Axial force identification method based on the frequency ratio method of rigid rod

Abstract

The present invention discloses a method for identifying axial forces of rigid rods using a frequency ratio method. The steps are as follows: (1) Based on engineering data, determine whether the rigid rod is a compression rod or a tension rod, and obtain relevant parameters of the rigid rod: the rigid rod linear density m, the rigid rod length L, and the rigid rod bending stiffness EI; (2) Use a vibration sensor to collect the vibration signal of the rigid rod on-site and analyze the multi-order frequencies of the rigid rod; (3) Select a corresponding method to calculate the frequency ratio of the rigid rod based on whether the rigid rod is a compression rod or a tension rod and the boundary conditions, and calculate the axial force of the rigid rod using the frequency ratio method; (4) Verify the relative bending stiffness ξ of the rigid rod and evaluate the accuracy of the axial force identification of the rigid rod. The method of the present invention establishes a unified calculation method for identifying the axial forces of rigid tension rods and compression rods using the frequency ratio method. The method is easy to use and has good accuracy, providing a practical new method for identifying the axial forces of rigid rods.

Description

Technical Field

[0001] The invention belongs to the field of engineering technology and relates to a method for identifying an axial force of a rigid rod, in particular to a method for identifying an axial force of a rigid rod using a frequency ratio method. Background Art

[0002] In beams and long-span spatial structures, rigid rods are critical load-bearing components, and their safety performance determines the overall structural safety. Rigid rods are often made of steel tubes or steel sections. They generally bear tension, but can also partially experience compression under live loads. Steel is known for its excellent tensile and compressive properties, but improper design of compressive rods can lead to overall or localized instability. Therefore, when conducting bridge load tests, it is crucial to employ appropriate technical methods to assess the stability and safety factor of compressive components, particularly to accurately identify the axial forces borne by bridge hangers. Identifying the axial forces in rigid rods is crucial for ensuring the safety and stability of cable-strut bridge structures. Axial force measurement is performed using various techniques in engineering and scientific research. Currently, the main axial force testing methods include hydraulic pressure gauges, pressure sensors, magnetic flux methods, and frequency methods. The jack oil pressure gauge reading method and pressure sensor method are only suitable for monitoring axial forces during the construction phase. The magnetic flux method, however, requires on-site installation of magnetic flux sensors for axial force testing on operational bridges, which is complex and unsuitable for large-scale axial force testing. The frequency method can be flexibly used in axial force detection of bridges at all stages. It is easy to operate and has high accuracy. Currently, most projects use the frequency method to detect axial forces on bridges.

[0003] Methods for calculating axial forces from rigid rod frequencies can be broadly categorized into model methods (finite element models, theoretical models) and formula calculation methods. Model methods can better account for the rigid rod's boundary conditions, intermediate supports, and other factors, but they generally require computer programming.

[0004] The formula calculation method requires the establishment of an explicit relationship between the axial force and the natural frequency. The frequency characteristic equation is established through the vibration differential equation of the rigid rod, and the equation is solved according to the boundary conditions. When the boundary of the rigid rod is hinged at both ends, an explicit expression of the axial force and frequency can be obtained. However, when the boundary conditions of the rigid rod are consolidated at both ends or consolidated-hinged, the frequency equation obtained is a transcendental equation, and it is difficult to obtain an explicit expression of the axial force and frequency. In response to this problem, Gong Lingling combined the basic principles of the vibration frequency method and the finite element method to determine the relationship between the axial force and frequency of the compression rod. Ai Yongzhen compiled a corresponding MATLAB optimization calculation program based on the correspondence between the axial force and the natural frequency of the rod. Substituting the measured frequency into the program can obtain the axial force and boundary stiffness. When Zhang Jing used the frequency method to test the axial force of the grid structure rod, he comprehensively considered the rod frequency test under the influence of multiple factors. By establishing a fitting equation between the measured frequency data of the rod and the actual axial force, he determined the relationship between the rod frequency and the axial force.

[0005] Compression bars are a common structural component in cable-strut bridges. Improper handling of compressive bars can lead to global or local instability, which can have serious consequences. Currently, research on frequency methods primarily focuses on tensioned cables, while relatively little research has applied this approach to identifying axial forces in compression bars. Therefore, simply measuring and determining the axial forces in rigid bars has become a key issue. Summary of the Invention

[0006] Aiming at the problem of rigid rod axial force identification using frequency method, the present invention proposes a rigid rod axial force identification method using frequency ratio method.

[0007] The present invention provides a method for identifying axial force using a rigid rod frequency ratio method, comprising the following steps:

[0008] (1) According to the engineering data, determine whether the rigid rod is a compression rod or a tension rod, and obtain the relevant parameters of the rigid rod: rigid rod linear density m, rigid rod length L, and rigid rod bending stiffness EI;

[0009] (2) The vibration signal of the rigid rod is collected on-site by a vibration sensor, and the frequency of the rigid rod is obtained by analysis;

[0010] (3) Select the appropriate method to calculate the axial force of the rigid rod according to whether it is a compression rod or a tension rod and the boundary conditions;

[0011] a) For a consolidated rigid bar, the frequency ratio and axial force are calculated as follows:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017] Where m, L, EI and T are the linear density, length, bending stiffness and axial force of the rigid rod respectively, z n is the ratio of the nth order frequency of the consolidation and the rigid rod hinged at both ends, f n is the nth order natural frequency of the rigid rod, ξ is the relative bending stiffness, when calculating the axial force of the rigid compression rod, use the calculation formula with ξ<0, when calculating the axial force of the rigid tension rod, use the calculation formula with ξ>0;

[0018] b) For a fixed-hinged rigid rod, the frequency ratio formula and axial force are calculated using the following method:

[0019]

[0020]

[0021]

[0022] (4) Calculate the relative bending stiffness ξ of the rigid rod:

[0023]

[0024] When the ξ of the rigid tie rod is greater than 6.9, the formula of this method is not applicable, and the relevant method in the existing literature is used for calculation; when the range is -2≤ξ≤2, the axial force of the rod is small. Although the relative error of the calculated axial force will exceed 4%, the absolute error is not large, and the calculation results of the formula are also applicable.

[0025] Specifically, in step (2), only one vibration sensor measurement point needs to be arranged, and the vibration sensor adopts an acceleration sensor, a velocity sensor or a displacement sensor.

[0026] Specifically, in step (2), only one vibration sensor measurement point needs to be arranged, and the vibration sensor uses an acceleration sensor, a velocity sensor, and a displacement sensor.

[0027] Specifically, in step (2), the vibration signal is used to identify the frequency of the cable using one of the peak method, power spectrum method, random subspace method, and random decrement method. For the rigid pull rod, at least the first order frequency is identified, and for the rigid compression rod, at least the first two order frequencies are identified.

[0028] Specifically, in step (2), the multi-order frequencies of the cable are in-plane vibration frequencies or out-of-plane vibration frequencies.

[0029] The beneficial effects of the present invention are as follows: Taking rigid rods as the research object, the present invention proposes a practical method for identifying axial forces in rigid rods using the frequency ratio method. Starting from the two aspects of frequency ratio and boundary conditions, the present invention uses linear regression to obtain a formula for calculating axial forces based on the frequency ratio, given the rigid rod stiffness and multiple natural frequencies. This establishes a simple and physically clear axial force formula, providing an explicit relationship between axial force and frequency. The method is verified through calculation examples and engineering examples, and its accurate axial force calculation provides a practical new method for identifying axial forces (tension or compression) in rigid rods. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart of the axial force identification method using the rigid rod frequency ratio method of the present invention.

[0031] Figure 2 It is the coordinate system of the rigid pull rod of the present invention.

[0032] Figure 3 It is the general boundary of the pull rod of the present invention.

[0033] Figure 4 It is the coordinate system of the rigid compression rod of the present invention.

[0034] Figure 5 The present invention is a fixed rigid rod y n -z n Relationship curve.

[0035] Figure 6 The invention is a solid-hinged rigid rod y n -z' n Relationship curve.

[0036] Figure 7 1 is a diagram of the axial force error of the rigid rods at the consolidation boundary and the consolidation-hinged boundary according to the first embodiment of the present invention.

[0037] Figure 8 This is the main bridge layout diagram of the hangers of the West Bridge of Sanshan Mountain in Example 2 of the present invention (unit: m). DETAILED DESCRIPTION

[0038] The present invention will be further described below with reference to the accompanying drawings and embodiments. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements.

[0039] Figure 1 This is a flow chart of the axial force identification method using the rigid rod frequency ratio method of the present invention.

[0040] The rigid rod frequency ratio method axial force identification method of the present invention has the following specific steps:

[0041] (1) According to the engineering data, determine whether the rigid rod is a compression rod or a tension rod, and obtain the relevant parameters of the rigid rod: rigid rod linear density m, rigid rod length L, and rigid rod bending stiffness EI;

[0042] (2) The vibration signal of the rigid rod is collected on-site by a vibration sensor, and the frequency of the rigid rod is obtained by analysis;

[0043] (3) Select the appropriate method to calculate the axial force of the rigid rod according to whether it is a compression rod or a tension rod and the boundary conditions;

[0044] (4) Verify the relative bending stiffness ξ of the rigid rod and evaluate the accuracy of the axial force identification of the rigid rod.

[0045] 1. Theoretical solution of free vibration of rigid rod

[0046] 1.1 Theoretical solution of free vibration of tie rod

[0047] For a rigid tie rod, the coordinate system is as follows Figure 2, ignoring the influence of its sag and damping, formula (1) is the free vibration equation of the rod.

[0048] (1)

[0049] Where u is the displacement of each point on the tie rod at time t; m, L, EI and T are the linear density, length, bending stiffness and tension of the tie rod, respectively, all of which are constants and do not change with time and position.

[0050] The formula is solved by separation of variables method, and the general solution is:

[0051] (2)

[0052] (3)

[0053] Where: A i (i=1,2,3,4) are the unknown coefficients related to the boundary conditions, and ω is the circular vibration frequency of the pull rod.

[0054] When both ends of the tie rod are elastically supported, their boundaries are as follows Figure 3 As shown, the boundary conditions are:

[0055] (4)

[0056] Where: k1 and k3 are the vertical support stiffness at both ends of the tie rod, and k2 and k4 are the rotational constraint stiffness at both ends of the tie rod.

[0057] For the boundary conditions of hinged ends, k1=k3=∞, k2=k4=0, the frequency equation is:

[0058] (5)

[0059] At the same time, the explicit relationship between the tension of the cable and the frequency when both ends are hinged can be obtained:

[0060] (6)

[0061] (7)

[0062] In formula (7): f n is the nth order natural frequency of the tie rod.

[0063] For the boundary conditions of one end fixed and the other end hinged, k1=k3=∞, k2=∞, k4=0, the frequency equation is:

[0064] (8)

[0065] For the boundary conditions of consolidation at both ends, k1=k3=k2= k4=∞, the frequency equation is:

[0066] (9)

[0067] When the two ends of the tie rod have arbitrary rotational stiffness, k1=k3=∞, and Equation (4) is substituted into Equation (2) to obtain the frequency equation:

[0068] (10)

[0069] Substituting the physical parameters of the tie rod into equations (6), (8) and (9), we can obtain the circular vibration frequency ω of the tie rod when both ends are hinged, fixed-hinged and fixed at both ends, respectively: nss 、ω nfh and ω nff ; n is the nth order natural frequency of the tie rod; Equations (8), (9) and (10) are transcendental equations, so no explicit solution can be obtained.

[0070] 1.2 Theoretical solution of free vibration of compression rod

[0071] For a compression rod, the coordinate system is as follows Figure 4 , ignoring the influence of its sag and damping, Equation (11) is the free vibration equation of the compression rod.

[0072] (11)

[0073] Where u is the displacement of each point on the compression rod at time t; m, L, EI, and N are the linear density, length, bending stiffness, and applied pressure of the compression rod, respectively. These are all constants that do not vary with time or position. For ease of subsequent analysis, T is used to represent the axial force. A positive T value indicates tension, while a negative T value indicates compression. In other words, when the axial force is compressive, N is expressed as N = -T.

[0074] The formula is solved by separation of variables method, and the general solution is:

[0075] (12)

[0076] (13)

[0077] Where: A i (i=1,2,3,4) are the unknown coefficients related to the boundary conditions, and ω is the circular vibration frequency of the compression rod.

[0078] For the boundary conditions of hinged ends, k1=k3=∞, k2=k4=0, the frequency equation is:

[0079] (14)

[0080] At the same time, the explicit relationship between the axial force of the compression rod and the frequency when both ends are hinged can be obtained:

[0081] (15)

[0082] (16)

[0083] In formula (16): f n is the nth order natural frequency of the compression rod.

[0084] For the boundary conditions of consolidation at both ends, k1=k3=k2= k4=∞, the frequency equation is:

[0085] (17)

[0086] For the boundary conditions of one end fixed and the other end hinged, k1=k3=∞, k2=∞, k4=0, the frequency equation is:

[0087] (18)

[0088] Substituting the physical parameters of the compression rod into equations (14), (17), and (18), we can obtain the circular vibration frequency ω of the compression rod when both ends are hinged, both ends are consolidated, and consolidated-hinged, respectively: nss 、ω nff and ω nfh ; n is the nth natural frequency of the compression rod; Equations (17) and (18) are transcendental equations, so no explicit solution can be obtained.

[0089] 2. Critical force of compression rod

[0090] When analyzing the axial force of a compression rod using the frequency method, only the case where the axial force is less than the critical force of the compression rod needs to be analyzed. When the axial force of the compression rod exceeds the critical force, the compression rod has become unstable, and the axial force identification of the compression rod at this time is meaningless. The Euler formula for calculating the critical force of a compression rod with hinged ends and the length coefficient μ are introduced. μ represents the length ratio of the compression rod under different boundary conditions to the hinged compression rod at both ends. The unified formula for the critical force of the compression rod is expressed as:

[0091] (19)

[0092] The values ​​of μ under different boundary conditions are as follows:

[0093] Table 1 Compression rod length coefficient

[0094]

[0095] 3. Frequency ratio analysis of rigid rods under different boundaries

[0096] 3.1 Relationship between frequency ratio and relative stiffness

[0097] According to the frequency equations under different boundaries given by the theoretical formula of tension rod vibration, the vibration circular frequency ω of the tension rod when both ends are hinged, consolidated-hinged and both ends are consolidated can be obtained by solving it. nss 、ω nfh and ω nff .

[0098] Combining equations (9) and (5) yields the frequency ratio z of the fixed tie rods at both ends to the hinged tie rods at both ends: n See formula (20).

[0099] (20)

[0100] Combining equations (8) and (5) yields the theoretical frequency ratio of the consolidation-hinged tie rod to the two-end hinged tie rod: As shown in formula (21).

[0101] (twenty one)

[0102] The relative stiffness ξ is introduced in Equation (22). This parameter comprehensively considers the effects of the tension, length, and bending stiffness of the cable. Using the frequency equation solver developed in MATLAB, the frequency values ​​of the cable are calculated for the same relative stiffness ξ but different cable lengths, cable forces, and bending stiffnesses. Substituting these frequency values ​​into Equations (20) and (21) yields the frequency ratio.

[0103] (twenty two)

[0104] Taking the tie rods with two-end consolidation and consolidation-hinged boundaries as an example, the relative stiffness ξ of the tie rods ranges from 13 to 36. The physical parameters of the tie rods are shown in Table 2. The calculated frequency results under different boundary conditions are shown in Tables 3 to 5. The frequency ratios under two-end consolidation and consolidation-hinged boundaries are shown in Tables 6 and 7.

[0105] Table 2 Tie rod parameters

[0106]

[0107] Table 3 The first five frequencies under the two-end consolidation boundary conditions (Hz)

[0108]

[0109] Table 4 The first five frequencies under consolidation-hinged boundary conditions (Hz)

[0110]

[0111] Table 5 The first five frequencies under the two-end hinge boundary conditions (Hz)

[0112]

[0113] Table 6 Frequency ratio of the consolidation boundaries at both ends

[0114]

[0115] Table 7 Consolidation-hinged boundary frequency ratio

[0116]

[0117] According to the results in Tables 6 and 7, under the boundary conditions of consolidation at both ends and consolidation-hinging, as long as the relative stiffness ξ is the same, the frequency ratio is the same even if the physical parameters of the tie rods are different. This proves that the frequency ratio is unique to the relative stiffness ξ. That is, no matter how the tie rod length, tension, and bending stiffness are adjusted, the frequency ratio will not change as long as the relative stiffness ξ of the tie rod remains unchanged.

[0118] 3.2 Frequency analysis of rigid rods under different boundary conditions

[0119] Similarly, the relative stiffness ξ is used to comprehensively consider the axial force, rod length and bending stiffness of the compression rod. Unlike the tension rod, the pressure is less than 0, and the calculation of ξ is shown in formula (23). Taking the compression rod with two ends consolidated and consolidated-hinged boundary as an example, when the compression rod is in the critical state, the critical relative stiffness ξ can be obtained by substituting formula (19) into formula (23): cr , see formula (24).

[0120] (twenty three)

[0121] (twenty four)

[0122] After simplifying equation (24), we can get the two-end consolidated compression rod , consolidated-hinged compression strut , hinged pressure rods at both ends , these three values ​​are constant and will not change with the physical parameters of the pressure rod. Therefore, when analyzing the pressure, only the value of ξ is studied. cr ~0. In the previous section, it has been proved that the frequency ratio and the calculation error of the formula are unique to the relative stiffness ξ. Therefore, when studying the suspenders with different relative stiffness ξ, the present invention only needs to change the axial force without changing other physical parameters. cr The parameters of the hanger within the range of ≤ξ≤6.9 are shown in Table 8 (Note: when ξ>6.9, there is a corresponding cable force calculation formula). The first six natural frequencies of the hanger under the boundary conditions of consolidation at both ends and consolidation-hinged are shown in Tables 9 to 11.

[0123] Table 8 Boom parameters

[0124]

[0125] Table 9 The first six frequencies under the consolidation boundary at both ends of the hanger (Hz)

[0126]

[0127] Table 10 The first six frequencies under the hanger consolidation-hinged boundary (Hz)

[0128]

[0129] Table 11 The first 6 frequencies at the hinged boundary at both ends of the boom (Hz)

[0130]

[0131] There are two special cases in Tables 9 to 11. First, when the axial force of the compression rod under the three boundary conditions is equal to the critical force, the first-order frequency is equal to 0. In particular, when the axial force of the compression rod hinged at both ends is equal to 4 times the critical force, the second-order frequency will also be 0. Second, for the compression rod hinged at both ends, when the pressure exceeds the critical force, <0, the first-order frequency obtained at this time is an imaginary number, which is replaced by a horizontal line in the table.

[0132] 4. Axial force calculation formula based on frequency ratio

[0133] When m, L, EI and T are known, the dimensionless parameter y is proposed n See formula (25), combining formula (14) and formula (17) to obtain the frequency ratio z of the cable with two ends fixed and the cable with two ends hinged n The same as formula (20), combined with formula (14) and formula (18), can obtain the theoretical frequency ratio of the consolidation-hinged compression rod and the two-end hinged compression rod: Same as formula (21).

[0134] (25)

[0135] Tables 12 to 15 below list the relative stiffness ξ cr In the range of ≤ξ≤6.9, under the boundary conditions of consolidation at both ends and consolidation-hinged n The above frequency data may have special cases of 0 or imaginary numbers. The frequency of 0 will cause y n It is meaningless to discuss the frequency ratio of the boom when the frequency is an imaginary number, so the frequency ratio is not discussed for these special cases, and these abnormal values ​​are filled with horizontal lines in the table.

[0136] Table 12 y of the consolidation boundary hangers at both ends n and frequency ratio z n (n=1,2,3)

[0137]

[0138] Table 13 y of the two-end consolidation boundary hangers n and frequency ratio z n (n=4,5,6)

[0139]

[0140] Table 14 y of the consolidation-hinged boundary hanger n and frequency ratio (n=1,2,3)

[0141]

[0142] Table 15 y of the consolidation-hinged boundary hanger n and frequency ratio (n=4,5,6)

[0143]

[0144] According to the y calculated in Tables 12 to 15 n The value and the ratio of each frequency order will be used to fit the relationship between frequency and axial force.

[0145] 4.1 Fitting of the two-end consolidation axial force formula

[0146] Figure 5 The ratio of the frequencies of the above-mentioned booms to y n The relationship curve of y is shown in the figure. The first-order frequency ratio and the second-order frequency ratio increase with y. n The change of is a curve; as the order increases, the frequency ratio of each order changes with y n The change is closer to a straight line, and there is no sudden change in the 6 line segments. n -z n Polynomial fitting of the relationship.

[0147] When using the first-order frequency and the second-order frequency for calculation, because the frequency ratio of some ξ values ​​appears abnormal during calculation, for the relationship between y1 and z1, only the booms with ξ between 0 and 6.9 are used for fitting. The functional relationship between y1 and z1 is:

[0148] (26)

[0149] When analyzing the second-order frequency ratio, when the 1st to 25th booms are selected for fitting, the fitting formula accuracy is poor, so it is possible to consider segmented fitting. The fitting formulas are shown in Equations (27) and (28).

[0150] When 0<ξ≤6.9:

[0151] (27)

[0152] When -5.88≤ξ<0:

[0153] (28)

[0154] The fitting formulas for the first two orders are polynomial fitting, and the y n -z n The relationship fits the same principle, and the boom frequency ratio of -6.28≤ξ≤6.9 can be calculated as follows:

[0155] (29)

[0156] The frequency ratio is calculated according to equations (26) to (29), and the axial force calculation formula (30) of the consolidation boundary hangers at both ends is obtained.

[0157] (30)

[0158] 4.2 Fitting of the consolidation-hinged axial force formula

[0159] Figure 6 The ratio of the frequencies of the above-mentioned booms to y n The relationship curve of Figure 6 It can be seen that the same situation occurs when one end is fixed and the other end is hinged as when both ends are fixed. The ratio of the first-order frequency and the ratio of the second-order frequency increase with y. n The change of is a curve, and as the order increases, the curve tends to be flat, closer to a straight line. There is no sudden change in the 6 line segments, so the same quadratic polynomial can be used to Fitting the relationship.

[0160] However, when using the first-order frequency for calculation, the frequency ratio of some ξ values ​​will have abnormal values, so for Only the booms with ξ between 0 and 6.9 are fitted, and for booms with ξ greater than the first order When calculating the relationship, the boom with ξ between -4.49 and 6.9 is selected for fitting.

[0161] For the first-order frequency ratio see Figure 6 , when 0<ξ≤6.9, the formula is as follows:

[0162] (31)

[0163] For frequency ratios of other orders see Figure 6 , can fit the boom with -4.49≤ξ≤6.9 Relationship, the fitting formula is:

[0164] (32)

[0165] The frequency ratio is calculated according to formulas (31) and (32), and then the axial force calculation formula (33) of the consolidation-hinged boundary hanger is obtained.

[0166] (33)

[0167] Example 1: Consolidated Boundary and Consolidated-Hinged Boundary Rigid Bars

[0168] To verify the accuracy of the axial force calculation formula for the rigid rod, the suspender rod in Table 8 was selected and the frequency data in Tables 9 and 10 were used for calculation.

[0169] Step 1: According to the engineering data, obtain the relevant parameters of the suspender: suspender linear density m, suspender length L, suspender bending stiffness EI, as shown in Table 8.

[0170] Step 2: For the actual boom, an acceleration vibration sensor measuring point can be arranged at the lower end of the boom to measure the vibration frequency in the boom plane. The peak value method is used to identify the multi-order frequencies of the boom using the vibration signal. The first 6 frequencies of the boom are identified as shown in Tables 9 and 10. The boom frequency of this embodiment is obtained through finite element simulation analysis.

[0171] Step 3: According to the fundamental frequency and related parameters of the boom, combined with the data in Table 9 and Table 10, select the corresponding f n With z n The axial force T is calculated from the value of . The calculation results are shown in Tables 16 and 17. In the table, T0 is the actual axial force, T n is the axial force calculated using the nth frequency.

[0172] Table 16 Axial force calculation results (consolidation at both ends)

[0173]

[0174] Table 17 Axial force calculation results (consolidation-hinged)

[0175]

[0176] Step 4: Verify the relative bending stiffness ξ of the rigid rod. Based on the hanger rod parameters in Table 8, the bending stiffness in this example meets the requirements. Next, calculate the relative error based on the axial force obtained from the formula. The results are shown in Tables 18 and 19.

[0177] Table 18 Relative error of the two-end consolidation hanger (%)

[0178]

[0179] Table 19 Relative error of consolidation-hinged hanger (%)

[0180]

[0181] The gray background data in the table indicates that the error exceeds 4%. The line graph of the axial force error of the boom in Table 16 and Table 17 is shown in Figure 16. Figure 7 .

[0182] It can be seen from the figure that when the relative stiffness is in the range of -2≤ξ≤2, the relative errors of the axial forces of the two boundary hangers are relatively large; the maximum error is 12.81% when the two ends are consolidated, and the maximum error is 4.05% when the consolidation is hinged. At this time, the true axial forces of the two are -15503N and 15000N respectively. Although the absolute errors are only 1986N and 607N, they will cause the relative errors to be relatively large. Overall, when the relative stiffness ξ is far away from 0, the axial force calculation formulas (30) and (33) of the two boundaries are more accurate, and the errors are mostly less than 3%.

[0183] Example 2: Sanshan West Bridge Suspension Rod

[0184] The span combination of Sanshan West Bridge is 45m+200m+45m, and the total length of the bridge is 290m. It is a steel tube concrete arch bridge. The main beam of the bridge has 33 pairs of hangers with a spacing of 5m. The specific structural form is as follows Figure 8 shown.

[0185] Step 1: Based on the engineering data, the shortest hanger C33 is selected for analysis. Its physical parameters are shown in Table 20. The hanger is only 2.56m long and has high stiffness. It can be regarded as a tie rod with two ends.

[0186] Table 20 Physical parameters of boom

[0187]

[0188] Step 2: To obtain the boom frequency, it is necessary to artificially excite it. The multi-order natural frequencies of the cable are determined by identifying the peaks in the amplitude spectrum of the recorded acceleration time history. The first two frequencies are shown in Table 21.

[0189] Step 3: Calculate the frequency ratio and axial force of the suspender rod based on the frequency and related parameters of the rigid tie rod.

[0190] Table 21 compares the tension results calculated by the proposed method and Huang (Formula (34)). For the C33 hanger, the cable tension results obtained by Formula (34) are inaccurate, with the minimum error reaching 5%. However, the cable tension obtained by the proposed method using the fundamental frequency is relatively accurate, with a relative error of less than 1%. This shows that the proposed method has good accuracy when calculating short cables (relative stiffness ξ is small), and the calculation is more concise and convenient.

[0191] (34)

[0192] (35)

[0193] (36)

[0194] Table 21 Calculation results

[0195]

[0196] The above are only two embodiments of the present invention. All equivalent changes and modifications made according to the scope of the patent application of the present invention are within the scope of the present invention.

Claims

1. A method for identifying axial force using a rigid rod frequency ratio method, characterized in that The steps include: (1) According to the engineering data, determine whether the rigid rod is a compression rod or a tension rod, and obtain the relevant parameters of the rigid rod: rigid rod linear density m, rigid rod length L, and rigid rod bending stiffness EI; (2) The vibration signal of the rigid rod is collected on-site by a vibration sensor, and the frequency of the rigid rod is obtained by analysis; (3) Select the appropriate method to calculate the axial force of the rigid rod according to whether it is a compression rod or a tension rod and the boundary conditions; a) For a consolidated rigid bar, the frequency ratio and axial force are calculated as follows: ； ； ； ； ； Among them, m, L, EI and T are the linear density, length, bending stiffness and axial force of the rigid rod respectively. is the ratio of the nth order frequency of the consolidation and the rigid rod hinged at both ends, f n is the nth order natural frequency of the rigid rod, ξ is the relative bending stiffness, when calculating the axial force of the rigid compression rod, use the calculation formula with ξ<0, when calculating the axial force of the rigid tension rod, use the calculation formula with ξ>0; b) For a fixed-hinged rigid rod, the frequency ratio formula and axial force are calculated using the following method: ； ； ； (4) Calculate the relative bending stiffness ξ of the rigid rod: 。 2. The method for identifying axial force using the rigid rod frequency ratio method according to claim 1, characterized in that: In step (2), only one vibration sensor measurement point needs to be arranged, and the vibration sensor adopts an acceleration sensor, a velocity sensor or a displacement sensor.

3. The method for identifying axial force using the rigid rod frequency ratio method according to claim 1, characterized in that: In step (2), the vibration signal is identified by using one of the peak method, power spectrum method, random subspace method, and random decrement method to identify the frequency of the cable. For the rigid pull rod, at least the first order frequency is identified, and for the rigid compression rod, at least the first two order frequencies are identified.

4. The method for identifying axial force using the rigid rod frequency ratio method according to claim 2, characterized in that: The multi-order frequencies of the cable are in-plane vibration frequencies or out-of-plane vibration frequencies.

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