Rigid rod frequency ratio method axial force identification method

Abstract

The invention discloses a rigid rod frequency ratio method axial force identification method. The method comprises the following steps: (1) according to engineering data, obtaining whether a rigid rod is a pressure rod or a pull rod, and obtaining related parameters of the rigid rod: the linear density m of the rigid rod, the length L of the rigid rod and the flexural rigidity EI of the rigid rod; (2) vibration signals of the rigid rod are collected on site through a vibration sensor, and multi-order frequency of the rigid rod is obtained through analysis; (3) selecting a corresponding method to calculate the frequency ratio of the rigid rod according to whether the rigid rod is a compression rod or a pull rod and boundary conditions, and calculating the axial force of the rigid rod through a frequency ratio method; and (4) checking the relative flexural rigidity xi of the rigid rod, and evaluating the axial force identification precision of the rigid rod. According to the method, a unified calculation method for identifying the axial force of the rigid pull rod and the pressing rod is established through a frequency ratio method, the method is easy to use and has good precision, and a practical new method is provided for identifying the axial force of the rigid rod.

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 by using a frequency ratio method. Background Art

[0002] In beams and large-span space structures, rigid rods are important load-bearing components, and their safety performance will determine the safety of the entire structure. Rigid rods are mostly made of steel pipes or steel sections. Under normal circumstances, they bear tension, but they may also partially experience compression under live loads. As we all know, steel has good tensile and compressive properties, but for compressive rods, if the design is improper, overall instability or local instability may occur. Therefore, when conducting bridge load tests, it is crucial to use appropriate technical methods to evaluate the stability and safety factor of compressive components, especially to accurately identify the axial force borne by the hanger in the bridge. Identifying the axial force of rigid rods is a key link in ensuring the safety and stability of cable-strut system bridge structures. Different technical means are used to measure axial force in engineering and scientific research. At present, the main methods for testing axial force include hydraulic gauge method, pressure sensor method, magnetic flux method and frequency method. The jack oil pressure gauge reading method and pressure sensor method are only suitable for axial force monitoring during the construction phase; when using the magnetic flux method to test the axial force of an operating bridge, it is necessary to install a magnetic flux sensor on site, which is complicated to operate and not suitable for large-scale axial force testing. The frequency method can be flexibly used in axial force detection of bridges at various stages. It is easy to operate and has high accuracy. Currently, most projects use the frequency method to detect axial force on bridges.

[0003] The methods for calculating axial force through rigid rod frequency can be mainly divided into model methods (finite element model, theoretical model) and formula calculation methods. The model method can better consider the boundary conditions and intermediate supports of the rigid rod, but such methods 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, the explicit expression of the axial force and frequency can be obtained. When the boundary conditions of the rigid rod are consolidation or consolidation-hinging at both ends, the obtained frequency equation 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 corresponding relationship 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, the relationship between the rod frequency and the axial force was determined.

[0005] In cable-strut bridges, compression rods are also a common structural member. If the rods with compression areas are not properly handled, they may lead to overall or local instability, which will bring serious consequences. At present, the research on frequency method is mainly focused on tensioned cables, while the research on applying this idea to the identification of compression rod axial force is relatively small. Therefore, how to easily test and obtain the axial force of rigid rods becomes a key issue. Summary of the invention

[0006] In order to solve the problem of rigid rod frequency normal axial force identification, the present invention proposes a rigid rod frequency ratio normal axial force identification method.

[0007] The present invention provides a method for identifying axial force using a rigid rod frequency ratio method, and the steps are as follows:

[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: the rigid rod linear density m, the rigid rod length L, and the 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 corresponding 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. n is the ratio of the nth 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 of ξ<0, when calculating the axial force of the rigid tension rod, use the calculation formula of ξ>0;

[0018] b) For a consolidated-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 in the range of -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 result of the formula is also applicable.

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

[0027] Specifically, in step (2), the vibration signal adopts one of the peak method, power spectrum method, random subspace method, and random decrement method to identify the frequency of the cable, and 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: the present invention takes a rigid rod as the research object, and proposes a practical method for identifying the axial force of a rigid rod by using the frequency ratio method. The present invention starts from the two aspects of frequency ratio and boundary conditions, and uses the linear regression method to obtain the axial force calculation formula based on the frequency ratio when the rigid rod stiffness and multi-order natural frequency are known, and establishes an axial force formula with a simple form and clear physical meaning, providing an explicit relationship between axial force and frequency. The method is verified by calculation examples and engineering examples, and the method accurately calculates the axial force, providing a practical new method for identifying the axial force (tension or pressure) of a rigid rod. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of the axial force identification method of 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 consolidates the 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 It is a rigid rod axial force error diagram of the consolidation boundary and consolidation-hinged boundary according to the first embodiment of the present invention.

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

[0038] The present invention is further described below in conjunction with 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 comprises 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: the rigid rod linear density m, the rigid rod length L, and the 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 corresponding 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 Figure 2, ignoring the influence of its sag and damping, equation (1) is the free vibration equation of the rod.

[0048] (1)

[0049] Where: u is the displacement of each point of 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, which are all 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, 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 relationship between the tension and frequency of the pull rod 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 pull rod.

[0063] For the boundary condition 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=∞, substituting equation (4) into equation (2) yields 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: 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 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 of 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, which are all constants and do not change with time and position. In order to facilitate subsequent analysis, T is used to represent the axial force. When the value of T is positive, it means that the axial force is tension. When the value of T is negative, it means that the axial force is pressure, that is, when the axial force is pressure N, it is represented by 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 frequency of vibration 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 condition 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 fixed and fixed-hinged respectively: nss ,ω nff and ω nfh ; n is the nth order 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 the compression rod

[0090] When analyzing the axial force of a compression rod using the frequency method, it is only necessary to analyze the case where the axial force is less than the critical force of the compression rod. 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 is meaningless at this time. The Euler formula for calculating the critical force of the compression rod with hinges at both ends and the length coefficient μ are introduced. μ represents the length ratio of the compression rod under different boundary conditions converted into 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 Length coefficient of compression rod

[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, fixed-hinged and fixed at both ends can be obtained by solving it. nss ,ω nfh and ω nff .

[0098] Combining equations (9) and (5) we can get the frequency ratio z of the two-end fixed tie rod and the two-end hinged tie rod: n See formula (20).

[0099] (20)

[0100] Combining equations (8) and (5), we can obtain the theoretical frequency ratio of the fixed-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 as shown in formula (22). This parameter can comprehensively consider the influence of the tension, length and bending stiffness of the pull rod. According to the frequency equation solving program established by MATLAB, the frequency value of the cable under the same relative stiffness ξ, different cable lengths, cable forces and bending stiffness is calculated, and then the frequency value is substituted into formulas (20) and (21) to obtain the frequency ratio.

[0103] (twenty two)

[0104] Taking the two-end consolidation and consolidation-hinged boundary tie rods as examples, 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 calculation results of the frequencies under different boundary conditions are shown in Tables 3 to 5. The frequency ratios under the 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 two-end consolidation boundaries

[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-hinged, as long as the relative stiffness ξ is the same, the frequency ratio is the same even though the physical parameters of the tie rod 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, as long as the relative stiffness ξ of the tie rod remains unchanged, the frequency ratio will not change.

[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 two-end consolidation and consolidation-hinged boundary compression rod as an example, when the compression rod is in a critical state, substituting formula (19) into formula (23) can obtain the critical relative stiffness ξ cr , see formula (24).

[0120] (twenty three)

[0121] (twenty four)

[0122] After simplifying equation (24), we can get the value of 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 suspension rods 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 Suspension rod parameters

[0124]

[0125] Table 9 The first 6 frequencies under the consolidation boundary at both ends of the hanger (Hz)

[0126]

[0127] Table 10 The first 6 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 fixed cable at both ends and the hinged cable at both ends: n The same as (20), combined with (14) and (18), we can get the theoretical frequency ratio of the fixed-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 joints, y n The above frequency data may have special cases of 0 or imaginary numbers. A frequency of 0 will cause y n It is meaningless to discuss the frequency ratio of the boom when the frequency is infinite and the frequency is an imaginary number. Therefore, 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 two-end consolidation boundary hangers 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 Consolidation-hinged boundary hanger y n and frequency ratio (n=1,2,3)

[0141]

[0142] Table 15 Consolidation-hinged boundary hanger y 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 suspension rods 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 y1-z1 relationship, only the hangers with ξ between 0 and 6.9 are fitted. The functional relationship of y1-z1 is:

[0148] (26)

[0149] When analyzing the second-order frequency ratio, when selecting the 1st to 25th booms for fitting, the fitting formula has poor accuracy. Therefore, it is possible to consider performing segmented fitting. The formulas after fitting 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 fittings, 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 then 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 suspension rods 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 first-order frequency ratio and the second-order frequency ratio 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. 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 those with ξ greater than the first order When calculating the relationship, the hanger 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 , we 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 equations (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] In order to verify the accuracy of the axial force calculation formula of the rigid rod, the suspension 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 hanger: hanger line density m, hanger length L, hanger 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 vibration signal uses the peak method to identify the multi-order frequencies of the boom. 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 Tables 9 and 10, select the corresponding f n With z n The axial force T is calculated based on 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. According to the suspension rod parameters in Table 8, the bending stiffness of this example meets the requirements. The relative errors are calculated based on the axial force obtained in the formula. The results are shown in Tables 18 and 19.

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

[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 is drawn based on the axial force error of the suspender rod in Table 16 and Table 17. 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 is 12.81% when the two ends are consolidated, and the maximum is 4.05% when consolidated-hinged. At this time, the real 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 too large; from the overall perspective, 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 most of the errors are 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: According to 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 a large 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 frequency of the hanger, it needs to be artificially excited. 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 hanger rod based on the frequency and related parameters of the rigid tie rod.

[0190] Table 21 compares the tension results calculated by the method of the present invention and Huang (Formula (34)). For the C33 hanger, the cable tension results obtained by Formula (34) are inaccurate, and the minimum error is 5%. However, the cable tension obtained by the present method using the fundamental frequency is relatively accurate, with a relative error of less than 1%. This shows that the 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: the rigid rod linear density m, the rigid rod length L, and the 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 corresponding method to calculate the axial force of the rigid rod according to whether the rigid rod 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 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 of ξ<0, when calculating the axial force of the rigid tension rod, use the calculation formula of ξ>0; b) For a consolidated-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: ； 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 in the range of -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 result of the formula is also applicable.

2. The method for identifying axial force of a rigid rod by 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 of a rigid rod by 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 a rigid tension rod, at least the first order frequency is identified, and for a rigid compression rod, at least the first two order frequencies are identified.

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

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