A spatial torsional vibration simulation method for cableway bridges in complex environments

Abstract

The present invention relates to a method for simulating the spatial torsional vibration of a cableway bridge suitable for complex environments, the method comprising the following steps: 1) establishing a three-dimensional spatial model of the cableway bridge using vector finite elements; 2) importing environmental monitoring data and defining simulation conditions; 3) completing the spatial torsional vibration simulation of the cableway bridge by iteratively solving the displacement and internal force of the model within each integral step. Beneficial effects of the present invention: based on the characteristic that vector finite elements do not require the assembly of an overall stiffness matrix, the simulation method reduces the difficulty of solving large deformation and spatial torsional vibration problems of flexible structures such as cableway bridges; compared with theoretical analytical methods and traditional finite element methods, the method simplifies the modeling and solution process, and the vector finite element method is easy to program, and the method can be extended to structural spatial vibration problems under different environmental characteristics, structural properties, and load combinations.

Description

Technical Field

[0001] The present invention relates to the fields of bridge engineering design and vibration simulation, and in particular to a method for simulating spatial torsional vibration of a cableway bridge suitable for complex environments. Background Art

[0002] Cableway bridges are widely used in highway, railway, and hydropower station construction projects across complex terrain such as mountainous canyons. They offer strong spanning capacity, low cost, and convenient construction. However, the primary load-bearing components of cableway bridges are steel strands or high-strength steel cables, which exhibit nonlinear characteristics. The overall stiffness of the bridge is relatively soft and the frequency is low. These vibrations are susceptible to spatial torsional vibrations under eccentric loads, wind loads, and the regular movement of pedestrians, posing a serious threat to the safety of the cableway bridge structure.

[0003] At present, torsional vibration coupling is often ignored in most designs, and cables are only calculated as planar structures. As a result, the design is relatively conservative and cannot better exert the structural performance. The theoretical analytical method is used to solve such spatial torsional vibration problems. There are many assumptions and variables, the formulas are complicated, and the applicability is relatively limited. The vector finite element method discretizes the structural form into a group of particles connected to each other by massless units, and describes the mechanical behavior of the structure in a physical model. There is no need to calculate the overall stiffness matrix, which avoids the matrix singularity problem of traditional finite elements. It is suitable for spatial nonlinear calculations of flexible structures and greatly reduces the difficulty of solving such spatial torsional vibration problems. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a spatial torsional vibration simulation method for cableway bridges that has high simulation accuracy and is easy to develop and is suitable for complex environments, thereby reducing the difficulty of analyzing spatial torsional vibration problems in bridge engineering design, construction, and operation and maintenance, and providing reliable and efficient technical support for vibration reduction simulation analysis.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] In a first aspect, the present invention provides a method for simulating spatial torsional vibration of a cableway bridge suitable for complex environments, the method comprising the following steps:

[0007] Step 1: Based on the cableway bridge layout information, a vector finite element three-dimensional space model of the cableway bridge is established and pre-processing operations are performed;

[0008] Step 2: Import environmental data and set simulation load conditions;

[0009] Step 3: Define the integration time and step size, and iteratively solve the displacement and internal force of the cableway bridge vector finite element model within each integration step;

[0010] Step 4: Determine whether the integration termination condition is met. If the integration termination condition is met, execute step 5; otherwise, repeat step 3.

[0011] Step 5: Outputting the spatial torsional vibration simulation data of the cableway bridge;

[0012] Preferably, in step 1, the establishment of a vector finite element three-dimensional space model of the cableway bridge and the pre-processing operation include:

[0013] Step 1.1. Discretize the cableway bridge into a group of mass points connected by massless units. The spatial position of each mass point is expressed by the linear displacement and angular displacement of the mass point along the coordinate axis of the global coordinate system. The formula is:

[0014] ;

[0015] ;

[0016] Step 1.2: Obtain the material properties of the relevant components, such as cross-sectional area, material density, elastic modulus, and damping coefficient; select massless unit types according to the different load-bearing components of the cableway bridge, using rod units for cables and beam units for beams; define the system damping coefficient and the linear displacement of each mass point at the initial time t0 , initial velocity , initial acceleration , angular displacement , initial angular velocity , initial angular acceleration , particle axial force and external axial force , particle bending moment and external bending moment ;

[0017] Preferably, in step 2, importing environmental data and setting simulation load conditions include:

[0018] Step 2.1: Collect relevant monitoring or empirical data for the project area, such as wind speed spectrum, earthquake spectrum, rainfall (snow) statistics, seasonal temperature curve, and traffic volume. Select the corresponding environmental monitoring data based on the calculation requirements, set the simulation load conditions, and generate load time history data.

[0019] Step 2.2: According to the load distribution characteristics, convert it into a particle external force, and then distribute it to each particle to form an external force. matrix;

[0020] Preferably, in step 3, the iterative solution includes:

[0021] Step 3.1: Use the central difference method as the integration method in the vector finite element analysis process, according to the time tn The spatial position of the particle and , particle axial force , particle bending moment , external axial force and external bending moment Solve time t n+1 The spatial position of the particle and ;

[0022] Step 3.2, solve the equation of each particle at time t by using the virtual reverse motion and the principle of virtual work. n+1 The axial force of the particle and particle bending moment ;

[0023] As a preference, in step 3.1, the central difference method is used as the integral method in the vector finite element analysis process, according to the time t n The spatial position of the particle and , particle axial force , particle bending moment , external axial force and external bending moment Solve time t n+1 The spatial position of the particle and , expressed as:

[0024] ;

[0025] ;

[0026] Among them, m N is the mass of particle N; is the moment of inertia of particle N; h is the integration step length; and is the particle at time t n-1 spatial location; , C is the damping coefficient matrix in the vector finite element model of the cableway bridge.

[0027] As a preference, in step 3.2, the virtual reverse motion and the principle of virtual work are used to solve the problem of each particle at time t n+1 The axial force of the particle and particle bending moment , expressed as:

[0028] ;

[0029] Where i and j represent the numbers of the two mass points connected to the two ends of the massless unit respectively; num represents the total number of massless units connected to mass point N; is the internal force generated by the massless element.

[0030] When calculating axial forces, ;

[0031] When calculating the bending moment, ;

[0032] When calculating torque, ;

[0033] Where E represents the elastic modulus of the connection unit, G represents the shear modulus of the connection unit, A represents the cross-sectional area of ​​the connection unit, I represents the corresponding section moment of inertia of the connection unit, and a and b represent the bending moment calculation coefficients that need to be determined according to the boundary conditions of the beam.

[0034] In a second aspect, a computer storage medium is provided, in which a computer program is stored; when the computer program is run on a computer, the computer executes any of the cableway bridge spatial torsional vibration simulation methods applicable to complex environments described in the first aspect.

[0035] In a third aspect, a computer program product is provided. When the computer program product is run on a computer, the computer is caused to execute the cableway bridge spatial torsional vibration simulation method applicable to complex environments as described in any one of the first aspects.

[0036] The beneficial effects of the present invention are as follows: (1) the simulation method is based on the characteristic of vector finite element that does not require the assembly of the overall stiffness matrix, which reduces the difficulty of solving large deformation and spatial torsional vibration problems of flexible structures such as cableway bridges; (2) compared with theoretical analytical methods and traditional finite element methods, this method simplifies the modeling and solution process, and vector finite element is easy to program, and the method can be extended to structural spatial vibration problems under different environmental characteristics, structural properties and load combinations; (3) the method is widely applicable to the spatial torsional vibration simulation of cableway bridges and other complex structures with cables as load-bearing components, and builds a platform for monitoring and vibration reduction analysis in process design, construction, operation and maintenance. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art or ordinary technicians, other drawings can be obtained based on these drawings without paying any creative work.

[0038] Figure 1 An exploded view of the vector finite element model unit of the cableway bridge provided by the present invention;

[0039] Figure 2A schematic flow chart of a method for simulating spatial torsional vibration of a cableway bridge suitable for complex environments provided by the present invention;

[0040] Figure 3 This is an example diagram of the vector finite element space model of the cableway bridge provided by the present invention;

[0041] Figure 4 A time history diagram of the vertical displacement of cable No. 1 at the 1 / 5 position under a set load condition of the cable bridge provided by the present invention;

[0042] Figure 5 The spatial deformation moment diagram of beam No. 1 of the cableway bridge provided by the present invention under a set load condition;

[0043] Figure 6 This is a spatial position diagram of the cableway bridge provided by the present invention under a set load condition at t=60s. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0045] Example 1:

[0046] Cableway bridges are mainly composed of two types of load-bearing components: cables and beams. The present invention provides a cableway bridge spatial torsional vibration simulation method suitable for complex environments. Based on the vector finite element method, a multi-unit cableway bridge spatial model is established, such as Figure 1 As shown in the figure, the cables use rod elements and the beams use beam elements. Through the small deformation characteristics in each small time period, the problem of large deformation of spatial torsional vibration is transformed into an iterative solution of the small deformation displacement and internal force of each particle within the integral step, completing the spatial torsional vibration simulation of the cableway bridge, as shown in the figure. Figure 2 Shown, including:

[0047] Step 1: According to the cableway bridge layout information, a vector finite element three-dimensional space model of the cableway bridge is established;

[0048] For example, Figure 3 As shown, the cable bridge has a clear span of L = 160 m, 4 load-bearing cables, and the axial stiffness of the cable is E c A c =1.05×10 9 N, mass per unit length ρ c=110 kg / m, nominal tensile strength F=1779 MPa, assuming the first-order viscous damping ratio of the cable is 0.5%; there are 4 beams in total, and the axial stiffness of each beam is E b A b =1.45×10 10 N, bending stiffness E b I b =3.15×10 7 N﹒ m 2 , torsional stiffness G b I wb =8.27×10 6 N, mass per unit length ρ b =513kg / m; the uniformly distributed force of the second phase constant load is 7.0kN / m.

[0049] Step 2: Import environmental data and set simulation load conditions:

[0050] For example, based on the environmental conditions of the project area and the load condition data of similar projects, the cableway bridge in this embodiment is subjected to random fluctuating wind with an average wind speed of 20m / s, which is converted into particle external force and then distributed to each particle; at the same time, a car is set to pass with an eccentric load, and the driving time is 180s. The vehicle load adopts concentrated force to form an integrated external force. matrix;

[0051] Step 3: Define the integration time ET = 300 s and the integration step h = 0.0001, and iteratively solve the displacement and internal force of the cableway bridge vector finite element model within each integration step;

[0052] Step 4: Determine whether the integration termination condition is met. If the integration termination condition is met, execute step 5; otherwise, repeat step 3.

[0053] Step 5: Store the displacement data of each mass point in the model and output the spatial torsional vibration data of the cableway bridge under the set working conditions.

[0054] In step 1, a vector finite element model of the cableway bridge is established and pre-processing operations are performed, including:

[0055] Step 1.1, such as Figure 3 As shown in Figure 1, the cables and beams of the cableway bridge are discretized into mass points. The cables are connected with massless rod elements, and the beams are connected with massless beam elements. This forms a three-dimensional spatial model of the cableway bridge, which can be expressed as:

[0056] ;

[0057] ;

[0058] Step 1.2: Obtain the material properties of the relevant components, such as cross-sectional area, material density, elastic modulus, and damping coefficient; select massless unit types according to the different load-bearing components of the cableway bridge, using rod units for cables and beam units for beams; define the system damping coefficient and the linear displacement of each mass point at the initial time t0 , initial velocity , initial acceleration , angular displacement , initial angular velocity , initial angular acceleration , particle axial force and external axial force , particle bending moment and external bending moment The cable mass is evenly distributed among each mass point. Assuming the initial cable force T0 = 335 kN and taking it as the initial massless unit internal force, the initial mass point force is obtained. , set the initial velocity, acceleration, angular velocity, and angular acceleration of each particle to 0.

[0059] In step 3, the iterative solution includes:

[0060] Step 3.1: According to time t n The spatial position of the particle and , particle axial force , particle bending moment , external axial force and external bending moment Solve time t n+1 The spatial position of the particle and :

[0061] ;

[0062] ;

[0063] Among them, m N is the mass of particle N; is the moment of inertia of particle N; h is the integration step length; and is the particle at time t n-1 spatial location; , C is the damping coefficient matrix in the vector finite element model of the cableway bridge.

[0064] Step 3.2, solve the equation of each particle at time t by using the virtual reverse motion and the principle of virtual work. n+1 The axial force of the particle and particle bending moment , expressed as:

[0065] ;

[0066] Where i and j represent the numbers of the two mass points connected to the two ends of the massless unit respectively; num represents the total number of massless units connected to mass point N; is the internal force generated by the massless element.

[0067] When calculating axial forces, ;

[0068] When calculating the bending moment, ;

[0069] When calculating torque, ;

[0070] Where E represents the elastic modulus of the connection unit, G represents the shear modulus of the connection unit, A represents the cross-sectional area of ​​the connection unit, and I represents the corresponding section moment of inertia of the connection unit.

[0071] Specifically, if Figure 2 As shown in the figure, the program architecture is based on a While or For loop. The solution module is entered to solve the particle displacement of the analyzed component at the next moment, and the particle force at the next moment is solved according to the virtual reverse motion. When the integration termination condition is reached, the loop solution step is jumped out and the particle displacement at that moment is stored.

[0072] Figures 4 and 5 This paper shows some simulation results of the spatial torsional vibration of the cable bridge in this example. Figure 6 The spatial torsional vibration of a cableway bridge at t = 60s is demonstrated. This result is automatically calculated based on a set load condition. In practical applications, sensitive load conditions can be set based on actual engineering requirements to simulate the spatial torsional vibration of cableway bridges. This example demonstrates the dynamic nature of the proposed method for simulating the spatial torsional vibration of cableway bridges in complex environments. The simulation curves conform to practical logic, validating the scientific nature of the invention.

[0073] In summary, the cableway bridge spatial torsional vibration simulation method provided by the present invention is a simulation method with simple concept, strong applicability to flexible structures and good accuracy, which provides a reliable calculation means for the design and research of cableway bridges.

[0074] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the scope of the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for simulating spatial torsional vibration of a cableway bridge suitable for complex environments, characterized in that: include: Step 1: Based on the cableway bridge layout information, a vector finite element three-dimensional space model of the cableway bridge is established and pre-processing operations are performed; The establishment of the vector finite element three-dimensional space model of the cableway bridge and the pre-processing operation include: Step 1.

1. Discretize the cableway bridge into a group of mass points connected by massless units. The spatial position of each mass point is expressed by the linear displacement and angular displacement of the mass point along the coordinate axis of the global coordinate system. The formula is: ； ； Step 1.2: Obtain the material properties of the relevant components, including cross-sectional area, material density, elastic modulus, and damping coefficient. Select massless element types according to the different load-bearing components of the cableway bridge, using rod elements for cables and beam elements for beams. Define the system damping coefficient and the linear displacement of each mass point at the initial time t0. , initial velocity , initial acceleration , angular displacement , initial angular velocity , initial angular acceleration , particle axial force and external axial force , particle bending moment and external bending moment ; Step 2: Import environmental monitoring data and set simulation load conditions; Step 3: Define the integration time and step size, and iteratively solve the displacement and internal force of the cableway bridge vector finite element model within each integration step; Step 3.1: Use the central difference method as the integration method in the vector finite element analysis process, according to the time t n The spatial position of the particle and , particle axial force , particle bending moment , external axial force and external bending moment , solve for time t n+1 The spatial position of the particle and , expressed as: ； ； Among them, m N is the mass of particle N; is the moment of inertia of particle N; h is the integration step length; and is the particle at time t n-1 spatial location; , C is the damping coefficient matrix in the vector finite element model of the cableway bridge; Step 3.2, solve the equation of each particle at time t by using the virtual reverse motion and the principle of virtual work. n+1 The axial force of the particle and particle bending moment , expressed as: ； Where i and j represent the numbers of the two mass points connected to the two ends of the massless unit respectively; num represents the total number of massless units connected to mass point N; The internal forces generated by massless elements; When calculating axial forces, ; When calculating the bending moment, ; When calculating torque, ; Where E represents the elastic modulus of the connection unit, G represents the shear modulus of the connection unit, A represents the cross-sectional area of ​​the connection unit, I represents the corresponding section moment of inertia of the connection unit, and a and b represent the bending moment calculation coefficients that need to be determined based on the boundary conditions of the beam. Step 4: Determine whether the integration termination condition is met. If the integration termination condition is met, execute step 5; otherwise, repeat step 3. Step 5: Output the spatial torsional vibration simulation data of the cableway bridge.

2. The method for simulating spatial torsional vibration of a cableway bridge suitable for complex environments according to claim 1, characterized in that: In step 2, the environmental monitoring data is imported and the simulation load conditions are set, including: Step 2.1: Collect relevant monitoring or empirical data for the project area, including wind speed spectrum, earthquake spectrum, rainfall or snowfall statistics, seasonal temperature curve, and traffic volume. Select the corresponding environmental monitoring data based on the calculation requirements, set the simulation load condition, and generate load time history data. Step 2.2: According to the load distribution characteristics, convert it into a particle external force, and then distribute it to each particle to form an external force. matrix.

3. A computer storage medium, characterized in that The computer storage medium stores a computer program; when the computer program is run on a computer, the computer executes the cableway bridge spatial torsional vibration simulation method applicable to complex environments according to any one of claims 1 to 2.

4. A computer program product, characterized in that When the computer program product is run on a computer, the computer is enabled to execute the cableway bridge spatial torsional vibration simulation method applicable to complex environments as claimed in any one of claims 1 to 2.

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