Analysis method of wind-induced parametric vibration of long-span arch bridge cables using theory

Abstract

A method for analyzing the wind-induced parametric vibration theory of long-span arch bridge cables is disclosed, and a coupled theoretical model of wind vibration and cable parametric vibration is constructed to propose a method for analyzing the wind-induced parametric vibration theory of long-span arch bridge cables, so that a simulation calculation is performed for each cable that may generate vibration, and the corresponding parametric of the cable is pre-adjusted according to the simulated vibration situation before construction, so as to prevent unnecessary vibration from occurring during construction, thereby improving the safety of the arch rib construction of arch bridges using the inclined suspension method. The method of the present invention can fill the gap in the industry and provide theoretical support for the cable parametric vibration during the construction stage of large-span arch bridges using the inclined suspension method.

Description

[Technical field]

[0001] The present invention relates to the field of bridge engineering design technology, and more particularly to an analysis method for wind-induced parametric vibration theory in long-span arch bridge cables. [Background technology]

[0002] When constructing highways and railways across plateau canyons, long-span arch bridges are often chosen, because arch bridges fit the topography of the canyons, have good aesthetics, are advantageous in terms of construction costs, and are easy to maintain in the future, making them the more ideal method for bridges across canyons. However, due to the limitations of the topographical conditions, long-span arch bridges often use the cable-hanging method to construct the main arch, which requires a large number of lifting cables to be installed during actual construction, and because the topography of plateau canyons has a large wind volume, the wind vibration of the arch ribs during construction may induce parametric vibration of the cables, which has a significant impact on the safety of the structures under construction.

[0003] There is currently no precedent for relevant research on the parametric vibration of cables induced by wind vibration of suspended arch ribs during construction. The prior art is aimed at the design of long-span arch bridges constructed by the inclined suspension method, and many parametric selections for temporary cables are all based on the magnitude of the tensile force required for the cables during the construction stage, and do not consider the harm to structures caused by the parametric vibration that may be generated by the cables when the arch ribs are in a cantilevered state, making the prior art methods unsafe for bridge design during the construction stage.

[0004] Therefore, it is very important to establish an analysis method based on the theory of wind-induced parametric vibration in the hanging arch rib cable of a long-span arch bridge, and before construction, the parametric of the cable can be pre-adjusted based on the simulated vibration situation, so as to avoid the occurrence of unnecessary vibration during construction and improve the safety of bridge construction. Summary of the Invention [Problem to be solved by the invention]

[0005] Based on the shortcomings described in the background art above, the present invention discloses an analysis and control method for wind-induced parametric vibration theory in long-span arch bridge cables, which can be used as a guide for pre-construction engineering design and construction, to avoid the generation of parametric vibration in cables during suspension construction by arch rib diagonal suspension method, and reduce the construction risk. [Means for solving the problem]

[0006] The present invention discloses an analysis method for wind-induced parametric vibration theory of long-span arch bridge cables, which includes: In step 4, a theoretical model of the coupling between wind vibration and the parametric vibration of the cable is constructed, and vibration analysis is performed by taking the infinitesimal elements of the cable. According to Newton's second law, the vibration differential equation of the cable in the xy plane is constructed as shown in (1).

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[0007] Furthermore, step 5 specifically includes the following: TIFF0007689253000004.tif102166

[0008] Furthermore, in step 1, specifically, the wind environment of the pulsation at the bridge position is obtained by using a method of measuring on-site, and the cross-sectional area A n and the magnitude T of the cable force under static load at each construction stage are both calculated and obtained in advance by methods used in the prior art.

[0009] Furthermore, in step 4, The equations considering the hydrostatic balance of the cable further include:

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[0010] Furthermore, in step 4, the method further includes: Mechanical model A Cartesian coordinate system is constructed perpendicular to the axial direction of the cable, so that the static shape of the cable is

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[0011] Furthermore, in step 4, the frequency ψ of the simple harmonic motion of the nth cable displacement n , i.e., for the natural frequencies of the cable, the ratio of frequencies is satisfied ψ n / ω 1 It further includes that when = 2, the cable generates more significant vibration. Effect of the Invention

[0012] The present invention proposes a method for analysis and control of wind-induced parametric vibration theory in long-span arch bridge cables by constructing a coupled theoretical model of wind vibration and cable parametric vibration, and performs simulation calculations on each cable that may generate vibration, and then pre-adjusts the corresponding parametric vibration of the cable according to the simulated vibration situation before construction, so as to avoid unnecessary vibration during construction, thereby improving the safety of bridge construction. This method can fill the gap in the industry and provide theoretical support for the cable parametric vibration during the construction stage of the inclined suspension method for large-span arch bridges.

[0013] In order to more clearly describe the technical solutions in the present invention or the prior art, the accompanying drawings which need to be used in the embodiments are briefly described below. [Brief description of the drawings]

[0014] [Figure 1] FIG. 1 is a schematic diagram of the cable dynamic displacement control point in arch rib construction work using the oblique suspension method for a long-span arch bridge in the method of the present invention. [Diagram 2] FIG. 1 is a schematic diagram of cable arch connection point displacement decomposition in the method of the present invention. [Diagram 3] FIG. 2 is a schematic diagram of a cable parametric vibration model in the method of the present invention. [Figure 4] FIG. 1 is a schematic diagram of cable parametric vibration microelement dynamics in the method of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] In order to make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention are described below in a clear and complete manner in conjunction with the accompanying drawings of the embodiments of the present invention. It is clear that the described embodiments are only some of the embodiments of the present invention, but are not all of the embodiments. Based on the embodiments of the present invention, any other embodiments obtained by those skilled in the art without any creative efforts fall within the protection scope of the present invention.

[0016] The present invention provides a coupled vibration analysis and control method for wind-induced cable parametric vibration in arch ribs of long-span arch bridges during construction of the arch ribs of long-span arch bridges in plateau canyons using a cast-in-place cantilever diagonal suspension method, hereinafter referred to as the analysis and control method based on wind-induced parametric vibration theory in long-span arch bridges. Since the effect of wind is most significant and the number of cables is the largest in the maximum cantilever state, the present invention mainly takes the parametric vibration analysis and control in the maximum cantilever state as an example for explanation. Specifically, the method includes the following steps: TIFF0007689253000013.tif45166

[0017] Furthermore, taking the maximum cantilever state in Figure 1 in Step 1 as an example, in response to the problem that the design wind speed of a large bridge in a plateau gorge according to the conventional wind-resistant design rules is not safe, the present invention chooses to use a method of actual measurement on site to obtain the pulsating wind field environment at the bridge position and use it as a guideline design for the true construction. After building a finite element model in the construction stage of a long-span arch bridge using the inclined suspension method under the maximum cantilever state, the type of cable (cross-sectional area A n ) and the magnitude T of the cable force under static load at each construction stage are both calculated and obtained using the methods used in the prior art, and the measured wind field environment is further incorporated into the finite element model to perform calculations and analysis to obtain the dynamic displacement S of each cable arch connection point, and the dynamic displacement S occurring at the cable position can be described as simple harmonic motion, which can be used for subsequent analysis and calculation of the vibration situation. Simple harmonic motion is the most basic and simplest mechanical vibration, so when an object performs simple harmonic motion, the force it receives is directly proportional to the displacement, always points toward the equilibrium position, and is a periodic motion (for example, simple pendulum motion and spring pendulum motion) determined by its own systematic characteristics.

[0018] TIFF0007689253000014.tif32166

[0019] TIFF0007689253000015.tif51166

[0020] In step 4, a theoretical model of the coupling between wind vibration and the parametric vibration of the cable is constructed, and vibration analysis is performed on the infinitesimal elements of the cable as shown in Figure 4. According to Newton's second law, the vibration differential equation of the cable in the xy plane is constructed as shown in (1),

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[0021] The equation considering the hydrostatic balance of the cable is:

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[0022] TIFF0007689253000026.tif13166

[0023] Frequency ψ of the nth cable's simple harmonic displacement n , i.e., for the natural frequencies of the cable, the ratio of frequencies is satisfied ψ n / ω 1 = 2, the cable generates more significant vibrations.

[0024] In step 5, based on the first mode vibration differential equation in step 4, ψ n Find ψ n / ω 1 The value of determines whether the nth cable generates parametric vibration or not. If it does, the cross-sectional area A of the nth cable is n Adjust the effect and if it does not occur, perform step 6.

[0025] The specific judgment and adjustment methods are as follows: The ratio of the parametric excitation frequency to the natural frequency of the cable for all cables is ψ n / ω 1<1.8 or ψ n / ω 1 If 2.2 is satisfied, each cable does not generate parametric vibration and the cross-sectional area A of the nth cable n And the tensile force T is the final design value. TIFF0007689253000027.tif96166

[0026] It is worth mentioning that in order to reduce the influence of errors brought about by the simplified conditions in the calculation process of the vibration differential equation, the present invention recommends that 1.8≦ψ in practical engineering applications. n / ω 1 The range of the natural vibration frequency ratio that should be avoided in design is ≦2.2, and the specific values ​​of the range of the frequency ratio and the upper and lower limits can be selected according to the actual situation in the specific usage process.

[0027] In step 6, the above steps 2 to 5 are repeated until it is determined that none of the first to nth cables generates parametric vibration in a wind field environment. Then, the cross-sectional area (A n Somebody A' n ) and tensile force T are output as design values.

[0028] The parametric vibrations designed by this method can avoid unnecessary vibrations that occur in the cable under the action of actual wind fields, and can serve as a guideline for the design and construction of long-span arch bridges constructed using the inclined suspension method. It can be seen that this method can avoid safety risks caused by parametric vibrations generated by the cable during the construction stage, and improve the safety performance of temporary structures.

[0029] Finally, the above embodiments are merely for illustrating the technical solutions of the present invention, and are not intended to limit the technical solutions of the present invention. Although the present invention has been described in as much detail as possible with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments can still be modified or equivalently substituted for parts of the technical solutions. However, such modifications or substitutions do not cause the essence of the corresponding technical solutions to depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing wind-induced parametric vibration of long-span arch bridge cables, comprising the steps of: 【number】 Step 4: construct a coupled theoretical model of wind vibration and parametric vibration of the cable, and perform vibration analysis on the infinitesimal elements of the cable. According to Newton's second law, construct a vibration differential equation in the xy plane of the cable as shown in (1); [0010] In the formula, y is the static force shape function under the action of the cable's own weight, v is the lateral dynamic displacement function of the cable, T is the tangential static tension of the cable, τ is the tangential dynamic tension of the cable, m is the mass per unit length of the cable, g is the gravitational acceleration, α is the horizontal inclination angle of the cable, and c ｙ is the viscous damping coefficient per unit length of the cable in the y direction, s represents the arc-length coordinate of the cable, H is the initial axial tension of the cable, and h is the dynamic axial tension of the cable. The vibration differential equation for the first mode of the cable obtained using the Galerkin method is given by [0025] Step 5: Based on the first-order mode vibration differential equation, ψ ｎ Find ψ ｎ / ω １ Step 5: determining whether the n-th cable generates parametric vibration based on the value of (a), and if it does, adjusting the cross-sectional area of ​​the n-th cable; if it does not generate parametric vibration, performing the following step 6; Step 6: repeating steps 2 to 5 above until it is determined that none of the first to n cables generates parametric vibration in the measured wind field environment, and outputting the cross-sectional areas and tensile forces of all the cables as design values. A method comprising:

2. In step 5, The method for analyzing wind-induced parametric vibration of long-span arch bridge cables according to claim 1.

3. In step 1, The wind environment of the bridge is obtained by measuring the wind force at the bridge site on-site. The cross-sectional area An of the cable and the magnitude T of the cable force under static load at each construction stage are calculated and obtained in advance. The method for analyzing wind-induced parametric vibration of long-span arch bridge cables according to claim 2.

4. In step 4, The equation considering the hydrostatic balance of the cable is: [0030] and H is the initial axial tension in the cable, h is the dynamic axial tension in the cable, i.e. [0045] Substituting (2) and (3) into (1), we get [0050] [006] The length of the infinitesimal part of the cable in static equilibrium is ds ０ and at dynamic equilibrium, ds, i.e. [0070] [0080] It further includes that The method for analyzing wind-induced parametric vibration of long-span arch bridge cables according to claim 2.

5. In step 4, Mechanical model A Cartesian coordinate system is constructed perpendicular to the axial direction of the cable, so that the static shape of the cable is [0090] In the actual bridge, the cable slack is small, so the vibration mode of the cable is approximated as the vibration mode of a standard circular arc. Taking into account the boundary conditions of the cable, the solution of the second equation is given by: [0010] It further includes The method for analyzing wind-induced parametric vibration of long-span arch bridge cables according to claim 4.

6. In step 4, Frequency ψ of the nth cable's simple harmonic displacement n , i.e., for the natural frequencies of the cable, the ratio of frequencies is satisfied ψ n / ω 1 = 2, it further includes that the cable generates more significant vibrations. The method for analyzing wind-induced parametric vibration of long-span arch bridge cables according to claim 5.

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