Structural frequency design method and device based on root-mean-square response

Abstract

The invention belongs to the field of structure frequency design, and particularly relates to a structure frequency design method and device based on root-mean-square response, and the method comprises the steps: obtaining an initial transfer function of a structure; translating the initial transfer function by a series of values according to changes of rigidity and quality to obtain a series of new transfer functions; subtracting the set excitation frequency from the attention frequencies of all the new transfer functions to obtain a plurality of frequency differences; respectively comparing the root-mean-square response of all the new transfer functions under the set excitation with the root-mean-square response of the initial transfer function under the set excitation to obtain a plurality of response ratios; fitting a relation curve of the frequency difference and the response ratio; and taking a frequency difference corresponding to a point of which the curvature of the relation curve is smaller than a preset value as a critical frequency difference. According to the frequency response curve characteristics of the structure and the root-mean-square response before and after adjustment, the design criterion of the difference between the inherent frequency and the excitation frequency of the structure is given, and the designable range of the inherent frequency of the structure is greatly widened.

Description

Technical Field

[0001] The present application belongs to the field of structural frequency design, and in particular relates to a structural frequency design method and device based on root mean square response. Background Art

[0002] The existing method is basically based on the difference of 3Hz, 5%, half power bandwidth, times as an indicator. This design criterion can generally provide a good guide for frequency design work. However, sometimes the target structure is large and complex, with many modes, resulting in the natural frequencies being very close. At this time, the above indicator is difficult to achieve. Summary of the invention

[0003] In order to solve the above problems, the present application provides a structural frequency design method based on root mean square response, which is characterized by comprising:

[0004] Step S1: Obtaining the initial transfer function of the structure;

[0005] Step S2: translating the initial transfer function by a series of values ​​according to the changes in stiffness and mass to obtain a series of new transfer functions;

[0006] Step S3: subtract the set excitation frequency from the concerned frequencies of all new transfer functions to obtain a plurality of frequency differences; and compare the root mean square responses of all new transfer functions under the set excitation with the root mean square responses of the initial transfer functions under the set excitation to obtain a plurality of response ratios;

[0007] Step S4: fitting the relationship curve between frequency difference and response ratio;

[0008] Step S5: taking the frequency difference corresponding to the point where the curvature of the relationship curve is less than a preset value as the critical frequency difference, and taking the critical frequency difference as a recommended value for structural frequency design.

[0009] Preferably, the method for obtaining the initial transfer function includes:

[0010] Perform frequency response analysis on the finite element model of the structure;

[0011] The real and imaginary responses at each frequency point in the X, Y, and Z directions of the structure in the frequency response analysis results are extracted, and then synthesized to obtain the initial transfer function of the structure.

[0012] Preferably, the specific steps of extracting the real and imaginary responses at each frequency point in the X, Y, and Z directions of the structure in the frequency response analysis results include:

[0013] A dynamic finite element model is established for the actual structural three-dimensional digital model, and a unit load is applied to the finite element model according to the actual loading mode of the structure;

[0014] And use patran software to perform frequency response analysis on the finite element model;

[0015] The f06 file in the frequency response analysis results is used to extract the real and imaginary responses of the structure at each frequency point in the X, Y, and Z directions.

[0016] Preferably, the root mean square response of the structure is obtained according to the load magnitude applied to the structure and the transfer function; after translating the transfer function according to the change of stiffness and mass, the root mean square response of the structure is obtained according to the load magnitude applied to the structure.

[0017] Preferably, the calculation formula of the root mean square response includes:

[0018]

[0019] Where rms stands for root mean square, f0 and f1 represent the upper and lower limits of the integration frequency band, H(w) represents the transfer function, and PSD represents the load.

[0020] Preferably, the difference between the natural frequency of the structure and the excitation frequency is greater than or equal to the critical frequency difference, and the structure avoids the resonance region.

[0021] A structural frequency design module based on root mean square response, using the structural frequency design method based on root mean square response, comprising:

[0022] A reading module for obtaining the initial transfer function of the structure;

[0023] A translation module is used to translate the initial transfer function by a series of values ​​according to the changes in stiffness and mass to obtain a series of new transfer functions;

[0024] A calculation module is used to subtract the set excitation frequency from the concerned frequencies of all new transfer functions to obtain multiple frequency differences; and to compare the root mean square responses of all new transfer functions under the set excitation with the root mean square responses of the initial transfer functions under the set excitation to obtain multiple response ratios;

[0025] Fitting module: used to fit the relationship curve between frequency difference and response ratio;

[0026] The output module is used to output the frequency difference corresponding to the point where the curvature of the relationship curve is less than a preset value as a critical frequency difference, and the critical frequency difference is used as a recommended value for structural frequency design.

[0027] Preferably, it also includes:

[0028] Analysis module for frequency response analysis of finite element models of structures;

[0029] The synthesis module is used to extract the real and imaginary responses of the structure at each frequency point in the X, Y, and Z directions in the frequency response analysis results, and then synthesize them to obtain the initial transfer function of the structure.

[0030] Preferably, it also includes:

[0031] Modeling module, used to establish a dynamic finite element model for the actual structural three-dimensional digital model, and apply unit load to the finite element model according to the actual loading mode of the structure;

[0032] Preferably, the analysis module calls patran software to perform frequency response analysis on the finite element model.

[0033] Preferably, the synthesis module uses the f06 file in the frequency response analysis result to extract the real and imaginary responses at each frequency point in the X, Y, and Z directions of the structure.

[0034] Preferably, the formula used in the calculation module to calculate the root mean square response is:

[0035]

[0036] Where rms stands for root mean square, f0 and f1 represent the upper and lower limits of the integration frequency band, H(w) represents the transfer function, and PSD represents the load.

[0037] The advantages of this application include: for complex structures, the 3Hz frequency difference of the traditional design method is difficult to meet. This method provides a clearer frequency difference design value based on the frequency response characteristics and root mean square response of the specific structure, which greatly broadens the designable range of the natural frequency of the complex structure at low frequency, thereby reducing the difficulty of frequency design. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a technical route flow chart of a preferred implementation method of this application;

[0039] Figure 2 It is a transfer function diagram of a preferred embodiment of the present application;

[0040] Figure 3 This is a narrow-band excitation load diagram of a preferred embodiment of the present application;

[0041] Figure 4 This is a schematic diagram of the transfer function translation of a preferred embodiment of the present application;

[0042] Figure 5 This is a curve diagram of the change of the root mean square response ratio with the frequency difference in a preferred embodiment of the present application. DETAILED DESCRIPTION

[0043] In order to make the technical solution and advantages of the present application clearer, the technical solution of the present application will be further described in detail in detail and in detail in conjunction with the accompanying drawings. It can be understood that the specific embodiments described here are only partial embodiments of the present application, which are only used to explain the present application, not to limit the present application. It should be noted that, for the convenience of description, only the parts related to the present application are shown in the accompanying drawings, and other related parts can refer to the general design. In the absence of conflict, the embodiments in the present application and the technical features in the embodiments can be combined with each other to obtain new embodiments.

[0044] The technical route of the frequency design method involved in the present invention is as follows Figure 1 As shown, the specific steps are as follows:

[0045] The first step is to establish a dynamic finite element model based on the actual structural three-dimensional digital model, and correctly set the connection relationship and boundary conditions. The accuracy of the finite element model will directly affect the accuracy of subsequent calculation results.

[0046] In the second step, unit loads are applied according to the actual loading mode of the structure, and the finite element model established in the first step is analyzed by frequency response using patran software.

[0047] In the third step, because the frequency response characteristic (transfer function) curve in patran does not consider the imaginary part, the f06 file in the frequency response analysis results is used to extract the real and imaginary responses of the structure at each frequency point in the X, Y, and Z directions, and then synthesize them to obtain the actual transfer function curve of the structure.

[0048] The fourth step is to calculate the root mean square response of the structure based on the actual load size of the structure and the transfer function in the third step using the following formula.

[0049]

[0050] Where rms stands for root mean square, f0 and f1 represent the upper and lower limits of the integration frequency band, H(w) represents the transfer function, and PSD represents the load.

[0051] The fifth step is to simulate the change of structural stiffness and mass by translating the transfer function. The main purpose of this step is to adjust the natural frequency of the structure. The natural frequency of the structure is closely related to the transfer function, so the adjustment of the natural frequency can be converted into the adjustment of the transfer function. The shape of the transfer function is mainly related to the structural damping, so the change of structural stiffness and mass can be regarded as only the translation of the transfer function.

[0052] Step 6: Keep the excitation load unchanged and calculate the new RMS response based on the translated transfer function and formula (1).

[0053] In the seventh step, a series of new RMS responses can be calculated by shifting the transfer function by a series of values. The frequency of interest of the transfer function (a certain modal frequency, that is, a peak frequency of the transfer function) is subtracted from the excitation center frequency, and the new and old RMS responses are compared to obtain a curve of the relationship between the response ratio and the frequency difference.

[0054] Step 8. After obtaining the relationship curve between the response ratio and the frequency difference, observe the change in the slope of the curve and define the place where the slope suddenly slows down as the critical frequency difference. When it is less than this value, the natural frequency of the structure is close to the excitation frequency, the structural response changes dramatically, and a slight change in the natural frequency will bring about a sharp increase or decrease in the response. It can be considered that it has not yet escaped the influence of the resonance zone; when it is greater than this value, the change in the natural frequency has little effect on the response, and the response will no longer increase or decrease dramatically, which can be considered to have escaped the influence of the resonance zone.

[0055] The ninth step is to obtain the critical frequency difference based on the actual structural frequency response characteristics, and then use this value as the recommended value for structural frequency design. As long as the difference between the structural natural frequency and the excitation frequency is greater than or equal to the critical frequency difference, it can be considered that the resonance zone has been avoided, which greatly increases the design range of the structural natural frequency.

[0056] The present invention will be further described below with reference to the accompanying drawings and specific implementation examples:

[0057] The natural frequency corresponding to the highest peak of the transfer function is analyzed as the research object, and the results are as follows

[0058] Select a finite element model, use patran to calculate the frequency response, and extract the transfer function from the f06 file as follows Figure 2 As shown in the figure, the following description will be made based on the natural frequency corresponding to the highest peak of the transfer function.

[0059] Assume that the structure is subjected to a narrowband excitation of 14 Hz, such as Figure 3 As shown. According to formula (1), the root mean square response of the original structure can be calculated.

[0060] right Figure 2 The transfer function shown is translated left and right to simulate the change in frequency response characteristics caused by changes in structural stiffness and mass. The schematic diagram is shown in Figure 4 shown.

[0061] Keeping the excitation load unchanged, the RMS response after the transfer function is shifted is calculated using formula (1), and then the RMS response ratio before and after the shift changes with the frequency difference (i.e., the difference between the natural frequency corresponding to the highest peak and the excitation frequency) is obtained, as shown in Figure 5 shown.

[0062] It can be seen that when the frequency difference is between -0.4Hz and 0.5Hz, the RMS value becomes about 2.5 times the initial value, and this range can be considered as the resonance band; when the frequency difference increases from 0.5Hz to 0.7Hz, the RMS ratio decreases rapidly, from 2.5 to about 0.75; when the frequency difference continues to increase from 0.7Hz, the RMS ratio decreases slowly until it approaches 0. When the frequency difference decreases from -0.4Hz to -1.0Hz, the RMS ratio also decreases rapidly, from 2.5 to about 0.67; when the frequency difference continues to decrease from -1.0Hz, the RMS ratio decreases slowly until it approaches 0. Therefore, 0.7Hz and -1.0Hz are the critical frequency differences to avoid resonance, that is, greater than 18.7Hz or less than 17Hz is the recommended design value of the structural natural frequency.

[0063] The recommended frequency difference in this example is less than 1 Hz, which is much smaller than the 3 Hz given by the general frequency design criteria. Therefore, it greatly broadens the design range of the structural natural frequency and reduces the difficulty of frequency design of complex structures at low frequencies.

[0064] A structural frequency design module based on root mean square response, using the structural frequency design method based on root mean square response, comprising:

[0065] A reading module for obtaining the initial transfer function of the structure;

[0066] A translation module is used to translate the initial transfer function by a series of values ​​according to the changes in stiffness and mass to obtain a series of new transfer functions;

[0067] A calculation module is used to subtract the set excitation frequency from the concerned frequencies of all new transfer functions to obtain multiple frequency differences; and to compare the root mean square responses of all new transfer functions under the set excitation with the root mean square responses of the initial transfer functions under the set excitation to obtain multiple response ratios;

[0068] Fitting module: used to fit the relationship curve between frequency difference and response ratio;

[0069] The output module is used to output the frequency difference corresponding to the point where the curvature of the relationship curve is less than a preset value as a critical frequency difference, and the critical frequency difference is used as a recommended value for structural frequency design.

[0070] In some optional embodiments, it also includes:

[0071] Analysis module for frequency response analysis of finite element models of structures;

[0072] The synthesis module is used to extract the real and imaginary responses of the structure at each frequency point in the X, Y, and Z directions in the frequency response analysis results, and then synthesize them to obtain the initial transfer function of the structure.

[0073] In some optional embodiments, it also includes:

[0074] Modeling module, used to establish a dynamic finite element model for the actual structural three-dimensional digital model, and apply unit load to the finite element model according to the actual loading mode of the structure;

[0075] In some optional implementations, the analysis module calls patran software to perform frequency response analysis on the finite element model.

[0076] In some optional implementations, the synthesis module uses the f06 file in the frequency response analysis results to extract the real and imaginary responses at each frequency point in the X, Y, and Z directions of the structure.

[0077] In some optional implementations, the formula used in the calculation module to calculate the root mean square response is:

[0078]

[0079] Where rms stands for root mean square, f0 and f1 represent the upper and lower limits of the integration frequency band, H(w) represents the transfer function, and PSD represents the load.

[0080] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A structural frequency design method based on root mean square response, characterized in that: include: Step S1: obtaining the initial transfer function of the structure; Step S2: translating the initial transfer function by a series of values ​​according to the changes in stiffness and mass to obtain a series of new transfer functions; Step S3: subtract the set excitation frequency from the concerned frequencies of all new transfer functions to obtain a plurality of frequency differences; and compare the root mean square responses of all new transfer functions under the set excitation with the root mean square responses of the initial transfer functions under the set excitation to obtain a plurality of response ratios; Step S4: fitting the relationship curve between frequency difference and response ratio; Step S5: taking the frequency difference corresponding to the point where the curvature of the relationship curve is less than a preset value as the critical frequency difference, and taking the critical frequency difference as a recommended value for structural frequency design.

2. The structural frequency design method based on root mean square response according to claim 1, characterized in that: The method for obtaining the initial transfer function includes: Perform frequency response analysis on the finite element model of the structure; The real and imaginary responses at each frequency point in the X, Y, and Z directions of the structure in the frequency response analysis results are extracted, and then synthesized to obtain the initial transfer function of the structure.

3. The structural frequency design method based on root mean square response according to claim 2, characterized in that: The specific steps of extracting the real and imaginary responses of the structure at each frequency point in the X, Y, and Z directions in the frequency response analysis results include: A dynamic finite element model is established for the actual structural three-dimensional digital model, and a unit load is applied to the finite element model according to the actual loading mode of the structure; And use patran software to perform frequency response analysis on the finite element model; The f06 file in the frequency response analysis results is used to extract the real and imaginary responses of the structure at each frequency point in the X, Y, and Z directions.

4. The structural frequency design method based on root mean square response according to claim 1, characterized in that: The root mean square response of the structure is obtained according to the load size received by the structure and the transfer function; after translating the transfer function according to the change of stiffness and mass, the root mean square response of the structure is obtained according to the load size received by the structure.

5. The structural frequency design method based on root mean square response according to claim 1, characterized in that: The formula for calculating the RMS response is: Where rms stands for root mean square, f0 and f1 represent the upper and lower limits of the integration frequency band, H(w) represents the transfer function, and PSD represents the load.

6. The structural frequency design method based on root mean square response according to claim 1, characterized in that: The difference between the structural natural frequency and the excitation frequency is greater than or equal to the critical frequency difference, and the structure avoids the resonance zone.

7. A structural frequency design device based on root mean square response, using the structural frequency design method based on root mean square response according to any one of claims 1 to 6, characterized in that: include: A reading module for obtaining the initial transfer function of the structure; A translation module is used to translate the initial transfer function by a series of values ​​according to the changes in stiffness and mass to obtain a series of new transfer functions; A calculation module is used to subtract the set excitation frequency from the concerned frequencies of all new transfer functions to obtain multiple frequency differences; and to compare the root mean square responses of all new transfer functions under the set excitation with the root mean square responses of the initial transfer functions under the set excitation to obtain multiple response ratios; Fitting module: used to fit the relationship curve between frequency difference and response ratio; The output module is used to output the frequency difference corresponding to the point where the curvature of the relationship curve is less than a preset value as a critical frequency difference, and the critical frequency difference is used as a recommended value for structural frequency design.

8. The structural frequency design device based on root mean square response according to claim 7, characterized in that: Also includes: Analysis module for frequency response analysis of finite element models of structures; The synthesis module is used to extract the real and imaginary responses of the structure at each frequency point in the X, Y, and Z directions in the frequency response analysis results, and then synthesize them to obtain the initial transfer function of the structure.

9. The structural frequency design device based on root mean square response according to claim 8, characterized in that: Also includes: The modeling module is used to establish a dynamic finite element model for the actual structural three-dimensional digital model and apply unit loads to the finite element model according to the actual loading mode of the structure.

10. The structural frequency design device based on root mean square response according to claim 8, characterized in that: The analysis module calls the patran software to perform frequency response analysis on the finite element model.

11. The structural frequency design device based on root mean square response according to claim 10, characterized in that: The synthesis module uses the f06 file in the frequency response analysis results to extract the real and imaginary responses of the structure at each frequency point in the X, Y, and Z directions.

12. The structural frequency design device based on root mean square response according to claim 1, characterized in that: The formula used in the calculation module to calculate the RMS response is: Where rms stands for root mean square, f0 and f1 represent the upper and lower limits of the integration frequency band, H(w) represents the transfer function, and PSD represents the load.

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