frequency, k is the wavelength, ds is the unit area of ​​the sound source, l is the distance between the dipole sound sources, and θ is the angle between the dipole sound sources and the sound pressure point. By adding together the contributions of all the sound sources, we can get the total sound pressure at that point.

[0072] For finite element elements, this process is very simple because the node displacements are the unknown variables in the finite element equations. However, for spectral elements, since the unknown variables are the coefficients of the displacement spectrum in the spatial domain, this method cannot be directly applied and must be derived separately based on the definition of each type of element. In addition, because spectral elements are often geometrically large, to ensure accuracy, the element needs to be divided into multiple radiation regions. If we use the beam element mentioned above as an example, the specific steps are as follows:

[0073] 1. Divide the unit into multiple small segments. Each segment is regarded as a sound source point. The location of the sound source point is at the center of the end. The sound energy of the sound source point is the sum of the radiation energy of the segment.

[0074] 2. For each such sound source, the sound pressure contribution of the sound source at any point in space can be obtained using formula (8).

[0075] 3. For a certain point on the structure, by adding together the sound pressure contributions of all such sound sources in the system to that point, we can obtain the pressure generated by the vibration of the system on that point when the entire system is in a vibrating state.

[0076] 4. Considering the pressure as an additional external force on the system, the external work generated by this external force can also be expressed by Equation (4). Substituting this external work together with other external work into Equation (5), the unit vibration equation can be derived after considering the effects of acoustic radiation (added mass and radiation damping).

[0077] 5. Note that the unknowns in equations (4), (7), and (8) are all w, which is expressed by equation (1). Therefore, the final unknowns are the Fourier series expansion coefficients and the smoothing function coefficients, which are the same as the unknowns in the vibration equation (6) for this unit. If there are multiple units in the system, the radiation effects between each unit and the radiation effects of each unit on itself need to be considered.

[0078] 3) Provide a model for coupling spectral elements with finite elements and boundary elements

[0079] If the finite element and boundary element need to be coupled with the spectral element, the system equations and the corresponding equations can be further expressed as.

[0080]

[0081] Where K, M, A, and F represent the system stiffness matrix, mass matrix, variable vector, and force matrix respectively. The subscripts S, F, and B represent spectral elements, finite elements, and boundary elements respectively. couple represents the coupling stiffness term generated by the coupling. The coupling between the spectral element and other elements is achieved using a spring-like component. The specific matrix form can be obtained by following the steps described above for solving the spectral element. The derivation of the finite element and boundary element system matrices is not detailed here.

[0082] After obtaining the system vibration equation, the natural frequency, system response and other radiation parameters can be obtained by solving the vibration equation. Specifically: the natural frequency of the system can be obtained by using the eigenvalue method; the system equation can be solved to obtain the system Fourier series expansion coefficient and smoothing function coefficient, and the Fourier series expansion coefficient and smoothing function coefficient corresponding to a certain unit are brought back to the Fourier series form of the vibration solution of the unit, such as formula (1), to obtain the response of any point of the unit; using the obtained vibration amplitude of the unit, the contribution of the unit to the sound pressure at any point in space can be predicted by formula (7) or (8). Parameters such as radiation impedance and efficiency are then obtained by using the total system sound pressure at a certain point and the vibration amplitude information of the structure through formulas.

[0083] Example

[0084] This embodiment applies the above method to the vibration problem of suspended plate train tracks. The specific simulation and prediction process includes:

[0085] 1) Divide the track into units. The rails are T60 rails, the fasteners are DTVI2 type, and the specific geometric parameters of the floating plate are as follows: Figure 2 The material parameters are shown in Table 1. Here, the entire floating slab can be divided into a rectangular slab spectrum unit, and the two rails can be divided into two Timoshenko beam spectrum units.

[0086] 2) Apply spring support boundary conditions to the floating slab at the corresponding points, leaving the rail boundary free. Set an excitation point 1.5 meters from the left rail and apply a 1 kN vertical excitation. Set a response point 2.7 meters from the left rail.

[0087] Table 1 Parameters of T60 rail and DTVI2 fasteners

[0088]

[0089] 3) Point coupling is used between beam elements and plate elements to simulate the fastener connection between the track and the floating plate.

[0090] 4) Assemble the system matrix and solve it. The natural frequencies of the first 10 orders of the structure are shown in Table 2, and the vertical displacement amplitude of the response point 0-1500 Hz is shown in Figure 3 .

[0091] Table 2 The first 10 natural frequencies of the floating slab

[0092] Order Frequency (Hz) 1 4.2283e-05 2 4.6056e-05 3 6.4848 4 7.1346 5 7.3455 6 38.0354 7 41.8748 8 91.1985 9 91.6230 10 103.0473

[0093] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. An acoustic vibration simulation prediction method based on spatial spectrum unit, characterized in that: The following steps are involved: Performing unit division on the object to be predicted, dividing large structures into spatial spectrum units and other fine structures into finite elements, wherein the large structures include beams, plates, shells or pipes, and modeling the object to be predicted based on the unit division results; According to the actual situation of the object to be predicted, boundary conditions, excitation, response points and coupling between units are set and added to the constructed model; Calculate the coefficient matrix of each spectral unit in the current model, and assemble the coefficient matrix to obtain the system matrix in the system vibration equation; Solving the system vibration equation according to actual needs to obtain a solution result, wherein the solution result includes a natural frequency and a system response; Visualizing the constructed model based on the solution results; The method further includes: Construct a radiation model that divides each unit into multiple regions. Each region is considered a sound source. Based on the vibration amplitude of the unit in that region, the contribution of that sound source to the sound pressure at a certain point in the model is derived. The contributions of all sound sources are superimposed to obtain the total sound pressure at that point. The total sound pressure at each point on the element is taken into account when calculating the coefficient matrix of each element.

2. The acoustic vibration simulation prediction method based on spatial spectrum unit according to claim 1, characterized in that: When setting the coupling between the units, the elastic member is used as a coupling member, and the coupling includes point coupling, surface coupling or line coupling.

3. The acoustic vibration simulation prediction method based on spatial spectrum unit according to claim 1, characterized in that: The calculation of the coefficient matrix of the spectral unit is specifically as follows: Based on the use of Fourier series to obtain vibration solutions; Obtaining kinetic energy, potential energy, and external work based on the vibration solution; The coefficient matrix is ​​derived by using the Rayleigh-Ritz method and Hamilton equation, considering the steady state of the system.

4. The acoustic vibration simulation prediction method based on spatial spectrum unit according to claim 3, characterized in that: If the material and properties of the element vary with position, use numerical integration methods to compute the coefficient matrix.

5. The acoustic vibration simulation prediction method based on spatial spectrum unit according to claim 3, characterized in that: If there is coupling between elements, the effect of the coupling stiffness is added to the potential energy term.

6. The acoustic vibration simulation prediction method based on spatial spectrum unit according to claim 1, characterized in that: The sound source is a point sound source or a dipole sound source.

7. The acoustic vibration simulation prediction method based on spatial spectrum unit according to claim 1, characterized in that: When calculating the coefficient matrix of each unit, the total sound pressure at each point on the unit is considered to be: The total sound pressure is regarded as an external force added to the system, the external work generated by the external force is obtained, and a coefficient matrix is ​​calculated based on the superposition of the external work.

8. A computer-readable storage medium, characterized in that The method comprises one or more programs for execution by one or more processors of an electronic device, wherein the one or more programs include instructions for executing the acoustic vibration simulation prediction method based on the spatial spectrum unit according to any one of claims 1 to 7.

9. An electronic device, characterized in that: The system comprises one or more processors, a memory and one or more programs stored in the memory, wherein the one or more programs include instructions for executing the acoustic vibration simulation prediction method based on the spatial spectrum unit according to any one of claims 1 to 7.

Images