Cableway bridge space torsional vibration simulation method suitable for complex environment

Abstract

The invention relates to a cableway bridge space torsional vibration simulation method suitable for a complex environment. The method comprises the following steps: 1) establishing a cableway bridge vector type finite element three-dimensional space model; 2) importing environment monitoring data, and defining a simulation working condition; and 3) iteratively solving the displacement and the internal force of the model in each integral step to finish the spatial torsional vibration simulation of the cableway bridge. The method has the beneficial effects that the simulation method is based on the characteristic that a vector finite element does not need to assemble an overall stiffness matrix, and the solving difficulty of the problems of large deformation and spatial torsional vibration of the flexible structure such as the cableway bridge is reduced; compared with a theoretical analysis method and a traditional finite element method, the method has the advantages that the modeling and solving process is simplified, the vector type finite element is easy to program, and the method can be popularized to solve the structural space vibration problem under different environment characteristics, structural characteristics and load combinations.

Description

Technical Field

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

[0002] Cableway bridges are widely used in the construction of highways, railways and hydropower stations in complex terrains such as mountainous canyons. They are a type of bridge structure with strong spanning capacity, low cost and convenient construction. The main load-bearing components of cableway bridges are steel strands or high-strength steel wire ropes, which have nonlinear characteristics. The overall stiffness of the bridge is relatively soft and the frequency is low. Under the action of eccentric loads, wind loads, and regular footsteps of people, it is very easy to produce spatial torsional vibrations, which pose a serious threat to the safety of the cableway bridge structure.

[0003] At present, in most designs, torsional vibration coupling is often ignored, and the cable is only calculated as a plane structure. Therefore, 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, but it assumes many conditions and variables, has complicated formulas, and has limited applicability. The vector finite element discretizes the structural morphology 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, which 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 prior art and to provide a spatial torsional vibration simulation method for a cableway bridge 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 a complex environment, the method comprising the following steps:

[0007] Step 1: According to the layout information of the cableway bridge, 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 length, and iteratively solve the displacement and internal force of the cableway bridge vector finite element model in each integration step length;

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

[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] x={x 1,n ;x 2,n ;...;x N,n}={(x1,y1,z1);(x2,y2,z2);...;(x N ,y N ,z N )}

[0015] θ={θ 1,n θ 2,n ;...;θ N,n}={(θ x1 ,θ y1 ,θ z1 );(θ x2 ,θ y2 ,θ z2 );...;(θ xN ,θ yN ,θ zN )}

[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, use rod units for cables, and use beam units for beams; define the system damping coefficient, the linear displacement x of each mass point at the initial time t0 N,0 , initial speed Initial acceleration Angular displacement θ N,0 , initial angular velocity Initial angular acceleration Particle axial force fx N,0 and external axial force Px n,0 , particle bending moment fm N,0 and external bending moment Pm N,0 ;

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

[0018] Step 2.1: Collect relevant monitoring or empirical data of the project area, such as wind speed spectrum, earthquake spectrum, rainfall (snow) statistics, seasonal temperature curve, traffic flow, etc. Select the corresponding environmental monitoring data according to the calculation needs, set the simulation load condition, 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 P N,n 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 t n The spatial position of the particle x N,n and θ N,n 、Particle axial force fx N,n , particle bending moment fm N,n , external axial force Px N,n and external bending moment Pm N,n Solve for time t n+1 The spatial position of the particle x N,n+1 and θ N,n+1 ;

[0022] Step 3.2: Use the virtual reverse motion and the principle of virtual work to solve the equation for each particle at time t n+1 The particle axial force fx N,n+1 and particle bending moment fm N,n+1 ;

[0023] As a preferred method, 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 x N,n and θ N,n 、Particle axial force fx N,n , particle bending moment fm N,n , external axial force Px N,n and external bending moment Pm N,n Solve for time t n+1 The spatial position of the particle x N,n+1 and θ N,n+1 , expressed as:

[0024]

[0025] Among them, m N is the mass of particle N; is the moment of inertia of particle N; h is the integration step; x N,n-1 and θ N,n-1is 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.

[0026] As a preferred embodiment, in step 3.2, the virtual reverse motion and virtual work principle are used to solve the problem of each particle at time t n+1 The particle axial force fx N,n+1 and particle bending moment fm N,n+1 , expressed as:

[0027]

[0028] Where i and j represent the numbers of the two mass points connected to the two ends of the massless unit; num represents the total number of massless units connected to mass point N; f e is the internal force generated by the massless element.

[0029] When calculating the axial force, When calculating the bending moment, When calculating torque,

[0030] 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.

[0031] 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 as described in the first aspect.

[0032] In a third aspect, a computer program product is provided. When the computer program product is run on a computer, the computer is enabled to execute the spatial torsional vibration simulation method of a cableway bridge applicable to a complex environment as described in any one of the first aspects.

[0033] 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 an 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 elements are easy to program. This method can be extended to structural spatial vibration problems under different environmental characteristics, structural properties and load combinations; (3) This method is widely applicable to the spatial torsional vibration simulation of cableway bridges and other complex structures with cables as load-bearing components, and provides a platform for monitoring and vibration reduction analysis in process design, construction, and operation and maintenance. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. 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 creative work.

[0035] Figure 1 The decomposition diagram of the vector finite element model unit of the cableway bridge provided by the present invention;

[0036] Figure 2 A schematic flow chart of a method for simulating spatial torsional vibration of a cableway bridge suitable for a complex environment provided by the present invention;

[0037] Figure 3 An example diagram of the vector finite element space model of the cableway bridge provided by the present invention;

[0038] Figure 4 A vertical displacement time history diagram of the No. 1 cable at the 1 / 5 position under a set load condition of the cableway bridge provided by the present invention;

[0039] Figure 5 The spatial deformation time diagram of the No. 1 beam of the cableway bridge provided by the present invention under the set load condition;

[0040] Figure 6 The present invention provides a spatial position diagram of the cableway bridge at t=60s under a set load condition. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0042] Embodiment 1:

[0043] The cableway bridge is 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. A multi-unit cableway bridge spatial model is established based on vector finite elements, such as Figure 1 As shown in the figure, the cables are made of rod elements and the beams are made of beam elements. Through the small deformation characteristics in each tiny period of time, the problem of large deformation of spatial torsion is transformed into an iterative solution of the small deformation displacement and internal force of each particle within the integral step, thus completing the spatial torsional vibration simulation of the cableway bridge. Figure 2 As shown, including:

[0044] Step 1: According to the cableway bridge layout information, the establishment of the cableway bridge vector finite element three-dimensional space model is completed;

[0045] For example, Figure 3 As shown, the cableway bridge has a clear span of L = 160m, 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 =110kg / m, nominal tensile strength F = 1779MPa, assuming that 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.

[0046] Step 2: Import environmental data and set simulation load conditions:

[0047] For example, according to the environmental conditions of the project area and the load condition data of similar projects, the average wind speed of the random pulsating wind borne by the cableway bridge in this embodiment is 20m / s, which is converted into a particle external force and 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 a concentrated force to form an integrated external force P N,0 matrix;

[0048] Step 3: define the integration time ET = 300 s, the integration step h = 0.0001, and iteratively solve the displacement and internal force of the cableway bridge vector finite element model in each integration step;

[0049] Step 4: determine whether the integral termination condition is met. If the integral termination condition is met, execute step 4, otherwise repeat step 2;

[0050] Step 5: Store the displacement data of each particle in the model and output the spatial torsional vibration data of the cableway bridge under the set working conditions.

[0051] In step 1, a vector finite element model of the cableway bridge is established and pre-processing operations are performed, including:

[0052] Step 1.1: Figure 3As shown in the figure, 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 to form a three-dimensional space model of the cableway bridge, which can be expressed as:

[0053] x={x 1,n ;x 2,n ;...;x N,n}={(x1,y1,z1);(x2,y2,z2);...;(x N ,y N ,z N )}

[0054] θ={θ 1,n θ 2,n ;...;θ N,n}={(θ x1 ,θ y1 ,θ z1 );(θ x2 ,θ y2 ,θ z2 );...;(θ xN ,θ yN ,θ zN )}

[0055] 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, use rod units for cables, and beam units for beams; define the system damping coefficient, the linear displacement x of each mass point at the initial time t0 N,0 , initial velocity Initial acceleration Angular displacement θ N,0 , initial angular velocity Initial angular acceleration Particle axial force fx N,0 and external axial force Px n,0 , particle bending moment fm N,0 and external bending moment Pm N,0 The mass of the cable is shared by each mass point. Assume that the initial cable force T0 = 335 kN and use it as the initial massless unit internal force to obtain the initial mass point force f N,0 , set the initial velocity, acceleration, angular velocity, and angular acceleration of each particle to 0.

[0056] In step 3, the iterative solution includes:

[0057] Step 3.1: According to time t n The spatial position of the particle x N,n and θ N,n 、Particle axial force fx N,n , particle bending moment fm N,n, external axial force Px N,n and external bending moment Pm N,n Solve for time t n+1 The spatial position of the particle x N,n+1 and θ N,n+1 :

[0058]

[0059] Among them, m N is the mass of particle N; is the moment of inertia of particle N; h is the integration step; x N,n-1 and θ n,n-1 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.

[0060] Step 3.2: Use the virtual reverse motion and the principle of virtual work to solve the equation for each particle at time t n+1 The particle axial force fx N,n+1 and particle bending moment fm N,n+1 , expressed as:

[0061]

[0062] Where i and j represent the numbers of the two mass points connected to the two ends of the massless unit; num represents the total number of massless units connected to mass point N; f e Internal forces generated by massless elements.

[0063] When calculating the axial force, When calculating the bending moment, When calculating torque,

[0064] Wherein 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.

[0065] Specifically, Figure 2 As shown, with While or For loop as the basic program framework, 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 integral termination condition is reached, the loop solution step is jumped out and the particle displacement at that moment is stored.

[0066] Figures 4-5 The simulation results of some of the spatial torsional vibrations of the cableway bridge are shown in this example. Figure 6The spatial torsional vibration form of the cableway bridge at t=60s is shown. This result is automatically solved based on the set load condition. In application, the spatial torsional vibration phenomenon of the cableway bridge can be simulated according to the sensitive load condition set in the actual project. This embodiment is based on the cableway bridge spatial torsional vibration simulation method suitable for complex environments proposed by the present invention. It is a dynamic process, and the simulation curve conforms to the actual logic, which verifies the scientific nature of the present invention.

[0067] 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.

[0068] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope 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: According to the layout information of the cableway bridge, a vector finite element three-dimensional space model of the cableway bridge is established and pre-processing operations are performed; Step 2: Import environmental monitoring data and set simulation load conditions; Step 3: Define the integration time and step length, and iteratively solve the displacement and internal force of the cableway bridge vector finite element model in each integration step length; Step 4: determine whether the integral termination condition is met. If the integral termination condition is met, execute step 3, otherwise repeat step 5; 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 1, the vector finite element three-dimensional space model of the cableway bridge is established and pre-processed, including: 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: x={x 1,n ;x 2,n ;...;x N,n }={(x1,y1,z1);(x2,y2,z2);...;(x N y N ,z N )} θ={θ 1，n ;θ 2，n ;...;θ N,n }={(θ x1 ,the y1 ,the z1 );(θ x2 ,the y2 ,the z2 );…;(θ xN ,the yN ,the zN )}; Step 1.2, obtain the material properties of the relevant components, including 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, use rod units for cables and beam units for beams; define the system damping coefficient, the linear displacement x of each mass point at the initial time t0 N，0 , initial speed Initial acceleration Angular displacement θ N，0 , initial angular velocity Initial angular acceleration Particle axial force fx N,0 and external axial force Px N,0 , particle bending moment fm N，0 and external bending moment Pm N，0 .

3. The method for simulating spatial torsional vibration of a cableway bridge suitable for complex environments according to claim 2, characterized in that: In step 2, the environmental monitoring data is imported and the simulated load conditions are set, including: Step 2.1: Collect relevant monitoring or empirical data in the project area, including wind speed spectrum, earthquake spectrum, rainfall or snowfall statistics, seasonal temperature curve, and vehicle flow. Select the corresponding environmental monitoring data according to the calculation needs, 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 P N，n matrix.

4. The method for simulating spatial torsional vibration of a cableway bridge suitable for complex environments according to claim 3 is characterized in that: In step 3, the iterative solution includes: 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 x N,n and θ N，n 、Particle axial force fx N，n , particle bending moment fm N,n , external axial force Px N,n and external bending moment Pm N，n , solve for time t n+1 The spatial position of the particle x N,n+1 and θ N,n+1 ; Step 3.2: Use the virtual reverse motion and the principle of virtual work to solve the equation for each particle at time t n+1 The particle axial force fx N,n+1 and particle bending moment fm N,n+1 .

5. The method for simulating spatial torsional vibration of a cableway bridge suitable for complex environments according to claim 4, characterized in that: In step 3.1, the central difference method is used as the integration method in the vector finite element analysis process. According to the time t n The spatial position of the particle x N,n and θ N，n 、Particle axial force fx N，n , particle bending moment fm N，n , external axial force Px N,n and external bending moment Pm N，n Solve for time t n+1 The spatial position of the particle x N,n+1 and θ N,n+1 , 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; x N，n-1 and θ N,n-1 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.

6. The method for simulating spatial torsional vibration of a cableway bridge suitable for complex environments according to claim 5, characterized in that: 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 particle axial force fx N,n+1 and particle bending moment fm N，n+1 , expressed as: Where i and j represent the numbers of the two mass points connected to the two ends of the massless unit; num represents the total number of massless units connected to mass point N; f e Internal forces generated by massless elements; When calculating the axial force, When calculating the bending moment, When calculating torque, Among them, 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.

7. A computer storage medium, characterized in that: The computer storage medium stores a computer program; when the computer program is executed on a computer, the computer executes the cableway bridge spatial torsional vibration simulation method applicable to complex environments as described in any one of claims 1 to 6.

8. 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 6.

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