Young modulus calculation method of square section rod

Abstract

The invention relates to the technical field of material mechanical parameter testing, and discloses a Young modulus calculation method of a square section rod, which comprises the following steps: acquiring section side length, length and mass information of a sample by using a high-precision measuring tool; acquiring time domain sound pressure signals under two supporting states by using a professional microphone; converting a time domain sound pressure signal into a frequency domain signal, and respectively identifying a second-order damping bending vibration frequency and a third-order damping bending vibration frequency on a spectrogram; the damping influence is ignored; calculating h / l to obtain a corresponding coefficient; substituting all parameters into a formula to obtain a Young modulus value; and calculating the average Young modulus. According to the method, the universality of the calculation method for the square section rod in different practical application scenes is enhanced, and the Young modulus can be accurately calculated as long as corresponding parameters are obtained and substituted no matter how the size of the sample changes.

Description

Technical Field

[0001] The invention relates to the technical field of material mechanical parameter testing, in particular to a method for calculating the Young's modulus of a square cross-section rod. Background Art

[0002] In the engineering field, many structures and components use rod-shaped components, and understanding the Young's modulus of these components can help engineers evaluate their deformation under different load conditions and ensure the safety and reliability of the structure. For example, in building structures, the design of components such as beams and columns needs to consider the Young's modulus of the material to determine its bearing capacity and stability. In mechanical engineering, the design of parts such as shafts and rods is also inseparable from the accurate value of the Young's modulus.

[0003] With the continuous advancement of science and technology, people have higher and higher requirements for the measurement of mechanical properties of materials. The traditional Young's modulus calculation method can no longer meet the needs of modern engineering and scientific research in some aspects. In a greenhouse environment, factors such as temperature and humidity may affect the mechanical properties of materials. In addition, noise and interference in a greenhouse environment may also affect the accuracy of the measurement results.

[0004] Therefore, it is necessary to develop a more accurate, convenient and universal Young's modulus calculation method to solve the problem of how to overcome the influence of environmental factors and accurately measure the Young's modulus of square cross-section rods. Summary of the invention

[0005] The embodiment of the present application provides a method for calculating the Young's modulus of a square cross-section rod, thereby solving the problem in the related art of overcoming the influence of environmental factors and accurately measuring the Young's modulus of a square cross-section rod.

[0006] According to one aspect of an embodiment of the present application, a method for calculating the Young's modulus of a square cross-section rod is provided, comprising the following steps:

[0007] S100: Use high-precision measuring tools to obtain the cross-sectional side length, length, and mass information of the sample;

[0008] S200: A professional microphone is used to obtain the time domain sound pressure signals in two support states;

[0009] S300: Convert the time domain sound pressure signal into a frequency domain signal and identify the second-order damped bending vibration frequency on its spectrum diagram and the third-order damped bending vibration frequency

[0010] S400: Ignore the damping effect, that is

[0011] S500: Calculate h / l, substitute it into the formula to obtain the coefficient function

[0012] S600: Substitute the coefficient and the side length l, length h, mass m, the second-order ideal natural bending vibration frequency f α2 and the third-order ideal natural bending vibration frequency f α3 into the formula to obtain its Young's modulus value E α2 、E α3 ;

[0013] S700: Calculate its average Young's modulus E Avg =(E α2 +E α3 ) / 2.

[0014] Furthermore, the S400 results in the experimentally measured low-order natural bending vibration frequency being lower than the ideal value under the damping effect. Since the damping effect of most materials is very small, the second-order damped natural bending vibration frequency and the third-order damped natural bending vibration frequency measured for the specimen material in two support states can be directly substituted into the coefficient function formula for calculating the Young's modulus of the material.

[0015] Furthermore, in the S500, the coefficient function formulas are respectively:

[0016]

[0017] Furthermore, in the S600, establish the relationship existing between the low-order ideal natural bending vibration frequency (10 < h / l < 100) and the first-order ideal natural longitudinal stretching vibration frequency f β1 , and substitute the parameters into the following formula:

[0018]

[0019] where f α2 (Hz) is the second-order natural bending vibration frequency of the square-section rod; f α3 (Hz) is the third-order natural bending vibration frequency of the square-section rod; h (m) is the rod length; l (m) is the side length of the square section; m (kg) is the mass of the square-section rod; E α2 、E α3 are respectively the Young's modulus values of the material measured at different bending frequencies, and for the same material, their values are approximately equal.

[0020] Furthermore, perform signal filtering processing on the signal acquired by the microphone.

[0021] Furthermore, the collected digital signal is input into the designed filter for filtering operation, the discrete Fourier transform algorithm is used to convert the time domain signal to the frequency domain, and then the signal is filtered in the frequency domain, and finally the filtered frequency domain signal is converted back to the time domain through inverse transformation.

[0022] Furthermore, the spectral analysis of the filtered signal is performed again and compared with the spectrum before filtering to calculate the degree of improvement in the signal-to-noise ratio of the signal before and after filtering. By comparing the ratio of signal power to noise power before and after filtering, the effect of filtering on improving signal quality is quantitatively evaluated.

[0023] Furthermore, the possible sources of error are analyzed. In addition to considering noise interference, the accuracy error of the measurement tool and the error caused by the change of the microphone position must also be considered to evaluate each error source and determine its influence on the calculation results of Young's modulus.

[0024] Furthermore, an error correction model is established based on the results of the error analysis. If the accuracy error of the measuring tool is in a linear relationship, it is corrected through the linear regression method. If the error is caused by the change in microphone position, the relationship model between position and signal characteristics is established by measuring the signals at different positions multiple times to compensate for the error.

[0025] Furthermore, a mechanical model of the square cross-section rod was established using the finite element analysis numerical simulation method to predict the vibration characteristics and Young's modulus of the square cross-section rod under different conditions. The Young's modulus obtained by experimental measurement was compared with the numerical simulation results, the difference between the two was analyzed, and the experimental method and numerical model were adjusted and optimized.

[0026] Furthermore, on the basis of filtering processing, signal enhancement technology such as signal amplification and deconvolution is combined to further improve the quality of the signal.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] 1. The present invention uses high-precision measuring tools to obtain the cross-sectional side length, length and mass information of the sample, ensuring the accuracy of the basic data. These parameters are crucial for subsequent calculations, and high-precision measurements can reduce the Young's modulus calculation deviation caused by data errors.

[0029] 2. The present invention is applicable to square cross-section rods of different materials, whether metal materials, plastic materials or composite materials, and the Young's modulus can be measured by this method. This provides a universal measurement method for engineering applications in different fields. For square cross-section rods of different sizes, the method also has good applicability. It is only necessary to adjust the measurement tools and parameters according to the actual situation to accurately measure the Young's modulus of square cross-section rods of various sizes.

[0030] 3. The measuring tools and equipment used in the present invention are relatively common, such as high-precision measuring tools and professional microphones, etc. The operation is relatively simple and does not require complex professional skills and training. This makes the method easier to promote and use in practical applications.

[0031] The technical solution of the present application is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The accompanying drawings, which constitute a part of the specification, illustrate embodiments of the present application and, together with the description, serve to explain the principles of the present application.

[0033] The present application can be more clearly understood from the following detailed description with reference to the accompanying drawings, in which:

[0034] Figure 1 A schematic diagram of a flow chart of a method for calculating the Young's modulus of a square cross-section rod proposed in this application;

[0035] Figure 2 This is a test schematic diagram of a method for calculating the Young's modulus of a square cross-section rod proposed in this application. DETAILED DESCRIPTION

[0036] Various exemplary embodiments of the present application will now be described in detail with reference to the accompanying drawings. It should be noted that unless otherwise specifically stated, the relative arrangement of components and steps, numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present application.

[0037] At the same time, it should be understood that for the convenience of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship.

[0038] The following description of at least one exemplary embodiment is merely illustrative in nature and is not intended to limit the present application, its application, or uses.

[0039] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered part of the specification.

[0040] It should be noted that like reference numerals and letters refer to similar items in the following figures, and therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0041] In addition, the technical solutions between the various embodiments of the present application can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by this application.

[0042] It should be noted that all directional indications in the embodiments of the present application (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0043] Combine the following Figure 1-Figure 2 To describe a method for calculating the Young's modulus of a square cross-section rod according to an exemplary embodiment of the present application. It should be noted that the following application scenarios are only shown to facilitate understanding of the spirit and principles of the present application, and the embodiments of the present application are not limited in this regard. On the contrary, the embodiments of the present application can be applied to any applicable scenario.

[0044] The present application also proposes a method for calculating the Young's modulus of a square cross-section rod.

[0045] Figure 1 The following schematically shows a flow chart of a method for calculating the Young's modulus of a square cross-section rod according to an embodiment of the present application. Figure 1 As shown, the method is applied in a greenhouse environment and comprises the following steps:

[0046] Step 1: Use high-precision measuring tools to obtain the cross-sectional side length, length, and mass information of the sample.

[0047] Specifically, for smaller square-section rods, a vernier caliper or digital caliper can be used, which can accurately measure the length below the millimeter and reduce the reading error. For length measurement with higher precision requirements, for larger square-section rods, a laser rangefinder can be used, which determines the distance by emitting a laser beam and measuring the time of reflected light, with the advantages of fast, accurate, and non-contact measurement.

[0048] Specifically, in order to improve the reliability of the measurement results, multiple repeated measurements can be performed. For length and side length, multiple measurements can be performed at different locations and the average value can be taken as the final result. For mass, multiple weighings can be performed and the average value can be taken to reduce errors.

[0049] Step 2: Use a professional microphone to obtain the time domain sound pressure signals in two supporting states;

[0050] Specifically, choose a microphone with appropriate directivity according to the experimental environment and requirements. If there is a lot of background noise interference in the experimental environment, a cardioid directional microphone can be used. It has a strong receiving ability for the sound signal coming from the front (that is, the sound pressure signal from the square cross-section rod), and has a certain inhibitory effect on the background noise from other directions, which helps to improve the signal-to-noise ratio of the acquired sound pressure signal.

[0051] It is understandable that a square cross-section rod will exhibit different vibration modes under different support conditions. Figure 2 The figure shows a square cross-section rod in two support states, and the vibration characteristics of the different support states are significantly different. By setting these two support states, the second-order and third-order damped bending vibration modes of the square cross-section rod specimen can be excited respectively, so that the acquired sound pressure signal contains more information about the mechanical properties and material properties of the rod, which is helpful for the subsequent more comprehensive and accurate calculation of Young's modulus.

[0052] Step 3: Convert the time domain sound pressure signal into a frequency domain signal and identify the second-order damped bending vibration frequency on its spectrum. and the third-order damped bending vibration frequency

[0053] It is understandable that multiple measurements and corresponding spectrograms are required to ensure the accuracy of recognition. Under different measurements, due to certain measurement errors and slight changes in experimental conditions, the peak position and amplitude on the spectrum may fluctuate slightly, but for the second-order and third-order damped bending vibration frequencies, they should remain relatively stable within a reasonable fluctuation range. By comparing the results of multiple measurements, the identified frequencies are verified, and erroneous recognitions that may be caused by abnormal conditions are eliminated, thereby improving the reliability of the final recognition results.

[0054] Step 4: Ignore the damping effect, that is

[0055] Step 5: Calculate h / l and substitute it into the formula to get the coefficient function

[0056] Step 6: Coefficient and side length l, length h, mass m, second-order ideal natural bending vibration frequency f α2 and the third-order ideal natural bending vibration frequency f α3 Substitute into the formula to obtain its Young's modulus value E α2 、E α3 ;

[0057] Step 7: Calculate the average Young's modulus E Avg =(E α2 +E α3 ) / 2.

[0058] Specifically, in step 4, the low-order natural bending vibration frequency measured in the experiment under the damping effect is lower than the ideal value. Since the damping effect of most materials is very small, the second-order damped natural bending vibration frequency of the sample material measured under two support states can be and the third-order damped natural bending vibration frequency Directly substitute into the coefficient function formula to calculate the Young's modulus of the material.

[0059] It can be understood that the geometry of the square cross-section rod can be taken into account by calculating h / l, which is the ratio of the length of the rod to the cross-sectional dimensions. Different values ​​of h / l correspond to different geometries, and the coefficient function is adjusted according to this change in geometry. This makes the calculation result more accurately reflect the Young's modulus of the material under a specific geometry, avoiding the error that may be caused by using only a general formula and ignoring the influence of geometry.

[0060] For square cross-section bars of different sizes, by calculating h / l and substituting it into the formula to obtain the coefficient function, the same set of calculation methods can be applied to a variety of different geometric sizes. This improves the versatility and applicability of the method and reduces the need to develop separate calculation methods for bars of different sizes.

[0061] Specifically, in step 4, the damping effect causes the experimentally measured low-order natural bending vibration frequency to be lower than the ideal value. Since the damping effect of most materials is very small, this approximate value can be directly substituted into the coefficient function formula to calculate the Young's modulus of the material.

[0062] It is understandable that since the damping effect of most materials is small, if the complex influence of damping is considered comprehensively and carefully in the process of calculating Young's modulus, many additional parameters and complex mathematical operations will be introduced. For example, it is necessary to accurately measure the change relationship of the damping coefficient with time, temperature and other factors, and to incorporate these changes into the calculation formula of Young's modulus derived from vibration theory, which will undoubtedly greatly increase the difficulty and workload of the calculation;

[0063] Substituting the approximate value of the ideal natural bending frequency directly into the coefficient function formula simplifies the calculation process without significantly affecting the calculation accuracy of the final Young's modulus. This is because when the damping is small, ignoring its more subtle changes to the vibration frequency and the chain reaction in the subsequent calculation process, the result can still meet the accuracy requirements of actual application scenarios such as engineering design and material performance evaluation.

[0064] Specifically, the coefficient function in S500 is The formulas are:

[0065]

[0066] Specifically, the relationship between the low-order ideal natural bending vibration frequency and the first-order ideal natural longitudinal telescopic vibration frequency f of a square-section rod (10 < h / l < 100) is established in the S600, and the parameters are substituted into the following formula: β1 and substitute the parameters into the following formula:

[0067]

[0068] where f α2 (Hz) is the second-order natural bending vibration frequency of the square-section rod; f α3 (Hz) is the third-order natural bending vibration frequency of the square-section rod; h (m) is the rod length; l (m) is the side length of the square section; m (kg) is the mass of the square-section rod; E α2 and E α3 are ideal isotropic materials.

[0069] Specifically, signal filtering processing is performed on the signal acquired by the microphone.

[0070] Specifically, the collected digital signal is input into a designed filter for filtering operation. The discrete Fourier transform algorithm is used to convert the time-domain signal to the frequency domain, then the signal is filtered in the frequency domain, and finally the filtered frequency-domain signal is converted back to the time domain through inverse transformation.

[0071] Specifically, the filtered signal is subjected to spectral analysis again, compared with the spectrogram before filtering, and the improvement degree of the signal-to-noise ratio of the signal before and after filtering is calculated. By comparing the ratio of the signal power to the noise power before and after filtering, the improvement effect of the filtering process on the signal quality is quantitatively evaluated.

[0072] As can be seen from the above, the signal acquired by the microphone often contains various noise interferences, such as environmental noise, electromagnetic interference, etc. These noises will reduce the signal quality and affect the accurate identification of the second-order and third-order damping bending vibration frequencies subsequently. Through signal filtering processing, these noises can be effectively removed.

[0073] Furthermore, for the vibration signal of a square-section rod, after being converted to the frequency domain by discrete Fourier transform (DFT), the amplitude magnitudes of each frequency component can be clearly seen. Among them, the frequency components corresponding to the second-order and third-order damping bending vibration frequencies will show specific peaks in the frequency domain.

[0074] It is understandable that by comparing the signal-to-noise ratio before and after filtering, we can clearly understand the improvement effect of filtering on signal quality. If the signal-to-noise ratio is significantly improved, it means that the filtering method has effectively removed noise interference and improved the quality of the signal. This is crucial for accurately calculating Young's modulus, because a signal with a high signal-to-noise ratio can reduce errors and improve the accuracy of the calculation results.

[0075] Specifically, in addition to considering noise interference, the possible sources of error should also be analyzed. The accuracy error of the measurement tool and the error caused by the change in microphone position should be considered to evaluate each error source and determine its impact on the calculation results of Young's modulus.

[0076] From the above, we can see that by analyzing the errors caused by the accuracy errors of the measurement tools and the changes in the microphone position in detail, we can clearly understand the specific impact of each error source on the experimental results. For example, we can understand how much deviation the Young's modulus calculation results will cause when the accuracy error of the frequency measurement equipment is within a certain range, and the quantitative impact of the slight movement or angle change of the microphone position on the measurement results.

[0077] It is understandable that based on the evaluation of the error, targeted measures can be taken to reduce the error, thereby improving the accuracy and reliability of the experiment. If it is found that the insufficient accuracy of the measuring tool is one of the main sources of error, it can be considered to replace the measuring tool or measuring equipment with higher accuracy; if the change in microphone position has a greater impact, a more stable fixture can be designed to ensure the consistency of the microphone position, thereby improving the accuracy of the Young's modulus measurement.

[0078] Specifically, an error correction model is established based on the results of error analysis. If the accuracy error of the measuring tool is linearly related, it is corrected through linear regression method. If the error is caused by changes in microphone position, the relationship model between position and signal characteristics is established by measuring the signals at different positions multiple times to compensate for the error.

[0079] Specifically, the measurement tool accuracy error correction based on the linear relationship:

[0080] First, you need to collect a certain amount of measurement sample data, which should include the values ​​measured by the measuring tool and the corresponding accurate standard values ​​(the standard values ​​can be obtained through higher-precision measuring tools or known standard samples). For example, for a caliper that measures the side length of a square cross-section rod, use it to measure a series of standard rods with known accurate side lengths, and record the caliper measurement value and the actual side length value of the standard rod.

[0081] The collected data are sorted, with the measured value as the independent variable x, and the difference between the measured value and the standard value (i.e. error) as the dependent variable y. A linear regression algorithm (such as the common least squares method) is used to fit a straight line equation y=ax+b, where a and b are the slope and intercept of the regression line, respectively, which reflect the law of error changing with the measured value.

[0082] When the measuring tool is used for actual measurement later, the measured value x new , calculate the corresponding error estimate y based on the fitted straight line equation new , then the measured value x new Subtract the error estimate y new , we get a result that is closer to the true value after error correction.

[0083] Specifically, microphone position variation error compensation based on the relationship between position and signal characteristics:

[0084] In the experimental environment of the square cross-section rod, the position of the microphone is systematically changed (it can be arranged according to a certain coordinate grid, angle interval, etc.), and the corresponding vibration sound pressure signal is collected at each position. For each position, the specific position parameters of the microphone (such as the distance from the rod, the relative angle, etc.) and the collected signal characteristics are recorded. The signal characteristics can include the amplitude of the time domain waveform, the amplitude of the key vibration frequency in the frequency domain, etc.

[0085] Using the collected multiple sets of position parameters and the corresponding signal feature data, a relationship model between the two is established using appropriate mathematical methods (such as multiple regression analysis, neural network, etc., selected according to the characteristics of the data). For example, if it is found that the signal amplitude is inversely proportional to the distance from the microphone to the pole and is directly proportional to the cosine value of the relative angle, a mathematical expression containing these variables can be constructed to describe this relationship.

[0086] When actually measuring the Young's modulus, record the actual position parameters of the microphone and substitute them into the established relationship model to calculate the degree of influence of the position change on the signal. Then, make a reverse adjustment to the collected signal to eliminate the error caused by the position change and make the signal as close as possible to the actual signal collected at the standard position. Then, perform subsequent operations such as vibration frequency identification and Young's modulus calculation.

[0087] Specifically, a mechanical model of a square cross-section rod is established using the finite element analysis and numerical simulation method. This is used to predict the vibration characteristics and Young's modulus of the square cross-section rod under different conditions. The Young's modulus obtained from experimental measurements is compared with the numerical simulation results, the difference between the two is analyzed, and the experimental method and numerical model are adjusted and optimized.

[0088] Specifically, by comparing the Young's modulus obtained by experimental measurement with the numerical simulation results, if the two are relatively close, it means that the experimental method is reliable and can accurately measure the Young's modulus of the material. On the contrary, if the difference is large, it indicates that there may be problems in the experimental process, such as improper use of measurement tools, errors in signal acquisition and processing, or inadequate consideration of some influencing factors, which prompts careful inspection and improvement of the experimental method.

[0089] It is understandable that the comparison results can also reflect the rationality of the construction of the numerical model. If the numerical simulation results deviate significantly from the experimental measurement values, it may mean that the model simplification is unreasonable during geometric modeling, the material property assignment is inaccurate, or the boundary conditions are inconsistent with the actual situation. This requires re-examination and adjustment of the relevant settings of the numerical model to make it more in line with the actual situation and improve the accuracy and credibility of the numerical simulation.

[0090] Specifically, on the basis of filtering processing, signal enhancement techniques such as signal amplification and deconvolution are combined to further improve the quality of the signal.

[0091] It is understandable that when performing relevant measurements on square cross-section rods, although filtering can remove most of the noise interference and make the signal more "pure" in the frequency domain and time domain, there may still be some problems with the original signal that affect the subsequent accurate extraction of key information such as vibration frequency and the precise calculation of Young's modulus. For example, the amplitude of the useful signal may be small, resulting in the peaks corresponding to some characteristic frequencies on the spectrum graph not being prominent enough; or because the signal undergoes a certain degree of distortion during the propagation and acquisition process, the real information it contains is obscured. At this time, the signal high enhancement technology can further explore and highlight the useful components in the signal on the basis of filtering, improve the signal quality, and provide better data support for subsequent analysis.

[0092] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the invention disclosed herein. The present application is intended to cover any variations, uses or adaptations of the present application, which follow the general principles of the present application and include common knowledge or customary techniques in the art that are not disclosed in the present application. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present application are indicated by the following claims.

[0093] It should be understood that the present application is not limited to the precise structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. A method for calculating the Young's modulus of a square cross-section rod, characterized in that: The following steps are involved: S100: Use high-precision measuring tools to obtain the cross-sectional side length, length, and mass information of the sample; S200: A professional microphone is used to obtain the time domain sound pressure signals in two support states; S300: Convert the time domain sound pressure signal into a frequency domain signal and identify the second-order damped bending vibration frequency on its spectrum diagram and the third-order damped bending vibration frequency S400: Ignore the damping effect, that is S500: Calculate h / l and substitute it into the formula to get the coefficient function S600: The coefficient and side length l, length h, mass m, second-order ideal natural bending vibration frequency f α2 and the third-order ideal natural bending vibration frequency f α3 Substitute into the formula to obtain its Young's modulus value E α2 、E α3 ; S700: Calculate the average Young's modulus E Avg =(E α2 +E α3 ) / 2.

2. The method for calculating the Young's modulus of a square cross-section rod according to claim 1, characterized in that: The second-order damped natural bending vibration frequency of the sample material measured under two support states is and the third-order damped natural bending vibration frequency Directly substitute into the coefficient function formula to calculate the Young's modulus of the material.

3. The method for calculating the Young's modulus of a square cross-section rod according to claim 1, characterized in that: The coefficient function in S500 The formulas are:

4. The method for calculating the Young's modulus of a square cross-section rod according to claim 1, characterized in that: In the step S600, the low-order ideal natural bending vibration frequency and the first-order ideal natural longitudinal stretching vibration frequency f of the square cross-section rod are established. β1 The relationship between them is shown in Figure 1, and the parameters are substituted into the following formula: Among them, f α2 (Hz) is the second-order natural bending vibration frequency of the square cross-section rod; f α3 (Hz) is the third-order natural bending vibration frequency of the square cross-section rod; h (m) is the rod length; l (m) is the side length of the square cross-section; m (kg) is the mass of the square cross-section rod; E α2 、E α3 They are the Young's modulus values ​​of the materials measured at different bending frequencies, and their values ​​are approximately the same for the same material.

5. The method for calculating the Young's modulus of a square cross-section rod according to claim 1, characterized in that: Perform signal filtering on the signal obtained by the microphone.

6. The method for calculating the Young's modulus of a square cross-section rod according to claim 5, characterized in that: The collected digital signal is input into the designed filter for filtering operation, the discrete Fourier transform algorithm is used to convert the time domain signal to the frequency domain, and then the signal is filtered in the frequency domain, and finally the filtered frequency domain signal is converted back to the time domain through inverse transformation.

7. The method for calculating the Young's modulus of a square cross-section rod according to claim 6, characterized in that: The filtered signal is analyzed again by spectrum analysis and compared with the spectrum before filtering. The degree of improvement in the signal-to-noise ratio of the signal before and after filtering is calculated. By comparing the ratio of signal power to noise power before and after filtering, the effect of filtering on improving signal quality is quantitatively evaluated.

8. The method for calculating the Young's modulus of a square cross-section rod according to claim 1, characterized in that: Analyze the existing error sources. In addition to considering noise interference, it is also necessary to consider the accuracy error of the measurement tool and the error caused by the change of the microphone position. Evaluate each error source and determine its influence on the calculation result of Young's modulus.

9. The method for calculating the Young's modulus of a square cross-section rod according to claim 8, characterized in that: An error correction model is established based on the results of error analysis. If the accuracy error of the measuring tool is linear, it is corrected through linear regression method. If the error is caused by the change of microphone position, the relationship model between position and signal characteristics is established by measuring the signals at different positions multiple times to compensate for the error.

10. The method for calculating the Young's modulus of a square cross-section rod according to claim 1, characterized in that: A mechanical model of a square cross-section rod is established using the finite element analysis and numerical simulation method. This model is used to predict the vibration characteristics and Young's modulus of the square cross-section rod under different conditions. The Young's modulus obtained by experimental measurement is compared with the numerical simulation results, the difference between the two is analyzed, and the experimental method and numerical model are adjusted and optimized.

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