Frequency method for axial force identification of rigid bar with modified boundary conditions

Abstract

The application discloses a frequency method for identifying axial force of rigid rod by correcting boundary coefficient, and comprises the following steps: (1) according to engineering data, it is determined whether the rigid rod is a compression rod or a tension rod, and relevant parameters of the rigid rod are obtained, including linear density m of the rigid rod, length L of the rigid rod and bending stiffness EI of the rigid rod; (2) vibration signals of the rigid rod are collected on site by a vibration sensor, and multiple order frequencies of the rigid rod are obtained by analysis; (3) according to whether the rigid rod is a compression rod or a tension rod and boundary conditions, a corresponding method is selected to calculate the axial force of the rigid rod; and (4) the relative bending stiffness ξ of the rigid rod is checked, and the axial force identification precision of the rigid rod is evaluated. The method of the application establishes a unified calculation method for identifying the axial force of the rigid tension rod and the rigid compression rod by the frequency method of correcting the boundary coefficient, is easy to use, has good precision, and provides a new practical method for identifying the axial force of the rigid rod.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of engineering technology, and relates to a rigid rod axial force identification method, in particular to a frequency method axial force identification method with a rigid rod correction boundary coefficient. BACKGROUND

[0002] In a beam and a large-span space structure, the safety performance of a rigid rod as an important load-bearing component will determine the safety of the entire structure. The rigid rod is usually made of a steel pipe or a section steel, and generally bears tension, but may also partially bear pressure under the action of a live load. As is known, steel has good tensile and compressive properties, but if a compressive rod is not properly designed, overall instability or local instability may occur. Therefore, when a bridge load is tested, it is crucial to use a proper technical method to evaluate the stability and safety factor of a compressive component, and in particular to accurately identify the axial force borne by a suspender in a bridge. Identifying the axial force of a rigid rod is a key link to ensure the safety and stability of a cable-strut system bridge structure. Different technical means are used in engineering and scientific research to measure the axial force. At present, the axial force testing methods mainly include a hydraulic gauge method, a pressure sensor method, a magnetic flux method, and a frequency method. The hydraulic gauge method and the pressure sensor method are only suitable for axial force monitoring in the construction stage. When the magnetic flux method is used to test the axial force of a bridge in operation, a magnetic flux sensor needs to be installed on site, and the operation is complex and not suitable for large-scale axial force testing. The frequency method can be flexibly used for axial force detection of a bridge at various stages, is convenient to operate, and has high precision, and at present, the frequency method is used by most projects to detect the axial force of a bridge.

[0003] The method for calculating the axial force of a rigid rod by frequency mainly includes a model method (a finite element model, a theoretical model) and a formula calculation method. The model method can well consider the boundary conditions and intermediate supports of the rigid rod, but generally needs computer programming.

[0004] The formula calculation method needs to establish an explicit relationship between the axial force and the boundary coefficient, and is to establish a frequency characteristic equation by a vibration differential equation of the rigid rod, and solve the equation 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 the frequency can be obtained, and when the boundary conditions of the rigid rod are fixed at both ends or fixed-hinged, the frequency equation is a transcendental equation, and it is difficult to obtain an explicit expression of the axial force and the frequency. In view of the problem, Gong Lingling determines the relationship between the axial force of a compressive rod and the frequency by combining the basic principles of the vibration frequency method and the finite element method. Ai Yongzhen compiles a corresponding MATLAB optimization calculation program according to the corresponding relationship between the axial force of a rod and the natural frequency, and the axial force and the boundary stiffness can be obtained by substituting the measured frequency into the program.

[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 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 present invention provides a frequency method for identifying axial forces by modifying boundary coefficients of a rigid rod, 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 axial force is calculated as follows:

[0012]

[0013]

[0014]

[0015] Among them, T ij is the axial force calculated using the boundary coefficient method using the i-order and j-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. 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 a rigid compression rod, use the calculation formula with ξ<0, when calculating the axial force of a rigid tension rod, use the calculation formula with ξ>0;

[0016] b) For a rigid rod with fixed joints, 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 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 22%, the absolute error is not large, and the calculation results of the formula are also applicable.

[0024] 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.

[0025] 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.

[0026] Specifically, in step (2), the vibration signal is analyzed 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: Taking rigid rods as the research object, the present invention proposes a practical method for identifying the axial force of rigid rods based on modified boundary coefficients. Starting from the frequency method and boundary coefficients, the present invention uses linear regression to obtain a formula for calculating the axial force based on the modified boundary coefficients when the rigid rod stiffness and multi-order natural frequencies are known. This establishes a simple axial force formula with clear physical meaning and provides an explicit relationship between the axial force and the boundary coefficients. The method is verified through 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 compression) of rigid rods. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is a flow chart of the frequency method axial force identification method for correcting boundary coefficients of a rigid rod according to 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 This invention is T 12 Relative error scatter plot.

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

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

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

[0037] Figure 9 This invention is T 34 / T 23 and T0 / T 12 Relationship curve (consolidation-hinging).

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

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

[0040] 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.

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

[0042] The frequency method for identifying axial force by using a rigid rod modified boundary coefficient according to 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: rigid rod linear density m, rigid rod length L, and 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 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;

[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 as follows Figure 2 , ignoring the influence of its sag and damping, formula (1) is the free vibration equation of the rod.

[0050] (1)

[0051] 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.

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

[0062] (6)

[0063] (7)

[0064] In formula (7): f n is the n-th natural frequency of the rod.

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

[0066] (8)

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

[0068] (9)

[0069] When the two ends of the rod have arbitrary rotational stiffness, k1=k3=∞, formula (4) is substituted into formula (2) to obtain the frequency equation:

[0070] (10)

[0071] Substituting the physical parameters of the rod into formula (6), formula (8), and formula (9), the circular frequencies ω nss , ω nfh , and ω nff of the rod under the boundary conditions of both ends hinged, fixed-hinged, and both ends fixed, respectively, are obtained; n is the n-th natural frequency of the rod; formula (8), formula (9), and formula (10) are transcendental equations, so explicit solutions cannot be obtained.

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

[0073] For a compression rod, the coordinate system is as shown in Figure 4 , and the effects of its sag and damping are ignored. Formula (11) is the free vibration equation of the compression rod.

[0074] (11)

[0075] In the formula: 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 constants and do not change with time and position. And for the convenience of subsequent analysis, T is used to represent the axial force. When the value of T is positive, it represents the tensile force; when the value of T is negative, it represents the compressive force, that is, when the axial force is the compressive force N, it is represented by N=-T.

[0076] The formula is solved by the 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 vibration frequency 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 conditions 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 consolidated, and both ends are consolidated and 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.

[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, consolidated-hinged and both ends are consolidated can be obtained by solving it. nss 、ω nfh and ωnff .

[0094] 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 (19).

[0095] (19)

[0096] 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 (20).

[0097] (20)

[0098] The relative stiffness ξ is introduced in Equation (21). 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 (19) and (20) yields the frequency ratio.

[0099] (twenty one)

[0100] 2.2 Critical force of compression rod

[0101] 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:

[0102] (twenty two)

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

[0104] Table 1 Compression rod length coefficient

[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 compression rod with two ends consolidated and consolidated-hinged boundary as an example, when the compression rod is in the 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 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. The applicant's previous invention patent for a frequency-based cable force calculation method for unknown rotationally constrained boundary cables (Application No. 2024103326321) has already demonstrated the uniqueness of the frequency ratio and the calculation error with respect to the relative stiffness ξ. Therefore, when studying hangers with different relative stiffnesses ξ, the present invention only requires changing 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-hinge. When the relative stiffness ξ>6.9, it is found that the frequency ratio gradually decreases with the increase of the frequency order; 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. The formula of the applicant's previous invention patent (application number 2024103326321) is used, see formula (25), to calculate the cable force with arbitrary rotational constraint stiffness as the boundary conditions at both ends. The present invention uses this method to calculate the axial force of the hanger, and then corrects the calculation results to obtain the true axial force of the hanger under the two boundary conditions of consolidation at both ends and consolidation-hinge.

[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 frequencies are calculated, the axial forces are calculated by entering them into 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.ij is the axial force calculated by formula (25) using the i-order and j-order frequencies. The axial force results are 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 six 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 (%)

[0125]

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

[0127]

[0128] Table 8 Relative error of the consolidation-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, where the axial force error reaches 2000%; when ξ>0, the axial force error decreases as ξ increases, and when ξ<0, the axial force error decreases as ξ decreases. In order to specifically analyze the situation where the error changes with the value of ξ, Figure 5 .

[0131] observe Figure 5 It can be seen that for a hanger with two consolidated boundaries, when the ξ value is within the range of 0, the axial force error changes rapidly with ξ. As the ξ value gradually changes from 0 to the opposite sides, the axial force error decreases gradually and gradually. At the same time, the overall shape shows that the axial force error and ξ value have an inversely proportional relationship. Similarly, analysis shows that the hanger error under the consolidation-hinged boundary condition follows this law.

[0132] The axial force error calculated using formula (25) is unacceptable and 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. Therefore, it is considered to fit in two stages.

[0133] Select T0 / T (i-1)i As the dependent variable, T i(i+1) / T (i-1)i As an 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 boom in Table 2 under two boundaries 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-hinging)

[0139]

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

[0141]

[0142] 3.2 Fitting of the axial force formula of the consolidation boundary at both ends

[0143] According to Tables 9 and 10, segmented fitting is now performed, 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, 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 All 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] When 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 Figure 9As shown below, the fitting method is the same as the axial force formula of the consolidation boundary at both ends, and 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 is fitted using 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, the functional relationship is:

[0163] (33)

[0164] Similarly, if Figure 9 As shown, for T 34 / T 23 and T0 / T 23 Perform segmented fitting, and the R of the two fitting formulas 2 All 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 of -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 can be obtained as follows:

[0170] When 0<ξ≤6.9:

[0171] (36)

[0172] When -4.49≤ξ<0:

[0173] (37)

[0174] Example 1: Consolidated Boundary Rigid Rod

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

[0176] 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 2.

[0177] Step 2: For an 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 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 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. Based on the hanger rod parameters in Table 2, 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 Table 13.

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

[0181]

[0182] The errors of the gray background in the table are all over 4%. According to the relative errors of the axial forces in Table 13, a line graph is drawn. Figure 10 .

[0183] Depend on Figure 10 It can be seen that the formula is highly accurate overall, with most errors less than 2%. However, when the relative stiffness is -2≤ξ≤2, the axial force errors of both boundary hangers are large. The maximum relative error when both ends are consolidated is -22.73% (the error before correction is approximately 2000%), and the absolute error is 3523N. The large relative error, but the small absolute error, is caused by the fact that the same absolute error can 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 rods in Table 2 were selected and the frequency data in Table 4 were used for calculation.

[0186] 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 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 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 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 boom, 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. Based on the hanger rod parameters in Table 2, 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 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. Figure 11 .

[0193] Depend on Figure 11 It can be seen that the formula is highly accurate overall, with most errors less than 2%. However, when the relative stiffness is -2≤ξ≤2, the axial force errors for both boundary hangers are large. The maximum relative error for the consolidation-hinging joint is -5.94% (the error before correction is approximately 1000%), and the absolute error is 921N. The large relative error, but the small absolute error, is caused by the fact that the same absolute error can lead to excessive relative errors 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 forces by modifying boundary coefficients of rigid rods, 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 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: a) For a consolidated rigid bar, the axial force is calculated as follows: ； ； ； Among them, T ij is the axial force calculated using the boundary coefficient method using the i-order and j-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. i 、f j is the i-th and j-th order natural frequency, λ is the boundary coefficient, 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 rigid rod with fixed joints, the axial force is calculated as follows: ； ； (4) Calculate the relative bending stiffness ξ of the rigid rod: ； When -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.

2. The frequency method for identifying axial forces using a rigid rod modified boundary coefficient 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 frequency method for identifying axial forces using a rigid rod modified boundary coefficient according to claim 1 is characterized by: In step (2), the vibration signal is identified 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.

4. The frequency method for identifying axial forces using a rigid rod modified boundary coefficient 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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