Frequency method axial force identification method of rigid rod correction boundary coefficient

Abstract

The invention discloses a frequency method axial force identification method of a rigid rod correction boundary coefficient. 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 axial force of the rigid rod according to whether the rigid rod is a pressure rod or a pull rod and boundary conditions; 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 method for correcting boundary coefficients, 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 a frequency method using a modified boundary coefficient. 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 boundary coefficient. 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 at both ends or consolidation-hinging, 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.

[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] Aiming at the problem of frequency method axial force identification of rigid rod modified boundary coefficients, the present invention proposes a frequency method axial force identification method of rigid rod modified boundary coefficients.

[0007] The frequency method for identifying axial force of a rigid rod by correcting boundary coefficients of the present invention comprises 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: 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 the rigid rod is a compression rod or a tension rod and the boundary conditions;

[0011] a) For a consolidated rigid bar, the axial force is calculated as follows:

[0012]

[0013]

[0014]

[0015] Among them, T ij is the axial force calculated by the boundary coefficient method using the i-th and j-th order frequencies, T 123 , T 234 are the modified axial forces calculated using the 1st, 2nd and 3rd order frequencies, the modified axial forces calculated using the 2nd, 3rd and 4th order frequencies, and are the identified axial forces of the rigid rod, f i 、f j is the i-th and j-th order natural frequency, 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;

[0016] b) For a consolidated-hinged rigid bar, the axial force is calculated as follows:

[0017]

[0018]

[0019]

[0020]

[0021] (4) Calculate the relative bending stiffness ξ of the rigid rod:

[0022]

[0023] 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 22%, the absolute error is not large, and the calculation result of the formula is also applicable.

[0024] 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.

[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 and a displacement sensor.

[0026] Specifically, 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, and at least the first three frequencies are identified.

[0027] Specifically, in step (2), the multi-order frequencies of the cable are in-plane vibration frequencies or out-of-plane vibration frequencies.

[0028] 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 based on a modified boundary coefficient. The present invention starts from the frequency method and the boundary coefficient. When the rigidity and multi-order natural frequency of the rigid rod are known, the linear regression method is used to obtain the axial force calculation formula based on the modified boundary coefficient, and an axial force formula with a simple form and clear physical meaning is established, providing an explicit relationship between the axial force and the boundary coefficient. The method is verified by calculation examples and engineering examples. The method calculates the axial force accurately, and provides a practical new method for identifying the axial force (tension or pressure) of a rigid rod. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flow chart of the frequency method axial force identification method of the rigid rod modified boundary coefficient of the present invention.

[0030] Figure 2 It is the coordinate system of the rigid pull rod of the present invention.

[0031] Figure 3 It is the general boundary of the rigid rod of the present invention.

[0032] Figure 4 It is the coordinate system of the rigid compression rod of the present invention.

[0033] Figure 5 The present invention 12 Relative error scatter plot.

[0034] Figure 6 The present invention 23 / T 12 and T0 / T 12 Relationship curve (consolidated at both ends).

[0035] Figure 7 The present invention 34 / T 23 and T0 / T 12 Relationship curve (consolidated at both ends).

[0036] Figure 8 The present invention 23 / T 12 and T0 / T 12 Relationship curve (consolidation-hinging).

[0037] Fig. 9 The present invention 34 / T 23 and T0 / T 12 Relationship curve (consolidation-hinging).

[0038] Fig.10 This is an axial force error diagram of the first embodiment of the present invention.

[0039] Fig.11 This is an axial force error diagram of the second embodiment of the present invention. DETAILED DESCRIPTION

[0040] 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.

[0041] Figure 1 This is a flow chart of the frequency method axial force identification method for rigid rod modified boundary coefficients of the present invention.

[0042] The frequency method for identifying axial force of a rigid rod with modified boundary coefficients of the present invention comprises the following specific steps:

[0043] (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;

[0044] (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;

[0045] (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;

[0046] (4) Verify the relative bending stiffness ξ of the rigid rod and evaluate the accuracy of the axial force identification of the rigid rod.

[0047] 1. Theoretical solution of free vibration of rigid rod

[0048] 1.1 Theoretical solution of free vibration of tie rod

[0049] 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.

[0050] (1)

[0051] 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.

[0052] The formula is solved by separation of variables method, and the general solution is:

[0053] (2)

[0054] (3)

[0055] 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.

[0056] When both ends of the tie rod are elastically supported, their boundaries are as follows Figure 3 As shown, the boundary conditions are:

[0057] (4)

[0058] 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.

[0059] For the boundary conditions of hinged ends, k1=k3=∞, k2=k4=0, the frequency equation is:

[0060] (5)

[0061] At the same time, the relationship between the tension and frequency of the pull rod when both ends are hinged can be obtained:

[0062] (6)

[0063] (7)

[0064] In formula (7): f n is the nth order natural frequency of the pull rod.

[0065] For the boundary condition of one end fixed and the other end hinged, k1=k3=∞, k2=∞, k4=0, the frequency equation is:

[0066] (8)

[0067] For the boundary conditions of consolidation at both ends, k1=k3=k2= k4=∞, the frequency equation is:

[0068] (9)

[0069] When the two ends of the tie rod have arbitrary rotational stiffness, k1=k3=∞, substituting equation (4) into equation (2) yields the frequency equation:

[0070] (10)

[0071] 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.

[0072] 1.2 Theoretical solution of free vibration of compression rod

[0073] 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.

[0074] (11)

[0075] Where: u is the displacement of each point of the compression rod at time t; m, L, EI and T 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.

[0076] The formula is solved by separation of variables method, and the general solution is:

[0077] (12)

[0078] (13)

[0079] 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.

[0080] For the boundary conditions of hinged ends, k1=k3=∞, k2=k4=0, the frequency equation is:

[0081] (14)

[0082] 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:

[0083] (15)

[0084] (16)

[0085] In formula (16): f n is the nth order natural frequency of the compression rod.

[0086] For the boundary conditions of consolidation at both ends, k1=k3=k2= k4=∞, the frequency equation is:

[0087] (17)

[0088] For the boundary condition of one end fixed and the other end hinged, k1=k3=∞, k2=∞, k4=0, the frequency equation is:

[0089] (18)

[0090] 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.

[0091] 2. Critical relative stiffness of compression rod

[0092] 2.1 Frequency ratio and relative stiffness

[0093] 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 ωnff .

[0094] 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 (19).

[0095] (19)

[0096] 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 (20).

[0097] (20)

[0098] The relative stiffness ξ is introduced as shown in formula (21). 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 (19) and (20) to obtain the frequency ratio.

[0099] (twenty one)

[0100] 2.2 Critical force of the compression rod

[0101] 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:

[0102] (twenty two)

[0103] The values ​​of μ under different boundary conditions are as follows:

[0104] Table 1 Length coefficient of compression rod

[0105]

[0106] 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 (22) into formula (23) can obtain the critical relative stiffness ξ cr , see formula (24).

[0107] (twenty three)

[0108] (twenty four)

[0109] After simplifying equation (24), we can get the fixed compression rod at both ends: , 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. The applicant's previous invention patent for the frequency method cable force calculation method for unknown rotation constraint boundary cables (application number 2024103326321) has proved that the frequency ratio and the calculation error of the formula are unique to the relative stiffness ξ. Therefore, when studying the hangers with different relative stiffness ξ, the present invention only needs to change the axial force without changing other physical parameters.

[0110] 3. Axial force calculation formula based on boundary coefficient

[0111] According to the applicant's previous invention patent on the frequency method for calculating the cable force of unknown rotational constraint boundary cables, there is a conclusion on the change of the frequency ratios of each order under the two boundary conditions of consolidation at both ends of the hanger and consolidation-hinging. When the relative stiffness ξ>6.9, it is found that with the increase of the frequency order, the frequency ratio gradually decreases; when ξ increases to a certain value, the frequency ratios of each order of the cable under different boundary conditions are close to the same, so the boundary condition coefficient λ is introduced, and the formula of the applicant's previous invention patent (application number 2024103326321), see formula (25), is used to calculate the cable force with arbitrary rotational constraint stiffness at both ends. The present invention uses this method to calculate the axial force of the hanger, and then corrects the calculation result to obtain the true axial force of the hanger under the two boundary conditions of consolidation at both ends and consolidation-hinging.

[0112] (25)

[0113] Where: λ is the boundary coefficient, m, L, EI and T are the linear density, length, bending stiffness and tension of the tie rod respectively, i and j are the frequency orders used in the calculation, f i 、f j is the natural frequency used in the formula calculation, is the axial force calculated by the i-th and j-th frequencies.

[0114] 3.1 Calculation results of axial force for unknown rotation constraint boundary formula

[0115] The suspenders in Table 2 are selected for analysis. After the frequency is calculated, the axial force is calculated by entering formula (25). The calculation results of the consolidation and consolidation-hinged boundary frequencies at both ends are shown in Tables 3 and 4, and the axial force results are shown in Tables 5 and 7, where Tij is the axial force calculated by formula (25) using the i-order and j-order frequencies. The axial force result is compared with the true axial force. The relative errors are shown in Tables 6 and 8.

[0116] Table 2 Boom parameters

[0117]

[0118] Table 3 The first six frequencies under the consolidation boundary at both ends of the hanger (Hz)

[0119]

[0120] Table 4 The first 6 frequencies at the hinged boundary at both ends of the boom (Hz)

[0121]

[0122] Table 5 Axial force results (consolidation at both ends)

[0123]

[0124] Table 6 Relative error of the two-end consolidation hanger rod (%)

[0125]

[0126] Table 7 Axial force results (consolidation-hinged)

[0127]

[0128] Table 8 Relative error of the fixed-hinged hanger (%)

[0129]

[0130] According to the results in Table 6 and Table 8, it can be found that the error of the axial force results calculated by formula (25) is unacceptable, especially for the two-end consolidation hangers with -2≤ξ≤2, the axial force error reaches 2000%; when ξ>0, the axial force error will decrease with the increase of ξ, and when ξ<0, the axial force error will decrease with the decrease of ξ. In order to specifically analyze the change of error with ξ value, Figure 5 .

[0131] observe Figure 5 It can be seen that for the hanger with two ends of the consolidation boundary, when the ξ value is in the range near 0, the axial force error changes very quickly with ξ. When the ξ value gradually changes from 0 to both sides, the speed at which the axial force error decreases gradually becomes gentle. At the same time, from its overall shape, it can be seen that the axial force error and the ξ value are inversely proportional. Similarly, the analysis shows that the hanger error under the consolidation-hinged boundary condition conforms to this law.

[0132] The axial force error calculated using formula (25) is unacceptable and the result must be corrected. This is because the axial force error and the ξ value are inversely proportional functions. If the entire range of -6.28≤ξ≤6.9 is fitted, the relationship is difficult to confirm, so consider fitting in two stages.

[0133] Select T0 / T (i-1)i As the dependent variable, T i(i+1) / T (i-1)i As the independent variable, try to find T i(i+1) / T (i-1)i With T0 / T (i-1)i Fitting relationship. First, calculate the T of the suspender under two boundaries in Table 2 i(i+1) / T (i-1)i and T0 / T (i-1)i For data, see Tables 9 to 12.

[0134] Table 9 T 23 / T 12 and T0 / T 12 Calculation results (consolidation at both ends)

[0135]

[0136] Table 10 T 34 / T 23 and T0 / T 23 Calculation results (consolidation at both ends)

[0137]

[0138] Table 11 T 23 / T 12 and T0 / T 12 Calculation results (consolidation-hinged)

[0139]

[0140] Table 12 T 34 / T 23 and T0 / T 23 Calculation results (consolidation-hinged)

[0141]

[0142] 3.2 Fitting of the axial force formula of the two-end consolidation boundary

[0143] According to Tables 9 and 10, segmented fitting is now carried out, and the axial force is divided into two cases: tension (0<ξ≤6.9) and pressure (-6.28≤ξ<0) for study.

[0144] like Figure 6 As shown, in the range of 0<ξ≤6.9, T0 / T12 Approximately about T 23 / T 12 A linear function is used, using linear fitting, R 2 is 0.9989, the fitting effect is good, and the functional relationship is:

[0145] (26)

[0146] In the range of -6.28≤ξ<0, the same is true for T0 / T 12 and T 23 / T 12 Perform linear fitting, R 2 is 1, and the functional relationship is:

[0147] (27)

[0148] Similarly, if Figure 7 As shown, for T 34 / T 23 and T0 / T 23 Perform segmented fitting, and the R of the two fitting formulas 2 Both are greater than 0.9985.

[0149] For the boom in the range of 0<ξ≤6.9:

[0150] (28)

[0151] For the boom in the range -6.28≤ξ<0:

[0152] (29)

[0153] Summarize the above fitting formula and simplify it, T 123 represents the axial force calculated from the 1st, 2nd and 3rd order frequencies, T 234 Similarly, the calculation formula for the axial force of the consolidation hangers at both ends is as follows:

[0154] 0<ξ≤6.9:

[0155] (30)

[0156] When -6.28≤ξ<0:

[0157] (31)

[0158] 3.3 Fitting of the consolidation-hinged axial force formula

[0159] According to Table 11 and Table 12, Figure 8 and Fig. 9As shown below, the fitting method is the same as the formula of the axial force at the two end consolidation boundaries. The axial force is still divided into two cases: pressure (-4.49≤ξ<0) and tension (0<ξ≤6.9) for study.

[0160] like Figure 8 As shown, in the range of 0<ξ≤6.9, T0 / T 12 With T 23 / T 12 The relationship between the two is linear fitting, R 2 is 0.9989, the fitting effect is good, and the functional relationship is:

[0161] (32)

[0162] In the range of -4.49≤ξ<0, for T0 / T 12 and T 23 / T 12 Perform linear fitting, R 2 is 1, and the functional relationship is:

[0163] (33)

[0164] Similarly, if Fig. 9 As shown, for T 34 / T 23 and T0 / T 23 Perform segmented fitting, and the R of the two fitting formulas 2 Both are greater than 0.9985.

[0165] For the boom in the range of 0<ξ≤6.9:

[0166] (34)

[0167] For the boom in the range -4.49≤ξ<0:

[0168] (35)

[0169] Summarizing formulas (32) to (35) and simplifying them, the calculation formula for the axial force of the consolidated-hinged hanger is as follows:

[0170] 0<ξ≤6.9:

[0171] (36)

[0172] When -4.49≤ξ<0:

[0173] (37)

[0174] Example 1: Consolidated Boundary Rigid Bar

[0175] In order to verify the accuracy of the axial force calculation formula of the consolidation boundary rigid rod, the hanger rod in Table 2 was selected and the frequency data in Table 3 was used for calculation.

[0176] 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 2.

[0177] Step 2: For the actual rigid rod, 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 Table 3. The boom frequency of this embodiment is obtained through finite element simulation analysis.

[0178] Step 3: According to the fundamental frequency and related parameters of the rigid rod, combined with the data in Table 3, select the corresponding value to calculate the axial force T. The calculation results are shown in Tables 5 and 6. In the table, T0 is the actual axial force, T 123 , T 234 These are the axial forces obtained using the 1st, 2nd and 3rd order frequencies, and the axial forces obtained using the 2nd, 3rd and 4th order frequencies.

[0179] Step 4: Verify the relative bending stiffness ξ of the rigid rod. According to the suspension rod parameters in Table 2, 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 Table 13.

[0180] Table 13 Axial force calculation results (consolidation at both ends)

[0181]

[0182] The gray-bottom errors in the table are all over 4%. A line graph is drawn based on the relative error of the axial force in Table 13. Fig.10 .

[0183] Depend on Fig.10 It can be found that the formula has high accuracy overall, and most of the errors are less than 2%. However, when the relative stiffness is -2≤ξ≤2, the axial force errors of the two boundary hangers are large; the maximum relative error when both ends are consolidated is -22.73% (the error before correction is about 2000%), and the absolute error is 3523N; the relative error is large, but the absolute error is not large. This is because the same absolute error will lead to excessive relative error when the hanger axial force is very small.

[0184] Example 2: Consolidated-Hinged Boundary Rigid Bar

[0185] In order to verify the accuracy of the axial force calculation formula of the consolidation-hinged boundary rigid rod, the hanger in Table 2 was selected and the frequency data in Table 4 was used for calculation.

[0186] 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 2.

[0187] 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 Table 4. The boom frequency of this embodiment is obtained through finite element simulation analysis.

[0188] Step 3: According to the fundamental frequency and related parameters of the suspender, combined with the data in Table 4, select the corresponding value to calculate the axial force T. The calculation results are shown in Tables 7 and 8. In the table, T0 is the actual axial force, T 123 、T 234 These are the axial forces obtained using the 1st, 2nd and 3rd order frequencies, and the axial forces obtained using the 2nd, 3rd and 4th order frequencies.

[0189] Step 4: Verify the relative bending stiffness ξ of the rigid rod. According to the suspension rod parameters in Table 2, 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 Table 14.

[0190] Table 14 Axial force calculation results (consolidation-hinged)

[0191]

[0192] The errors of the gray background in the table are all over 4%. According to the relative errors of the axial forces in Table 14, a line graph is drawn. Fig.11 .

[0193] Depend on Fig.11 It can be found that the formula has high accuracy overall, and most of the errors are less than 2%. However, when the relative stiffness is -2≤ξ≤2, the axial force errors of the two boundary hangers are large; the maximum relative error in consolidation-hinging is -5.94% (the error before correction is about 1000%), and the absolute error is 921N; the relative error is large, but the absolute error is not large. This is because the same absolute error will lead to excessive relative error when the hanger axial force is very small.

[0194] 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 frequency method for identifying axial force of a rigid rod by correcting boundary coefficients, 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 axial force is calculated as follows: ； ； 2. Among them, T ij is the axial force calculated by the boundary coefficient method using the i-th and j-th order frequencies, T 123 , T 234 are the modified axial forces calculated using the 1st, 2nd and 3rd order frequencies, the modified axial forces calculated using the 2nd, 3rd and 4th order frequencies, and are the identified axial forces of the rigid rod, f i 、f j is the i-th and j-th order natural frequency, 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 bar, the axial force is calculated as follows: ； ； (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 is up to 22% when both ends are consolidated and up to 5.94% when consolidated and hinged, the absolute error is not large, and the calculation results of the formula are also applicable.

3. The frequency method for identifying axial force of a rigid rod with modified boundary coefficients according to claim 1 is characterized by: 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.

4. The frequency method for identifying axial force of a rigid rod with modified boundary coefficients according to claim 1 is characterized by: 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, and at least the first three frequencies are identified.

5. The frequency method for identifying axial force of a rigid rod with modified boundary coefficients 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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