A method and system for calculating vertical natural vibration frequency and vibration mode of cable-stayed bridge

Abstract

The present invention discloses a method and system for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge, comprising the following steps: simplifying the cable-stayed bridge into a multi-cable cable-stayed beam composite structure considering the influence of axial force, dividing the composite structure into different beam sections, obtaining the main beam parameters, cable parameters and different boundary conditions of different beam sections; constructing the main beam mass matrix, the shear equivalent matrix basic formula and the axial force equivalent matrix basic formula; and correcting the basic formula to obtain the shear equivalent matrix and the axial force equivalent matrix; constructing the characteristic equation matrix of the natural vibration frequency and vibration mode; and obtaining the vertical natural vibration frequency and the corresponding vibration mode of the cable-stayed bridge. The method simplifies the cable-stayed bridge into a multi-cable cable-stayed beam composite structure considering the influence of axial force, corrects the basic formula, and establishes a characteristic equation matrix based on different boundary conditions in combination with the main beam mass matrix, which can quickly and effectively calculate the natural vibration frequency and vibration mode of a complex cable structure.

Description

Technical Field

[0001] The invention belongs to the field of design and evaluation of complex spatial cable structures in civil engineering, and relates to a method and system for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge. Background Art

[0002] Cables and their combined structures are widely used in bridges and temporary construction facilities. For example, cables and cross arms in cable-stayed bridges, hoisting towers or cranes, and grid structures can all be abstracted as cable-beam combined structures. Spatial cable-supported structures have high flexibility, low damping, and prominent nonlinear dynamic behavior, which can easily cause damper fatigue and cable relaxation, affecting the normal working performance of the structure. Taking cable-stayed bridges as an example, especially large-span, long-cable cable-stayed bridges, the dynamic coupling between cables and beams has a non-negligible influence on the dynamic characteristics of the overall structure, and its related dynamic problems have attracted widespread attention from researchers at home and abroad.

[0003] When the local natural vibration frequency of the cable and the vertical natural vibration frequency of the main beam meet a certain ratio relationship (1:1 or 1:2), the cable is subjected to axial periodic excitation, which may be very small, but will also cause the cable to resonate strongly. Compared with the vibration problem of a single cable under ideal excitation, the nonlinear vibration formation mechanism generated by this form of excitation is more hidden, with more inducing factors, larger vibration amplitude, and more prominent nonlinear behavior of the cable-beam composite structure under non-ideal excitation. A large number of single-cable-cantilever beam and multi-cable-beam model test data conducted by scholars at home and abroad have successively observed resonance phenomena with this characteristic. In the absence of wind and vehicles, the cable vibrates violently, with a maximum lateral amplitude of more than 2 meters, causing some shock absorbers to fall off. Based on the monitoring data of violent nonlinear vibration of the cable in the physical structure of a cable-stayed bridge on the Spanish-Portuguese border, Caetano studied and verified that the coupling between the natural vibration mode of the main beam and the local mode of the cable is the key excitation source of the violent nonlinear vibration of the cable.

[0004] Studies have shown that the formation mechanism of this type of resonance mainly stems from the coupling effect of the ratio of the natural vibration frequency of the structure as a whole and the natural vibration mode. Therefore, the key to avoiding this type of resonance is to set the resonance interval where the local vibration frequency of the cable is far away from the natural vibration frequency of the structure. A lot of research has been done on the simplified algorithm of the natural vibration characteristics of a single cable, and the natural vibration frequency and vibration mode of the structure, especially the main beam, have so far been mostly calculated and solved by the finite element method. Compared with the method of numerical simulation that requires the establishment and division of hundreds or thousands of finite elements, the analytical solution method is more convenient, more practical and more economical.

[0005] The main beam of a cable-stayed bridge can be simplified as a multi-point elastically supported Euler-Bernoulli beam under variable axial force. However, most of the current studies on multi-cable-beam structures have highly simplified or even ignored the influence of factors such as the horizontal projection of cable forces, the coupling effect between cables during vibration, and the influence of the main beam bending stiffness on the vibration characteristics of the structure, or the iterative analytical methods are cumbersome and complex, which is not conducive to the nonlinear dynamic research of group cable-beam structures. Summary of the invention

[0006] In view of the problems existing in the prior art, the present invention provides a method and system for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge, thereby achieving a method for quickly and effectively calculating the natural vibration frequency and vibration mode of a complex cable structure.

[0007] The present invention is achieved through the following technical solutions:

[0008] A method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge comprises the following steps:

[0009] S1: simplifying the cable-stayed bridge into a multi-cable cable-stayed-beam composite structure considering the influence of axial force, dividing the multi-cable cable-stayed-beam composite structure into different beam sections, and obtaining main beam parameters, cable parameters and different boundary conditions of different beam sections;

[0010] S2: constructing the main beam mass matrix, shear equivalent matrix basic formula and axial force equivalent matrix basic formula through the main beam parameters, cable parameters and different boundary conditions of the multi-cable cable-stayed-beam composite structure; and modifying the shear equivalent matrix basic formula and the axial force equivalent matrix basic formula to obtain the shear equivalent matrix and the axial force equivalent matrix;

[0011] S3: constructing the natural vibration frequency and mode shape characteristic equation matrix of the multi-cable cable-stayed-beam composite structure through the main beam mass matrix, shear force equivalent matrix and axial force equivalent matrix;

[0012] S4: Obtain the natural vibration frequency and mode shape of the cable-stayed bridge through the natural vibration frequency and mode shape characteristic equation matrix of the multi-cable cable-stayed-beam combination structure.

[0013] Preferably, it is characterized in that the main beam parameters of the different beam sections include the masses of the different beam sections, and the main beam mass matrix is ​​constructed by the masses of the different beam sections.

[0014] Preferably, the shear force equivalent matrix basic formula is specifically:

[0015] A(j,j)=6; A(j,j-1)=A(j,j+1)=-4; A(j,j-2)=A(j,j+2)=-1

[0016] In the formula,

[0017] A(j, j) is the diagonal element in the shear equivalent matrix;

[0018] A(j, j-1) is the element in row j and column j-1 in the shear equivalent matrix;

[0019] A(j, j+1) is the element in row j and column j+1 in the shear equivalent matrix;

[0020] A(j, j-2) is the element in row j and column j-2 of the shear equivalent matrix;

[0021] A(j, j+2) is the element in the jth row and j+2th column of the shear equivalent matrix.

[0022] Preferably, the shear force equivalent matrix basic formula is selected according to the boundary conditions of the cable-stayed bridge, and the shear force equivalent matrix basic formula is modified; when the beam end boundary form of the cable-stayed bridge is a simply supported-simply supported beam, the modification process of the shear force basic matrix is ​​specifically as follows:

[0023] A(j,j)=k ABi [A(j,j)+k C(jm)(jm) ]

[0024] In the formula, k ABi Assign coefficients to the shear equivalent matrix;

[0025] k C(jm)(jm) C jm# Equivalent spring stiffness of the cable.

[0026] Preferably, the axial force equivalent matrix basic formula is specifically:

[0027] D(j,j)=-2; D(j,j-1)=D(j,j+1)=1

[0028] Where:

[0029] D(j, j) is the diagonal element in the axial force equivalent stiffness matrix;

[0030] D(j, j-1) is the element in row j and column j-1 in the axial force equivalent stiffness matrix;

[0031] D(j, j+1) is the element in the jth row and j+1th column of the axial force equivalent stiffness matrix.

[0032] Preferably, the axial force equivalent matrix basic formula is selected according to the boundary conditions of the cable-stayed bridge, and the axial force equivalent matrix basic formula is corrected according to the equivalent stiffness of the cable on the main beam. When the beam end boundary form of the cable-stayed bridge is a simply supported-simply supported beam, the correction process of the axial force equivalent matrix basic formula is specifically as follows:

[0033] D(j, j) = D(j, j)*k DBi

[0034] Where: k DBi Assign coefficients to the axial force equivalent stiffness matrix.

[0035] Preferably, the natural vibration frequency and mode shape characteristic equation matrix of the multi-cable cable-stayed-beam composite structure is specifically:

[0036] F=inv(M)*G

[0037] Where, F is the natural vibration frequency and mode shape characteristic equation matrix of the multi-cable cable-stayed-beam composite structure;

[0038] M is the main beam mass matrix;

[0039] Inv represents the inverse of the matrix;

[0040] in,

[0041] [G]=[A]+[D]

[0042] In the formula,

[0043] G is the combined matrix of the shear force equivalent matrix and the axial force equivalent stiffness matrix.

[0044] A is the shear equivalent matrix;

[0045] D is the stiffness matrix equivalent to the axial force;

[0046] The natural vibration frequency and vibration mode of the cable-stayed bridge are obtained by the characteristic equation matrix of the multi-cable cable-stayed-beam combined structure as follows:

[0047] [B,C]=eig[F]

[0048] Wherein, [B] is the natural vibration mode of the cable-stayed bridge;

[0049] {C} is the natural vibration line frequency of the cable-stayed bridge;

[0050] eig means finding eigenvalues ​​and eigenvectors.

[0051] A calculation system for vertical natural vibration frequency and vibration mode of a cable-stayed bridge, comprising:

[0052] A parameter acquisition module, wherein the parameter acquisition module is used to simplify the cable-stayed bridge into a multi-cable cable-stayed-beam combination structure considering the influence of axial force, and divide the multi-cable cable-stayed-beam combination structure into different beam sections, and obtain main beam parameters and cable parameters of different beam sections;

[0053] A basic matrix construction and correction module, wherein the basic matrix construction and correction module constructs a main beam mass matrix, a shear equivalent matrix basic formula, and an axial force equivalent matrix basic formula through the main beam parameters of the multi-cable cable-stayed-beam composite structure and the cable parameters; and corrects the shear equivalent matrix basic formula and the axial force equivalent matrix basic formula to obtain a shear equivalent matrix and an axial force equivalent matrix;

[0054] A module for constructing a matrix of natural vibration frequency and mode shape characteristic equations, wherein the module is used to construct a matrix of natural vibration frequency and mode shape characteristic equations of the multi-cable cable-stayed-beam composite structure through the main beam mass matrix, the shear force equivalent matrix and the axial force equivalent matrix;

[0055] A module for obtaining natural vibration frequency and corresponding vibration mode, wherein the module is used to obtain the natural vibration frequency and corresponding vibration mode of the cable-stayed bridge through the characteristic equation matrix of the multi-cable cable-stayed-beam combination structure.

[0056] A terminal device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0057] A computer-readable storage medium stores a computer program, wherein the computer program implements the steps of the above method when executed by a processor.

[0058] Compared with the prior art, the present invention has the following beneficial technical effects:

[0059] A method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge simplifies the cable-stayed bridge into a multi-cable cable-stayed-beam composite structure considering the influence of axial force, considers the influence of axial force on the natural vibration of the main beam, effectively simulates the influence of the vertical bending stiffness of the main beam and the coupling effect between cables during vibration in the main beam discrete element parameter mass system based on shear force difference and axial force difference, constructs a characteristic equation for calculating the natural vibration frequency of the cable-stayed bridge, and proposes a method for solving the eigenvalues ​​and eigenvectors of the characteristic matrix to solve the natural vibration related parameters of the multi-cable cable-stayed structure. Compared with the previous finite element numerical simulation method, the simplified formula for cable-stayed bridge proposed in the present invention can quickly and effectively calculate the vertical natural vibration frequency and vibration mode of complex spatial cable structures such as cable-stayed bridges, and has strong convenience and operability. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0061] Figure 1 It is a flow chart of a practical calculation method of the vertical natural vibration frequency and vibration mode of a cable-stayed bridge according to an embodiment of the present invention;

[0062] Figure 2 It is a flow chart of calculation and analysis of the present invention;

[0063] Figure 3 This is a schematic diagram of the numbering rules corresponding to the main beam and the cables of the present invention;

[0064] Figure 4 The main beam discrete parameter quality system of the present invention;

[0065] Figure 5 The bending moment balance between the beam sections of the present invention;

[0066] Figure 6 It is a structural schematic diagram of a practical calculation system for the vertical natural vibration frequency and vibration mode of a cable-stayed bridge according to an embodiment of the present invention;

[0067] Figure 7 This is a bridge elevation diagram according to Embodiment 2 of the present invention;

[0068] Figure 8 These are the first three-order structural vibration modes of the cable-stayed bridge under three working conditions of Example 2 of the present invention. DETAILED DESCRIPTION

[0069] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0070] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0071] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0072] In the description of the embodiments of the present invention, it should be noted that if the terms "upper", "lower", "horizontal", "inner", etc. indicate an orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the invention is usually placed when in use, it is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0073] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", which does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0074] In the description of the embodiments of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "set", "install", "connect", and "connect" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal connection of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0075] like Figure 1 The figure shows a flow chart of a method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge in the present invention. The present invention simplifies the cable-stayed bridge into a multi-cable cable-stayed-beam combination structure that takes into account the influence of axial force, and takes into account the influence of axial force on the natural vibration of the main beam. Based on the shear force difference and axial force difference, the main beam vertical bending stiffness and the coupling effect between cables during vibration are effectively simulated in the main beam discrete element parameter mass system. The characteristic equation for calculating the natural vibration frequency of the cable-stayed bridge is constructed, and a method for solving the eigenvalues ​​and eigenvectors of the characteristic matrix is ​​proposed to solve the natural vibration related parameters of the multi-cable cable-stayed structure. Compared with the previous finite element numerical simulation method, the simplified formula for the cable-stayed bridge proposed by the present invention can quickly and effectively calculate the vertical natural vibration frequency and vibration mode of complex spatial cable structures such as cable-stayed bridges, and has strong convenience and operability.

[0076] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0077] Example 1

[0078] See also Figure 2 This embodiment discloses a method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge, comprising the following steps:

[0079] The present invention simplifies the vertical support function of the cable into a dynamic spring, converts the horizontal projection of the cable force into the axial force of the beam section, introduces the shear force on both sides of the micro-beam segment to simulate the influence of the main beam bending stiffness, the vibration coupling between the cables, etc., establishes a multi-point elastic support main beam considering the axial force, and through the moment balance between the micro-beam segments and the finite difference method, the simplified multi-cable cable-stayed structure quality parameter system is dynamically modeled and analyzed, and the vibration equation and correlation coefficient matrix under different boundary conditions are obtained. Finally, a method is obtained that can quickly and effectively calculate the natural vibration frequency and vibration mode of a complex cable structure with the help of tools such as Excel.

[0080] The cable-stayed bridge is simplified into a multi-cable cable-stayed-beam composite structure considering the influence of axial force. The dynamic modeling theory and natural vibration characteristics analysis method of the multi-cable cable-stayed structure and the matrix coefficients under different boundary conditions are given, including the following steps:

[0081] S1: Simplify the cable-stayed bridge into a multi-cable cable-stayed-beam composite structure considering the influence of axial force, divide the multi-cable cable-stayed-beam composite structure into different beam sections, and obtain the main beam parameters, cable parameters and different boundary conditions of the different beam sections.

[0082] S1.1: Input parameters according to actual situation

[0083] According to the actual situation of the target cable-stayed bridge, the main beam is divided into different areas according to the cross-section type and the calculated characteristic values ​​are assigned to each area. Then the beam section length L of each area is input respectively. B , elastic modulus E B 、Quality M B 、Area A B , vertical bending moment of inertia I B The cable-related parameters require the input of the cable elastic modulus E Cjm , anchoring position, area A Cjm Length L Cjm , Inclination angle (angle between cable and long mileage direction)θ Cjm , Soli H Cjm wait.

[0084] S1.2: Segmentation and data processing

[0085] According to the input parameters, the calculation parameters are obtained through preliminary calculation. The details are shown in Table 1. The schematic diagram of the main beam and cable numbering is shown in Figure 3 , and it is agreed that the parameters of the i#th beam segment are represented by the subscript bi, and the j#th beam segment is represented by the subscript bi.m #The parameters of the cable are subscripted with cj m express.

[0086] Table 1 Calculation parameter list

[0087]

[0088] S1.3: Simplify the model and establish a discrete system

[0089] In order to avoid the lengthy and error-prone iterative process of solving the vibration equation and its inelastic response, this patent establishes a discrete parameter quality system for the main beam, such as Figure 4 As shown in , the shear forces on both sides of the beam segment are solved by the moment balance between adjacent beam segments, as shown in Figure 5 As shown in the figure, the shear force difference can approximately simulate the influence of adjacent beam segments during the vibration process, that is, the shear force of the micro beam segment can be used to simulate the bending stiffness of the main beam and the vibration coupling between the cables. Then, by comprehensively considering the influence of the cables in the cable area on the stiffness of the beam segment and combining the D'Alembert principle, the vibration equation of the independent beam segment can be obtained.

[0090] S1.4 Establish the structural dynamic equilibrium equation based on boundary conditions

[0091] Since the mass system is densely distributed and the relative displacement between beam segments is small, the geometric relationship of vibration is simplified first. Then, the curvature of the beam segment is expressed by the second-order central difference, and finally the vibration equation is optimized by combining the Dirac function, and the vibration equation of the discrete parameter system of the cable-stayed bridge can be obtained:

[0092]

[0093] In the above formula, {V Bi}、 are all N-dimensional column vectors of the same form. The form is as follows:

[0094]

[0095] {ψ Bi} is an N-order coefficient diagonal matrix of the same form, and its specific expressions are shown in equations (2b) and (2c):

[0096]

[0097] Based on the above theoretical derivation, the characteristic equivalent matrix considering axial force and shear force can be obtained as shown in the following formula:

[0098] [A] = k ABi ·[Γ]

[0099] [D] = k DBi ·[Ξ]

[0100] In the above formula, the coefficient matrices [Γ] and [Ξ] are related to the structural boundary conditions and need to be substituted into the cable-stayed bridge boundary conditions to obtain the expression of the corresponding basic equivalent matrix. For ease of application, the present invention lists the basic matrix expressions of several commonly used structural forms, and the boundary conditions of the cable-stayed bridge structure can be obtained by looking up the table. For the shear equivalent matrix, due to space limitations, only the expression of simply supported-simply supported beams is listed here as shown in formula (3). For other boundary condition forms, refer to Table 2:

[0101] Table 2. Expressions of vibration equation coefficients under different main beam boundary conditions

[0102]

[0103]

[0104] [Ξ] is the derived sub-item coefficient matrix as shown in formula (4), which is related to the number of cables and the anchor position:

[0105]

[0106] Coefficient Matrix The specific form of the number of cables is related to the anchorage position and boundary conditions, where the simply supported-cantilever beam coefficient matrix [Ξ s ] As shown in formula (5); Consolidation-consolidation beam coefficient matrix [Ξ s ]As shown in formula (6):

[0107]

[0108] The essence of the simplification of this patent is to form a calculation matrix based on the complex boundary conditions in the physical structure of the cable-stayed bridge, and to bring the basic form of this coefficient matrix (such as formula (3), formula (5), formula (6) and Table 2) into the natural vibration frequency and vibration mode characteristic matrix of the structure to achieve the purpose of considering the boundary conditions of the physical structure. It should be noted that for the semi-floating system bridge with tower-beam consolidation, a spring with a default infinite stiffness is added vertically to the simplified beam section at the main tower to simulate its consolidation state, and the boundary conditions of the left and right beam sections are determined to be connected to the consolidation end.

[0109] S2: construct the main beam mass matrix, shear equivalent matrix basic formula and axial force equivalent matrix basic formula through the main beam parameters, cable parameters and different boundary conditions of the multi-cable cable-stayed-beam composite structure; and modify the shear equivalent matrix basic formula and the axial force equivalent matrix basic formula to obtain the shear equivalent matrix and the axial force equivalent matrix.

[0110] S2.1: Construct the main beam mass diagonal matrix

[0111] Since the main beam was divided into regions according to its different cross-sections and the mass per unit length of each region was input separately, it is necessary to assign the actual unit mass of the structure in different regions and form a diagonal matrix. The main diagonal elements of this matrix are the mass of each section, and this diagonal matrix is ​​the main beam mass matrix.

[0112] S2.2: Constructing the Shear Equivalence Matrix

[0113] According to the boundary conditions of the cable-stayed bridge, the basic form of the corresponding equivalent stiffness matrix is ​​selected. Due to space limitations, the common simply supported-simply supported cable-stayed bridge structures are listed here, and the basic form of establishing the shear equivalent matrix is ​​as shown in formula (7):

[0114] A(j,j)=6; A(j,j-1)=A(j,j+1)=-4; A(j,j-2)=A(j,j+2)=-1 Equation 7

[0115] in:

[0116] A(j, j) is the diagonal element in the shear equivalent matrix;

[0117] A(j, j-1) is the element in row j and column j-1 in the shear equivalent matrix;

[0118] A(j, j+1) is the element in row j and column j+1 in the shear equivalent matrix;

[0119] A(j, j-2) is the element in row j and column j-2 of the shear equivalent matrix;

[0120] A(j, j+2) is the element in row j and column j+2 of the shear equivalent matrix;

[0121] The basic form of the shear matrix formed is formula (8):

[0122]

[0123] According to the dynamic equation established above, the shear equivalent matrix of different beam sections on the main beam is assigned values, and the assigned values ​​are shown in Table 3:

[0124] Table 3. Shear force equivalent matrix assignment coefficient expression

[0125]

[0126] S2.2.1: Since the cable will affect the stiffness of the main beam, the matrix should be corrected according to the position of the cable. According to the drawings, the cable equivalent spring is assigned to the shear equivalent matrix at the cable anchorage. The shear equivalent matrix basic formula is selected through the boundary conditions of the cable-stayed bridge, and the shear equivalent matrix basic formula is corrected to finally form the shear equivalent matrix A. When the beam end boundary form of the cable-stayed bridge is a simply supported-simply supported beam, the correction process of the shear basic matrix is ​​shown in formula (9):

[0127] A(j,j)=k ABi [A(j,j)+k C(jm)(jm) Formula 9

[0128] in:

[0129] k ABi Assign coefficients to the shear equivalent matrix;

[0130] k C(jm)(jm) C jm# Equivalent spring stiffness of the cable.

[0131] Among them, the boundary conditions of the cable-stayed bridge include the location of the cables, the span layout of the cable-stayed bridge, and the boundary conditions of the large and small mileage side spans.

[0132] S2.3: Constructing the axial force equivalent stiffness matrix

[0133] First, according to the boundary conditions of the cable-stayed bridge, the basic form of the corresponding equivalent stiffness matrix is ​​selected. Due to space limitations, the common simply supported-simply supported cable-stayed bridge structures are listed here, and the basic form of the axial force equivalent stiffness matrix is ​​established as shown in formula (10):

[0134] D(j,j)=-2; D(j,j-1)=D(j,j+1)=1 Equation 10

[0135] in:

[0136] D(j, j) is the diagonal element in the axial force equivalent stiffness matrix;

[0137] D(j, j-1) is the element in row j and column j-1 in the axial force equivalent stiffness matrix;

[0138] D(j, j+1) is the element in row j and column j+1 in the axial force equivalent stiffness matrix;

[0139] The basic form of the axial force matrix is:

[0140]

[0141] According to the dynamic equation established above, it is necessary to assign values ​​to the axial force equivalent stiffness matrix of different beam sections of the main beam. The values ​​are shown in Table 4:

[0142] Table 4. Axial force equivalent stiffness matrix assignment coefficient expression

[0143]

[0144] S2.3.1: The axial force equivalent matrix basic formula is selected through the boundary conditions of the cable-stayed bridge, and the axial force equivalent matrix basic formula is modified according to the equivalent stiffness of the cable on the main beam. When the beam end boundary form of the cable-stayed bridge is a simply supported-simply supported beam, the modification process of the axial force equivalent matrix basic formula is shown in formula (12): D(j, j) = D(j, j)*k DBi Formula 12

[0145] Where: k DBi Assign coefficients to the axial force equivalent stiffness matrix.

[0146] S3: Construct the natural vibration frequency and mode shape characteristic equation matrix of the multi-cable cable-stayed-beam composite structure through the main beam mass matrix, shear force equivalent matrix and axial force equivalent matrix;

[0147] First, the obtained shear force equivalent matrix A and axial force equivalent stiffness matrix D are converted into matrix G according to formula (13).

[0148] [G]=[A]+[D] Formula 13

[0149] The natural vibration frequency and vibration mode characteristic equation matrix of the multi-cable cable-stayed-beam composite structure is as follows:

[0150] F=inv(M)*G Formula 14

[0151] in:

[0152] F is the constructed characteristic equation matrix;

[0153] M is the main beam mass matrix;

[0154] inv represents the inverse of the matrix;

[0155] G is the combined matrix of the shear force equivalent matrix and the axial force equivalent stiffness matrix.

[0156] S4: Obtain the natural vibration frequency and corresponding vibration mode of the cable-stayed bridge through the characteristic equation matrix of the multi-cable cable-stayed-beam combined structure. Specifically, the characteristic root and characteristic vector of the matrix are solved, and the arithmetic square root of the characteristic root is the circular frequency, and the characteristic vector is the vibration mode, as shown in formula (15):

[0157] [B,C]=eig[F] Formula 15

[0158] in:

[0159] B is the structural vibration mode;

[0160] C is the structural line frequency;

[0161] eig means finding eigenvalues ​​and eigenvectors;

[0162] In the above formula, the matrix [B] is the structural natural vibration mode shape, and {C} represents the corresponding structural natural vibration line frequency.

[0163] like Figure 6 As shown, the embodiment of the present invention discloses a practical calculation system for the vertical natural vibration frequency and vibration mode of a cable-stayed bridge, comprising:

[0164] A parameter acquisition module 100, which is used to simplify the cable-stayed bridge into a multi-cable cable-stayed-beam combination structure considering the influence of axial force, and divide the multi-cable cable-stayed-beam combination structure into different beam sections, and obtain main beam parameters and cable parameters of the different beam sections;

[0165] A basic matrix construction and correction module 200, wherein the basic matrix construction and correction module constructs a main beam mass matrix, a shear force equivalent matrix basic formula, and an axial force equivalent matrix basic formula through the main beam parameters of the multi-cable cable-stayed-beam combination structure and the cable parameters; and corrects the shear force equivalent matrix basic formula and the axial force equivalent matrix basic formula to obtain a shear force equivalent matrix and an axial force equivalent matrix;

[0166] A natural vibration frequency and mode shape characteristic equation matrix construction module 300, wherein the natural vibration frequency and mode shape characteristic equation matrix construction module is used to construct the natural vibration frequency and mode shape characteristic equation matrix of the multi-cable cable-stayed-beam composite structure through the main beam mass matrix, the shear force equivalent matrix and the axial force equivalent matrix;

[0167] The module 400 for acquiring the natural vibration frequency and the corresponding vibration mode is used to acquire the natural vibration frequency and the corresponding vibration mode of the cable-stayed bridge through the characteristic equation matrix of the multi-cable cable-stayed-beam combination structure.

[0168] A schematic diagram of a terminal device provided in an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps in the above-mentioned method embodiments are implemented. Alternatively, when the processor executes the computer program, the functions of the modules / units in the above-mentioned device embodiments are implemented.

[0169] The computer program may be divided into one or more modules / units, and the one or more modules / units are stored in the memory and executed by the processor to accomplish the present invention.

[0170] The terminal device may be a computing device such as a desktop computer, a notebook, a PDA, a cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0171] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0172] The memory may be used to store the computer program and / or module, and the processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0173] If the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0174] Example 2

[0175] In order to better understand the technical content of the present invention, Example 2 is specifically cited and described as follows in conjunction with the attached drawings. Aiming at the complex and difficult natural vibration analysis of a multi-cable cable-stayed structure of a cable-stayed bridge, the present invention uses simplified discrete models, finite difference method to optimize equations, and other methods to propose a dynamic modeling theory and natural vibration characteristic analysis method for a multi-cable cable-stayed structure considering axial force.

[0176] This paper uses a concrete cable-stayed bridge as a background case to carry out the analysis of the inherent vibration characteristics. The total length of the bridge is 166.8m (39m+88.8m+39m), with three spans, double platforms, double towers and double cable planes, and a symmetrical cable-stayed arrangement. The main bridge adopts a pier-tower consolidation and main beam semi-floating support system. There are 48 cable-stayed cables in the whole bridge, and the cables are numbered in order from the small mileage side span to the large mileage side span, namely C1#~C24# cables. The reinforced concrete main beam is formed by a combination of segmental prefabricated double box beams and prefabricated carriageway slabs. The box beam is 1.2m high and the net width of the bridge deck is 8.5m. A transverse tie beam is set at the anchor plate between the two box beams, with a longitudinal length of about 0.22m. For the convenience of reference, the parameters of each section of the main beam are summarized as shown in Table 5. The bridge pier is a reinforced concrete hollow thin-walled pier, and the foundation is 8 bored cast-in-place piles with a diameter of 1.5m and a pile length of 40m. The two abutments are gravity abutments. The bridge elevation is shown in Figure 7 The parameters of the inclined cable are shown in Table 6 (only one side is shown, the parameters of the other side are similar, and the elastic modulus of the inclined cable is 200 GPa after being corrected by the Ernst formula).

[0177] Table 5. Main beam parameter setting table

[0178]

[0179] Table 6. Cable-stayed cable parameter setting table

[0180]

[0181] For this example, in order to facilitate the explanation of the principle, the present invention uses MATLAB software for programming and calculation, and the specific process is as follows:

[0182] (1) According to actual conditions, input parameters (unit: N, m, rad, Pa):

[0183] % Input the elastic modulus of the main beam section. To save space, only list the B1# section.

[0184] E_1=2.8e+10;%1# beam section elastic modulus

[0185] % Input main beam mass and second phase paving mass

[0186] G=2.5e+4 / 9.806;% concrete material density

[0187] G_2=2.64e+4 / 9.806;%1#2nd phase bulk density

[0188] % Input the cross-sectional area of ​​the main beam. To save space, only list the B1# section S1=2.404; % Cross-sectional area of ​​1# beam

[0189] % Input the vertical bending inertia moment of the main beam section. To save space, only list the B1# section I1=0.408921; % 1# beam section moment of inertia

[0190] % Input cable mass and cable force. To save space, only C1# section is listed.

[0191] H1=416700;%C1#cable force

[0192] % Input the cable length, to save space, only list the C1# section

[0193] Lc1=12.28;%C1#length

[0194] % Input the cable angle, to save space, only list the C1# section

[0195] seta1=0.9123;%C1#inclination

[0196] % Input the cable cross-sectional area. To save space, only C1# section is listed.

[0197] Ac1=0.0012;%C1#inclination

[0198] % Input the elastic modulus of the cable. To save space, only C1# section is listed.

[0199] Ec1=2e11;%C1#elastic modulus

[0200] (2) Divide segments and process data

[0201] % Determine segment length and segment

[0202] L=166.8;% beam length

[0203] d=0.1;% segment length is 0.1m

[0204] %Calculate the mass per unit length of beam sections B1#~B4#, and only list the B1# section m1=G*S1*d+G_2*d to save space; %B1# beam section mass

[0205] % Calculate the equivalent strength of the cable, and only list the C1# cable to save space

[0206] k1=Ec1*Ac1*sin(seta1)^2 / (Lc1)=3552721;%C1# cable equivalent spring stiffness

[0207] % Calculate the axial force component of the cable, and only list the C1# cable to save space

[0208] N1=Hc1*cos(seta1)=254972.91;%C1# cable equivalent spring stiffness

[0209] (3) Simplify the model and establish a discrete system

[0210] % Divide the segments according to the segment length and the total length of the bridge

[0211] n=L / d; % The whole bridge is divided into 1668 segments, but has a total of 1667 degrees of freedom.

[0212] (4) Considering the boundary conditions, establish the equilibrium equation expression

[0213] % Consider the boundary conditions of the main beam

[0214] 1) The starting pile number of the small mileage is the simply supported end.

[0215] 2) The short mileage side of 1# pier is the consolidation end

[0216] 3) The long mileage side of 1# pier is the consolidation end

[0217] 4) The short mileage side of pier 2# is the consolidation end

[0218] 5) The long mileage side of 2# pier is the consolidation end

[0219] 6) The pile number at the end of a long mileage is a simply supported end

[0220] % Determine the cable anchorage position

[0221] % Determine the area where the main beams with different cross sections are located

[0222] (5) Construct the main beam mass diagonal matrix

[0223] % Construct the main beam mass diagonal matrix foundation form

[0224] a_M=ones(1,n-1); %Build a row vector

[0225] M = diag (a_M); % construct a diagonal matrix

[0226] % Assign the main beam mass matrix according to the area divided by the main beam with different cross-sections. Due to space limitations, only the first three are listed: M(1:9,:)=m2.*M(1:9,:);

[0227] M(10:73,:)=m1.*M(10:73,:);

[0228] M(74:76,:)=m2.*M(74:76,:);...

[0229] (6) Constructing the shear equivalent matrix

[0230] % Generate shear equivalent matrix basis form

[0231] a_1=-4.*ones(1,n-2);

[0232] A_1=diag(a_1,1);

[0233] a_2=ones(1,n-3);

[0234] A_2=diag(a_2,2);

[0235] a_3=ones(1,n-1);

[0236] A_3 = 6.*diag(a_3);

[0237] A_3(1,1)=A_3(1,1)-1;

[0238] A_3(n-1,n-1)=A_3(n-1,n-1)-1;

[0239] A_4=A_1+A_2+A_3;

[0240] A_5 = A_4.';

[0241] A_6 = tril(A_5, -1);

[0242] A=A_6+A_4;

[0243] % A = sparse(A);

[0244] % Assignment coefficients of shear equivalent matrix. Due to space limitations, only the first three are listed.

[0245] kAB1=E_1*I1 / (d^3);

[0246] kAB2=E_2*I2 / (d^3);

[0247] kAB3=E_3*I3 / (d^3); ...

[0249] % Assign values ​​to the shear equivalent matrix according to the drawings. Due to space limitations, only the first three are listed.

[0250] A(1:9,:)=kAB2.*A(1:9,:);

[0251] A(10:73,:)=kAB1.*A(10:73,:);

[0252] A(74:76,:)=kAB2.*A(74:76,:); ...

[0254] % According to the drawings, at the cable anchorage, assign the cable equivalent spring to the shear equivalent matrix. Due to space limitations, only the first three are listed.

[0255] A(1,1)=A(1,1)+k1;

[0256] A(75,75)=A(75,75)+k2;

[0257] A(135,135)=A(135,135)+k3; ..

[0259] % The equivalent spring at the main tower is assumed to be infinite, so it is 10 to the 21st power

[0260] Ks = 1*10e21;

[0261] % According to the drawings, assign the equivalent spring to the shear equivalent matrix at the main tower. Due to space limitations, only the first three are listed.

[0262] A(390,390)=A(390,390)+Ks;

[0263] A(1278,1278)=A(1278,1278)+Ks;

[0264] (7) Constructing the axial force equivalent stiffness matrix

[0265] % Generate the basic form of axial force equivalent stiffness matrix

[0266] d_1 = ones(1,n-2);

[0267] D_1 = diag(d_1,1);

[0268] d_2 = ones(1,n-1);

[0269] D_2 = -2.*diag(d_2);

[0270] D_3 = D_1.';

[0271] D=D_1+D_2+D_3;

[0272] D = -1.*D;

[0273] % Solve the axial force equivalent stiffness matrix assignment coefficients. Due to space limitations, only the first three are listed.

[0274] kDB1=1 / d;

[0275] N_1=N1*kDB1;

[0276] N_2 = N2*kDB1;

[0277] N_3=N3*kDB1; ...

[0279] % Assign values ​​to the left and right axial forces at the cable anchorage, "N_1_1", where N represents the axial force, the first "1" represents the 1# cable, the second "1" represents the left side, and "2" represents the right side. Due to space limitations, only the first three are listed.

[0280] N_1_1=0; % Assign the axial force on the left side of cable 1#

[0281] N_1_2=N_1;%Assign the axial force on the right side of cable 1#

[0282] D(1,1)=2*N_1_1+N_1;% Assign the axial force stiffness matrix at the 1# cable anchorage according to the main beam vibration equation coefficient

[0283] D(1,2)=N_1_2.*D(1,2); % Assign the right axial force stiffness matrix of the 1# cable anchorage according to the main beam vibration equation coefficient

[0284] D(2:74,:)=N_1_2.*D(2:74,:); % The force between 1# and 2# cables is regarded as a constant axial force, and the axial force of the beam section between 1# and 2# cables is assigned

[0285] N_2_1=N_1; % Assign the axial force on the left side of cable 2#

[0286] N_2_2=N_2_1+N_2;%Assign the right axial force of cable 2#

[0287] D(75,75)=2*N_2_1+N_2;% Assign the axial force stiffness matrix at the 2# cable anchorage according to the main beam vibration equation coefficient

[0288] D(75,74)=N_2_1.*D(75,74); % Assign the left axial force stiffness matrix of the 2# cable anchorage according to the main beam vibration equation coefficient

[0289] D(75,76)=N_2_2.*D(75,76); % Assign the right axial force stiffness matrix of the 2# cable anchorage according to the main beam vibration equation coefficient

[0290] D(76:134,:)=N_2_2.*D(76:134,:); % The force between 2# and 3# cables is regarded as a constant axial force, and the axial force of the beam section between 2# and 3# cables is assigned

[0291] N_3_1=N_2_2;

[0292] N_3_2=N_3_1+N_3;

[0293] D(135,135)=2*N_3_1+N_3;

[0294] D(135,134)=N_3_1.*D(135,134);

[0295] D(135,136)=N_3_2.*D(135,136); ...

[0297] % Considering the boundary conditions, the matrix values ​​of the degrees of freedom near the main tower are corrected based on the content of patent description (4) % Assignment Assignment of the axial force equivalent stiffness matrix at the 1# main tower

[0298] D(390,:)=0;

[0299] D(389,390)=0;

[0300] D(389,389)=-D(389,388);

[0301] D(391,390)=0;

[0302] D(391,391)=-D(391,392);

[0303] % Assignment Assignment 2# main tower axial force equivalent stiffness matrix

[0304] D(1278,:)=0;

[0305] D(1277,1278)=0;

[0306] D(1277,1277)=-D(1277,1276);

[0307] D(1279,1278)=0;

[0308] D(1279,1279)=-D(1279,1280);

[0309] (8) Calculation of frequency and vibration mode

[0310] % Combined shear force and axial force equivalent stiffness matrix

[0311] G = A + D;

[0312] % Form frequency feature matrix

[0313] F = inv(M)*G;

[0314] [B,C]=eig(F); % Solve the characteristic roots and eigenvectors of the characteristic matrix, B is the eigenvector matrix, C is the column vector of the characteristic roots,

[0315] C_1=diag(C);% diagonalized characteristic root

[0316] C_2=sqrt(C_1); %The arithmetic square root of the characteristic root is the circular frequency

[0317] f=C_2. / (2*pi); %Convert circular frequency into linear frequency

[0318] Based on this, the natural vibration frequency and vibration mode of the cable-stayed bridge with real structure are obtained and compared with the actual bridge measurement and finite element analysis results. The details of setting the reference example parameters are as follows:

[0319] Reference Condition 1# (RC1), solid structure finite element method: According to the actual bridge structure, commercial finite element software is used to analyze the dynamic characteristics of the bridge and identify the natural frequency and vibration mode characteristics of the structure.

[0320] Reference Condition 2# (RC2), field measurement method: Acceleration sensors are placed in the 0.4L section of the side span and the mid-span section of the middle span of the bridge, and the vibration test of the bridge structure is carried out using the pulsation excitation method to identify the dynamic characteristic parameters of the first three-order overall vibration of the bridge. The DHSAS spectrum analysis and modal analysis software is used to perform fast Fourier transform to obtain the corresponding power spectrum diagram, and further spectrum analysis can be performed to obtain the natural frequency and damping ratio of the bridge structure.

[0321] Reference Condition 3#, RC3, simplified model finite element method: Based on the actual bridge structure, Figure 2 (b) Structural simplification method: the cables are equivalent to dynamic springs, the horizontal projection of the cable force is equivalent to the longitudinal concentrated load on the main beam unit, and the rigid connection boundary condition is adopted at the tower-beam connection. The dynamic characteristics of the bridge are analyzed using commercial finite element software to identify the natural frequency and vibration mode characteristics of the structure.

[0322] Reference Condition 4# (RC4), simplified model analytical method: According to the simplified dynamic model and vibration equation of this paper, the tower-beam connection adopts the boundary condition of consolidated connection, and the large and small mileage combined piers adopt the simply supported boundary condition. The cables located in the same section of the main beam are considered as the parallel relationship of dynamic springs. Based on formula (17), the length of the micro-beam segment is respectively taken as

[0323] d 1 =0.1m Formula 2

[0324] The natural vibration characteristics of the structure are analyzed analytically.

[0325] Based on the above working condition settings, the first three-order natural frequencies of the bridge are calculated and shown in Table 7.

[0326] Table 7 Natural vibration frequency of cable-stayed bridge deck (Hz)

[0327]

[0328] Overall, the errors of the natural frequencies of the structures obtained by the four methods are small, and the maximum absolute error value is only 0.13Hz. The construction time of the bridge is relatively long, and the structural stiffness has decreased during traffic operation. Therefore, the structural fundamental frequency in RC1, which uses the design index parameters for the analysis of the natural vibration characteristics, is slightly higher than that of RC2. At the same time, the natural frequencies of RC3 and RC4, which use the same optimization calculation method for the cable structure, are relatively close, with an average error value of 0.0187Hz, and the average absolute error value of RC4 relative to RC1 is 0.0189Hz, and the average absolute error rate is 18‰. The above situation further illustrates the effectiveness of the method in this paper for calculating the natural vibration frequency of complex cable structures.

[0329] According to the finite element numerical simulation and analytical method in this paper, the first three vertical natural vibration modes of the cable-stayed bridge are solved as follows: Figure 8 shown.

[0330] Figure 8 The first three vibration modes of the structure under the three working conditions are consistent with each other, among which the vibration modes of RC3 and RC4 structures using the same simplified dynamic spring system are more similar. The above situation further verifies the feasibility of solving the vibration modes of multi-cable structures using the analytical formula in this paper.

[0331] in, Figure 1 In the formulas 16, 17 and 18, the specific formulas are:

[0332]

[0333] In the above formula:

[0334] According to C jm #The element of the j-1th row and jth column of the axial force equivalent stiffness matrix after correction of the axial force calculation formula of the main beam on the left side of the cable;

[0335] C ji #Projection of the cable force in the main beam's long mileage direction;

[0336] According to C jm #The element of the jth row and jth column of the axial force equivalent stiffness matrix after correction of the main beam axial force calculation formula of the cable anchor section;

[0337] According to C jm #The calculation formula for the axial force of the main beam on the right side of the cable is the element in the jth row and j+1th column of the axial force equivalent stiffness matrix after correction.

[0338] The present invention takes into account the influence of axial force on the natural vibration of the main beam, and effectively simulates the influence of the vertical bending stiffness of the main beam and the coupling effect between cables during vibration in the main beam discrete element parameter mass system based on shear force difference and axial force difference, constructs the characteristic equation for calculating the natural vibration frequency of the cable-stayed bridge, and proposes a method for solving the eigenvalues ​​and eigenvectors of the characteristic matrix to solve the natural vibration related parameters of the multi-cable cable-stayed structure. Compared with the previous finite element numerical simulation method, the simplified formula for the cable-stayed bridge proposed by the present invention can quickly and effectively calculate the vertical natural vibration frequency and vibration mode of complex spatial cable structures such as cable-stayed bridges by using tools such as Excel and Matlab, and has strong convenience and operability.

[0339] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge. It is characterized in that The following steps are involved: S1: simplifying the cable-stayed bridge into a multi-cable cable-stayed-beam composite structure considering the influence of axial force, dividing the multi-cable cable-stayed-beam composite structure into different beam sections, and obtaining main beam parameters, cable parameters and different boundary conditions of different beam sections; S2: constructing the main beam mass matrix, shear equivalent matrix basic formula and axial force equivalent matrix basic formula through the main beam parameters, cable parameters and different boundary conditions of the multi-cable cable-stayed-beam composite structure; and modifying the shear equivalent matrix basic formula and the axial force equivalent matrix basic formula to obtain the shear equivalent matrix and the axial force equivalent matrix; S3: constructing the natural vibration frequency and mode shape characteristic equation matrix of the multi-cable cable-stayed-beam composite structure through the main beam mass matrix, shear force equivalent matrix and axial force equivalent matrix; S4: Obtain the natural vibration frequency and mode shape of the cable-stayed bridge through the natural vibration frequency and mode shape characteristic equation matrix of the multi-cable cable-stayed-beam combination structure.

2. According to claim 1, a method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge, It is characterized in that The main beam parameters of the different beam sections include the masses of the different beam sections, and the main beam mass matrix is ​​constructed by the masses of the different beam sections.

3. According to claim 1, a method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge, It is characterized in that The shear force equivalent matrix basic formula is specifically: A(j,j)=6; A(j,j-1)=A(j,j+1)=-4; A(j,j-2)=A(j,j+2)=-1 In the formula, A(j, j) is the diagonal element in the shear equivalent matrix; A(j, j-1) is the element in row j and column j-1 in the shear equivalent matrix; A(j, j+1) is the element in row j and column j+1 in the shear equivalent matrix; A(j, j-2) is the element in row j and column j-2 of the shear equivalent matrix; A(j, j+2) is the element in the jth row and j+2th column of the shear equivalent matrix.

4. According to claim 3, a method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge, It is characterized in that The shear force equivalent matrix basic formula is selected according to the boundary conditions of the cable-stayed bridge, and the shear force equivalent matrix basic formula is modified; when the beam end boundary form of the cable-stayed bridge is a simply supported-simply supported beam, the modification process of the shear force basic matrix is ​​specifically as follows: A(j,j)=k ABi [A(j,j)+k C(jm)(jm) ] In the formula, k ABi Assign coefficients to the shear equivalent matrix; k C(jm)(jm) C jm# Equivalent spring stiffness of the cable.

5. According to claim 1, a method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge, It is characterized in that The axial force equivalent matrix basic formula is specifically: D(j,j)=-2; D(j,j-1)=D(j,j+1)=1 Where: D(j, j) is the diagonal element in the axial force equivalent stiffness matrix; D(j, j-1) is the element in row j and column j-1 in the axial force equivalent stiffness matrix; D(j, j+1) is the element in the jth row and j+1th column of the axial force equivalent stiffness matrix.

6. A method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge according to claim 5, It is characterized in that The axial force equivalent matrix basic formula is selected by the boundary condition of the cable-stayed bridge, and the axial force equivalent matrix basic formula is modified according to the equivalent stiffness of the cable on the main beam. When the beam end boundary form of the cable-stayed bridge is a simply supported-simply supported beam, the modification process of the axial force equivalent matrix basic formula is specifically as follows: D(j,j)=D(j,j)*k DBi Where: k DBi Assign coefficients to the axial force equivalent stiffness matrix.

7. The method for calculating the vertical natural vibration frequency and vibration mode of a cable-stayed bridge according to claim 1, It is characterized in that The natural vibration frequency and mode shape characteristic equation matrix of the multi-cable cable-stayed-beam composite structure is specifically: F=inv(M)*G Where, F is the natural vibration frequency and mode shape characteristic equation matrix of the multi-cable cable-stayed-beam composite structure; M is the main beam mass matrix; Inv represents the inverse of the matrix; in, [G]=[A]+[D] In the formula, G is the combined matrix of the shear force equivalent matrix and the axial force equivalent stiffness matrix; A is the shear equivalent matrix; D is the stiffness matrix equivalent to the axial force; The natural vibration frequency and vibration mode of the cable-stayed bridge are obtained by the characteristic equation matrix of the multi-cable cable-stayed-beam combined structure as follows: [B,C]=eig[F] Wherein, [B] is the natural vibration mode of the cable-stayed bridge; {C} is the natural vibration line frequency of the cable-stayed bridge; eig means finding eigenvalues ​​and eigenvectors.

8. A calculation system for the vertical natural vibration frequency and vibration mode of a cable-stayed bridge. It is characterized in that include: A parameter acquisition module, wherein the parameter acquisition module is used to simplify the cable-stayed bridge into a multi-cable cable-stayed-beam combination structure considering the influence of axial force, and divide the multi-cable cable-stayed-beam combination structure into different beam sections, and obtain main beam parameters and cable parameters of different beam sections; A basic matrix construction and correction module, wherein the basic matrix construction and correction module constructs a main beam mass matrix, a shear equivalent matrix basic formula, and an axial force equivalent matrix basic formula through the main beam parameters of the multi-cable cable-stayed-beam composite structure and the cable parameters; and corrects the shear equivalent matrix basic formula and the axial force equivalent matrix basic formula to obtain a shear equivalent matrix and an axial force equivalent matrix; A module for constructing a matrix of natural vibration frequency and mode shape characteristic equations, wherein the module is used to construct a matrix of natural vibration frequency and mode shape characteristic equations of the multi-cable cable-stayed-beam composite structure through the main beam mass matrix, the shear force equivalent matrix and the axial force equivalent matrix; A module for obtaining natural vibration frequency and corresponding vibration mode, wherein the module is used to obtain the natural vibration frequency and corresponding vibration mode of the cable-stayed bridge through the characteristic equation matrix of the multi-cable cable-stayed-beam combination structure.

9. A terminal device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, It is characterized in that When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program. It is characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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