Method and system for defining an effective analysis band of an engineering structure

Abstract

The application relates to a method and system for defining an effective analysis frequency band of an engineering structure, important parameters of statistical energy analysis of a target system are selected and ranges are defined, including a modal number, a modal overlap factor, a normalized attenuation factor and coupling strength; dimension analysis is carried out in combination with vibration characteristics and boundary conditions of the target system, dimensionless parameters corresponding to the important parameters are obtained, including a dimensionless wave number, a shape parameter, a damping loss factor and a Poisson ratio, according to a corresponding relationship between the dimensionless parameters and the important parameters, an effective diagram of statistical energy analysis of each subsystem is constructed to describe the distribution of the important parameters in the dimensionless parameter space; the effective diagram of statistical energy analysis is analyzed to obtain a dimensionless wave number value range of each subsystem, and then the effective frequency band of the target system is obtained in combination with a coupling relationship. The application has the advantages of rapidness, directness, accuracy and the like, and is helpful to improving the prediction accuracy of high-frequency dynamic response of an engineering structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of statistical energy analysis, in particular to a method and system for defining an effective analysis frequency band of an engineering structure. BACKGROUND

[0002] High-speed trains, launch vehicles and other engineering structures will face high-frequency vibration loads such as aerodynamic noise and explosive impact during service. Statistical energy analysis theory is a common method for predicting the dynamic response of structures under high-frequency loads. This method is based on the principles of statistical physics, divides the structure into several subsystems, uses vibration energy to characterize the high-frequency dynamic response and vibration load of the structure, and obtains the high-frequency dynamic response of the structure by solving the energy balance equations between the subsystems. Therefore, the reasonable division of the high-frequency band (effective frequency band) of the statistical energy analysis subsystem is the basis and key to carrying out statistical energy analysis.

[0003] At present, researchers mostly divide the high-frequency range of the structure subsystem according to engineering experience and modal number. The commonly used frequency division method is based on the range of modal number, and according to the modal number-frequency relationship curve, it is considered that the frequency range with modal number greater than 5 is the high-frequency range. This is an empirical determination, and there is no mature theoretical basis to prove that the results of statistical energy analysis under such high-frequency band division are accurate enough. For engineering structures, when the high-frequency region of statistical energy analysis is divided only by modal number, there is a problem that the theoretical basis is not solid, and it cannot accurately determine whether the application region of statistical energy analysis is indeed the effective frequency band of statistical energy analysis. This will lead to a decrease in the prediction accuracy of the high-frequency dynamic response of complex structures in subsequent statistical energy analysis, so it is urgent to develop a method for dividing the effective frequency band of statistical energy analysis. SUMMARY

[0004] In view of the deficiencies of the prior art, the present application provides a method and system for defining an effective analysis frequency band of an engineering structure, which solves the problem that the direct division of the high-frequency effective frequency band of the structure according to the modal number in the current statistical energy analysis method leads to rough and inaccurate division results.

[0005] The technical solutions adopted by the present application are as follows:

[0006] The present application provides a method for defining an effective analysis frequency band of an engineering structure, comprising:

[0007] Selecting important parameters for statistical energy analysis of the target system, including modal number N i , modal overlap factor M i , normalized attenuation factor and coupling strength γ ij, define threshold values of the important parameters, wherein subscript i represents the number of a subsystem constituting the target system, coupling strength γ ij for characterizing the flow strength of vibration energy between any two subsystems i and j with coupling in the target system;

[0008] According to the important parameters, the vibration characteristics and boundary conditions of the target system are combined to perform dimension analysis, and a dimensionless parameter corresponding to the important parameters is obtained, including dimensionless wave number κ i , shape parameter ε i , damping loss factor η i and Poisson's ratio v i According to the corresponding relationship between the dimensionless parameters and the important parameters, a statistical energy analysis effective diagram of each subsystem is constructed to describe the distribution of the important parameters in the dimensionless parameter space, which is a two-dimensional plane with dimensionless wave number κ i as one coordinate axis and any one of shape parameter ε i and damping loss factor η i as the other coordinate axis.

[0009] The statistical energy analysis effective diagram is analyzed to obtain the value range of the dimensionless wave number of each subsystem, the effective frequency band of each subsystem is obtained according to the relationship between the dimensionless wave number and the frequency, and the effective frequency band of the target system is obtained according to the coupling relationship of each subsystem.

[0010] Further technical solutions are as follows:

[0011] The threshold values of the important parameters are defined according to the statistical energy analysis assumption conditions, including:

[0012] The modal number N is large enough and N>>1;

[0013] The modal overlap factor M>>1;

[0014] The normalized attenuation factor

[0015] The coupling strength γ<<1.

[0016] The effective frequency band of the target system is obtained according to the coupling relationship of each subsystem, including:

[0017] According to the coupling relationship, the coupling strength is limited for the effective frequency band of each subsystem to obtain a modified effective frequency band, and the intersection of the modified effective frequency bands of each subsystem is taken as the effective frequency band of the target system.

[0018] The corresponding relationship between the important parameters and the dimensionless parameters includes:

[0019]

[0020]

[0021]

[0022]

[0023] ν i =ν i

[0024] In the formula, subscript i represents the number of the subsystem constituting the target system, τ ij represents the transmission efficiency, L ij is the coupling length between the subsystem i and the subsystem j, P i is the perimeter of the subsystem i.

[0025] The relationship between the dimensionless wave number and the frequency is obtained by the following formula:

[0026] Dk 4 -ρhω 2 =0

[0027] wherein, k, E, h, ρ, ν, ω are the wave number, the elastic modulus, the thickness, the density, the density, the Poisson's ratio and the circular frequency, respectively, the wave number k = 2πκ / l, κ is the dimensionless wave number, and l is a structure-related size parameter.

[0028] When analyzing the statistical energy analysis effective diagram, the shape parameter ε i can be set as a fixed value.

[0029] When analyzing the statistical energy analysis effective diagram, the damping loss factor η i can be set as a fixed value.

[0030] Another aspect of the present application provides a system for defining an effective analysis frequency band of an engineering structure, comprising:

[0031] The selecting module selects important parameters for statistical energy analysis of the target system, including the number of modes N i , the modal overlap factor M i , the normalized attenuation factor and the coupling strength γ ij , and defines threshold values of the important parameters, wherein subscript i represents the number of the subsystem constituting the target system, and the coupling strength γ ij is used to represent the flow strength of the vibration energy between any two subsystems i and j having coupling in the target system;

[0032] The mapping module: according to the important parameters, combining the vibration characteristics and boundary conditions of the target system to carry out dimension analysis, obtain the dimensionless parameters corresponding to the important parameters, including dimensionless wave number κ i , shape parameter ε i , damping loss factor η i and Poisson's ratio ν i , according to the corresponding relationship between dimensionless parameters and important parameters, construct the statistical energy analysis effective map of each subsystem to describe the distribution of the important parameters in the dimensionless parameter space, the dimensionless parameter space is a two-dimensional plane with dimensionless wave number κ i as one of the coordinate axes, shape parameter ε i and damping loss factor η i as the other coordinate axis.

[0033] The analysis module: analyzing the statistical energy analysis effective map, obtaining the value range of the dimensionless wave number of each subsystem, according to the relationship between the dimensionless wave number and the frequency, obtaining the effective frequency band of each subsystem, and according to the coupling relationship of each subsystem, obtaining the effective frequency band of the target system.

[0034] The beneficial effects of the present application are as follows:

[0035] The present application starts from the basic assumption of statistical energy analysis, and obtains the statistical energy analysis effective map in the dimensionless parameter space according to the dimension analysis, and according to the effective map and the parameters of the structural subsystem, the effective frequency band range of the structural subsystem under the premise of ensuring the effectiveness of statistical energy analysis can be deduced, thereby making up for the shortcomings of the existing frequency band division method.

[0036] The frequency band division method of the present application is fast, intuitive and accurate, which helps to improve the prediction accuracy of high-frequency dynamic response of engineering structure.

[0037] Other features and advantages of the present application will be set forth in the following description, and some of them will become apparent to those skilled in the art from the description, or will be learned by practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 The flowchart of the method of the present application.

[0039] Figure 2 The structure diagram of the coupling plate structure of the embodiment of the present application.

[0040] Figure 3 The η-κ plane statistical energy analysis effective map of the second subsystem of the embodiment of the present application.

[0041] Figure 4 The ε-κ plane statistical energy analysis effective map of the second subsystem of the embodiment of the present application.

[0042] Fig. 1, subsystem one; 2, subsystem two; 3, subsystem three. DETAILED DESCRIPTION

[0043] The specific embodiments of the present application are described below with reference to the accompanying drawings.

[0044] The present application provides a method for defining an effective analysis frequency band of an engineering structure, comprising:

[0045] Referring to Figure 1 , important parameters of statistical energy analysis of a target system are selected, including modal number N i , modal overlap factor M i , normalized attenuation factor and coupling strength γ ij , threshold values of the important parameters are defined, wherein subscript i represents the number of a subsystem constituting the target system, and coupling strength γ ij is used to represent the flow strength of vibration energy between any two subsystems i and j having coupling in the target system;

[0046] According to the important parameters, dimensional analysis is performed in combination with vibration characteristics and boundary conditions of the target system to obtain dimensionless parameters corresponding to the important parameters, including dimensionless wave number κ i , shape parameter ε i , damping loss factor η i and Poisson's ratio v i , according to the corresponding relationship between the dimensionless parameters and the important parameters, an effective diagram of statistical energy analysis of each subsystem is constructed to describe the distribution of the important parameters in the dimensionless parameter space, the dimensionless parameter space is a two-dimensional plane with dimensionless wave number κ i as one coordinate axis and any one of shape parameter ε i and damping loss factor η i as the other coordinate axis;

[0047] The effective diagram of statistical energy analysis is analyzed to obtain the value range of the dimensionless wave number of each subsystem, according to the relationship between the dimensionless wave number and the frequency, the effective frequency band of each subsystem is obtained, and according to the coupling relationship of each subsystem, the effective frequency band of the target system is obtained.

[0048] The target system to which the method of the present application is directed is coupled by multiple subsystems, or the target system is divided into several subsystems, the range of important parameters in statistical energy analysis is obtained based on the basic assumptions of statistical energy analysis, and the effective area of statistical energy analysis is represented in the form of an image in the dimensionless parameter space to form an effective diagram of statistical energy analysis, and the range of high-frequency area can be determined according to the parameters of the structural subsystem and the effective diagram.

[0049] The method of the present application starts from the theoretical assumption of statistical energy application, and obtains the accurate range of statistical energy analysis results, instead of using the frequency division standard of modal number in the past, so that the high frequency range result of statistical energy analysis is more accurate.

[0050] Specifically, the threshold of the important parameter is defined according to the statistical energy analysis assumption condition, including:

[0051] The modal number N is large enough, and N >> 1;

[0052] The modal overlap factor M >> 1;

[0053] The normalized attenuation factor

[0054] The coupling strength γ << 1.

[0055] The principle of the statistical energy analysis assumption condition is specifically as follows:

[0056] (1) In statistical energy analysis, energy is stored in a large number of modes, but the modal number is much smaller than Avogadro's constant (6.02×10 23 ), so statistical energy analysis is a statistical method suitable for small groups, and the relative error (variance divided by the square of the average value) is of the order of log(N / N 2 ), in order to ensure that the error is small enough, the modal number needs to be large enough, and the present application defines N >> 1, that is, the modal number is much larger than 1;

[0057] (2) Statistical energy analysis is a study of non-coherent vibration energy, and the disorder is an inherent characteristic of the statistical method, and the disorder in vibration means that the modal amplitude regarded as a random variable is not related. When there is no modal dominant system dynamics, that is, when the frequency response function is smooth, the state is reached. The modal overlap factor is a parameter for describing the degree of overlap of continuous modes in the frequency response function, and the standard for statistical energy analysis to have disorder in statistics is M >> 1, that is, the modal overlap factor is much larger than 1;

[0058] (3) The vibration energy density of any point of the subsystem of statistical energy analysis is uniform and isotropic (diffuse reflection field assumption). In order to reach this balanced state, the normalized attenuation factor must be low enough to ensure that the ray passes through the subsystem multiple times before being attenuated, that is, that is, the normalized attenuation factor is much smaller than 1;

[0059] (4) Compared with the internal dissipation of energy, the flow of vibration energy exchanged between subsystems is small (weak coupling assumption). That is, the coupling loss factor is much smaller than the internal loss factor, and the coupling strength is defined as γ ij = η ij / ηi , η i , η ij respectively represent the damping loss factor of the subsystem i and the damping loss factor of the subsystem i considering the coupling with the subsystem j. Wherein, for the target system generally coupled by plate units, the coupling strength γ ij <<1.

[0060] The corresponding relationship between the important parameters and the dimensionless parameters comprises:

[0061]

[0062]

[0063]

[0064]

[0065] ν i = ν i

[0066] In the formula, the subscript i represents the number of the subsystems constituting the target system, τ ij represents the transmission efficiency, L ij is the coupling length between the subsystem i and the subsystem j, and P i is the perimeter of the subsystem i.

[0067] According to the above corresponding relationship, the statistical energy analysis effective diagram of each subsystem can be established, and based on the aforementioned assumption conditions and the limitation of other parameters, the range of the dimensionless wave number can be directly obtained, and finally the effective frequency range of the entire target system considering the coupling strength is obtained.

[0068] The following further illustrates the method for defining the effective analysis frequency range of the engineering structure according to the embodiments.

[0069] Referring to Figure 2 , the structure of the target system aimed at by the embodiments is a coupled plate structure, which comprises three subsystems, a subsystem one 1, a subsystem two 2 and a subsystem three 3, the three subsystems are all rectangular plate structures and sequentially connected to form a coupling relationship, the subsystem two 2 is connected with the subsystem one 1 and the subsystem three 3 on both sides, the size and the material of each plate are the same, and the length and the width of the edge are both 300 mm, and the thickness is all 2 mm.

[0070] The material parameters are as follows: the elastic modulus is 102 GPa, the density is 2000 kg / m 3 , and the Poisson's ratio is 0.2.

[0071] In the important parameters: the transmission efficiency τ ijUnder the assumption of weak coupling, the value can be 1. The perimeter P of subsystem i... i That is, 1200mm.

[0072] Dimensionless parameters: shape parameters b is the coupling side length, that is, the side length of the connection side between two plates that have a coupling relationship, a i Given the plate width, it can be seen that both b and a are 300 mm in this embodiment; dimensionless wavenumber κ i =k i l i / 2π, where l is a structure-related dimensional parameter, k is the wave number, and l=πa i b / 2(a i +b)=0.23562.

[0073] Because the coupling relationships in this embodiment are simple, and subsystem 2 is coupled with the other two subsystems, the effective statistical energy analysis diagram of subsystem 2 can first be constructed based on the correspondence between the dimensionless parameters and important parameters of subsystem 2, such as... Figure 3 and Figure 4 As shown. Figure 3 and Figure 4 The diagram shown is a statistical energy analysis plot in dimensionless space, with the horizontal axis representing the dimensionless wavenumber and the vertical axis representing the damping loss factor and shape parameter, respectively. One plot can be selected based on the specific application.

[0074] The damping loss factor can be taken as a fixed value of 0.01. The shape parameter is fixed for a coupled plate system with a defined size, and since it is a rectangular plate, the shape parameter must be greater than 1. Based on the plate size, the shape parameter is a constant value of 1.1284. Therefore, the dimensionless wavenumber is... Figure 4 The middle is restricted to M=1 and On a horizontal line segment AC parallel to the x-axis, the range of dimensionless wavenumber κ∈(4.431,31.831) of subsystem 2 can be obtained.

[0075] Then, based on the relationship between dimensionless wavenumber and frequency, the corresponding frequency band range can be obtained:

[0076] The relationship between dimensionless wavenumber and frequency is obtained by the following formula:

[0077] Dk 4 -ρhω 2 =0

[0078] in, k, E, h, ρ, ν, and ω represent wave number, elastic modulus, thickness, density, density, Poisson's ratio, and circular frequency, respectively.

[0079] Then, according to The corresponding frequency band range can then be obtained.

[0080] In this embodiment, since the plate structure size is the same material, the coupling relationship is simple. After calculating the dimensionless wave number range of subsystem two 2, κ∈(4.431, 31.831), the dimensionless wave number range is directly corrected according to the coupling relationship, that is, the dimensionless wave number range of the target system is obtained, and then the effective frequency band of the target system is obtained by converting the frequency. The specific steps include:

[0081] Considering the coupling relationship, since the coupling strength is less than 1, it can be concluded that the dimensionless wave number range of subsystem two 2 under the coupling with subsystem one 1 is κ>7.958, and the dimensionless wave number range of subsystem two 2 under the coupling with subsystem three 3 is κ>7.958, so the dimensionless wave number is limited on the line segment BC in Figure 4 , and the dimensionless wave number range of subsystem 2 is κ∈(7.958, 31.8. According to the relationship between wave number and dimensionless wave number k=2πκ / l, l=πab / 2(a+b), l=0.23562, the wave number range of subsystem 2 is k∈(118.16, 848.83), so the wave number range of subsystem two 2 is k∈(212.21, 848.83).

[0082] According to the relationship between frequency and wave number Dk 4 -ρhω 2 =0, the circular frequency is obtained: wherein, h, ρ are known values. According to The statistical energy analysis effective frequency band of the coupled plate structure (target system) is f∈(9537.46, 482551.17), unit: Hz.

[0083] For the target system of this embodiment, since the coupling relationship is simple and the number of subsystems is small, and the size of the subsystems is consistent, subsystem two 2 can be used as the basis, and the coupling relationship of the remaining other subsystems is combined to further limit the effective frequency band in the statistical energy analysis effective diagram, that is, the statistical energy analysis effective frequency band of the coupled plate structure can be obtained. For systems with uncertain shape parameters and damping loss factors, the statistical energy analysis effective diagram can be analyzed by using Figure 3 .

[0084] Those skilled in the art can understand that for a complex target system, for example, the structure size of the subsystems is not the same, or the number of subsystems is large, and the coupling relationship is complex, the statistical energy analysis effective diagram of each subsystem needs to be obtained respectively (see Figure 3 or Figure 4obtaining the dimensionless wave number range and the corresponding frequency range of the subsystem, and then according to the coupling condition, limiting the obtained frequency range according to the size parameter and the coupling strength for each coupling relationship, further correcting the obtained frequency range of the different subsystems, and obtaining the final frequency range as the effective frequency range of the target system by means of intersection for the corrected frequency range of the different subsystems.

[0085] The application also provides a system for defining the effective analysis frequency range of an engineering structure, comprising:

[0086] a selection module for selecting important parameters for statistical energy analysis of the target system, including the number of modes N i , the modal overlap factor M i , the normalized attenuation factor , and the coupling strength γ ij , and defining the threshold values of the important parameters, wherein the subscript i represents the number of the subsystem constituting the target system, and the coupling strength γ ij is used to represent the flow strength of the vibration energy between any two subsystems i and j having coupling effect in the target system;

[0087] a mapping module for performing dimension analysis according to the important parameters, the vibration characteristics and the boundary conditions of the target system, obtaining dimensionless parameters corresponding to the important parameters, including the dimensionless wave number κ i , the shape parameter ε i , the damping loss factor η i , and the Poisson's ratio v i , constructing the statistical energy analysis effective map of each subsystem according to the corresponding relationship between the dimensionless parameters and the important parameters, so as to describe the distribution of the important parameters in the dimensionless parameter space, wherein the dimensionless parameter space is a two-dimensional plane with the dimensionless wave number κ i as one coordinate axis and any one of the shape parameter ε i and the damping loss factor η i as the other coordinate axis;

[0088] an analysis module for analyzing the statistical energy analysis effective map, obtaining the value range of the dimensionless wave number of each subsystem, obtaining the effective frequency range of each subsystem according to the relationship between the dimensionless wave number and the frequency, and obtaining the effective frequency range of the target system according to the coupling relationship of each subsystem.

[0089] Those skilled in the art can understand that the above only describes the preferred embodiments of the present application and is not used to limit the present application, and although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or make equivalent replacements to some technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for defining the effective analysis frequency band of an engineering structure, characterized in that, The method comprises the following steps: selecting important parameters of statistical energy analysis of the target system, including modal number , modal overlap factor , normalized attenuation factor and coupling strength , defining threshold values of the important parameters, wherein the subscript represents the number of a subsystem constituting the target system, and the coupling strength is used to represent the flow strength of vibration energy between any two subsystems with coupling in the target system and the subsystem . According to the important parameters, dimension analysis is conducted in combination with vibration characteristics and boundary conditions of a target system to obtain dimensionless parameters corresponding to the important parameters, including dimensionless wave number , shape parameter , damping loss factor and Poisson's ratio ; according to a corresponding relationship between the dimensionless parameters and the important parameters, a statistical energy analysis effective graph of each subsystem is constructed to describe a distribution of the important parameters in a dimensionless parameter space, which is a two-dimensional plane with the dimensionless wave number as one coordinate axis and any one of the shape parameter and the damping loss factor as the other coordinate axis. The corresponding relationship between the important parameter and the dimensionless parameter comprises: The relationship between the dimensionless wave number and the frequency is obtained by the following formula: ， ， ， ， ， wherein the subscript represents the number of subsystems constituting the target system, represents the transmission efficiency, is the length of the coupling between the subsystems and the subsystems , is the perimeter of the subsystem ; The threshold of the important parameter is defined according to the assumption condition of the statistical energy analysis, which comprises: ， wherein , , , , , , are the wavenumber, the elastic modulus, the thickness, the density, the density, the Poisson's ratio and the circular frequency, respectively, the wavenumber , is the dimensionless wavenumber, is a structure-dependent dimension parameter.

2. The method of defining an effective analysis band of an engineered structure of claim 1, wherein, The effective frequency band of the target system is obtained according to the coupling relationship of each subsystem, which comprises: modal number sufficiently large, and ; Modal overlap factor ; Normalized attenuation factor ; Coupling strength .

3. The method of defining an effective analysis band of an engineered structure of claim 1, wherein, According to the coupling relationship, the coupling strength of each subsystem is limited to obtain a modified effective frequency band, and the intersection of the modified effective frequency bands of each subsystem is taken as the effective frequency band of the target system. The method comprises the following steps:

4. The method of defining an effective analysis band of an engineered structure of claim 1, wherein, When analyzing the statistical energy analysis effective figure, the shape parameter is set to a fixed value.

5. The method of defining a band of interest for an engineered structure according to claim 1, wherein, When analyzing the statistical energy analysis effective graph, the damping loss factor is set to a fixed value.

6. A system for defining an effective analysis band of an engineered structure according to the method of any one of claims 1 to 5, characterized in that, The analysis module: the statistical energy analysis effective graph is analyzed to obtain the value range of the dimensionless wave number of each subsystem, the effective frequency band of each subsystem is obtained according to the relationship between the dimensionless wave number and the frequency, and the effective frequency band of the target system is obtained according to the coupling relationship of each subsystem. Selecting module: selecting important parameters for statistical energy analysis of a target system, including modal number , modal overlap factor , normalized attenuation factor , and coupling strength , defining threshold values of the important parameters, wherein the subscript represents the number of a subsystem constituting the target system, and the coupling strength is used to represent the flow strength of vibration energy between any two subsystems with coupling in the target system and the subsystem ; The mapping module: according to the important parameters, combining the vibration characteristics and boundary conditions of the target system, dimension analysis is carried out to obtain dimensionless parameters corresponding to the important parameters, including dimensionless wave number , shape parameter , damping loss factor and Poisson's ratio , according to the corresponding relationship between dimensionless parameters and important parameters, the statistical energy analysis effective map of each subsystem is constructed to describe the distribution of the important parameters in the dimensionless parameter space, which is a two-dimensional plane with dimensionless wave number as one of the coordinate axes, and any one of shape parameter and damping loss factor as the other coordinate axis; ​

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