A vibration reduction system for the cable ends of long suspension cables in a suspension bridge

Abstract

This invention discloses a vibration damping system for the cable ends of long suspension cables in a suspension bridge, comprising a vibration damping bracket and cable end damping components. The main cable of the suspension bridge is connected to the main beam of the bridge deck through several sets of long suspension cables, each set of long suspension cables including two or more parallel suspension cables. The vibration damping bracket includes a main cable clamp, a ring tie rod, and vertical support rods. The main cable clamp is locked and erected on the outside of the main cable. The ring tie rod is horizontally and coaxially sleeved on the outer circumference of one set of long suspension cables directly below the main cable, and the ring tie rod is connected to the main cable clamp through several vertical support rods. The cable end damping components are symmetrically arranged in the inner cavity of the ring tie rod, and the two ends of each set of cable end damping components are connected to the corresponding suspension cable and the ring tie rod, respectively. Each set of cable end damping components includes two cable end dampers arranged in a V-shape or L-shape. This invention can effectively control wind vibration at the upper end of long suspension cables exceeding 200m, prevent detachment, and save manufacturing costs.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering, and in particular to a vibration reduction system for the cable ends of long suspension cables in a suspension bridge. Background Technology

[0002] A suspension bridge is a bridge structure in which cables suspended from towers and anchored to both banks serve as the main load-bearing components of the superstructure. It is one of the most competitive bridge types for long-span bridges. Currently, some ultra-long-span suspension bridges have spans exceeding 2000 meters. The 1915 Chhatkale Bridge, opened in 2022, has a main span of 2023 meters, and the Zhangjinggao Bridge under construction even reaches a main span of 2300 meters. For suspension bridges, the cables are a crucial component of the force transmission path, and safe and reliable cables are essential for the normal operation of the bridge. Due to the inherent characteristics of low damping, small mass, and low frequency of cables, they are highly susceptible to large-amplitude vibrations under wind loads, and even cable-to-cable contact may occur. The emergence of ultra-long-span suspension bridges has placed increasingly higher demands on wind-induced vibration control of long cables.

[0003] Currently, the main methods for controlling sling vibration include installing rigid damping frames between the slings, installing high-energy-consuming rubber dampers between the slings, and installing dampers at the bottom of the sling. Installing rigid damping frames between the slings is one of the simplest control methods, but its control capability is limited because it has no inherent damping energy dissipation capacity. While installing high-energy-consuming rubber dampers between the slings can provide sufficient additional damping, its material durability is poor and it is easily damaged. Furthermore, both of these control methods carry the risk of the control device falling off. In addition, the control effect on the upper end of the sling exceeding 200m in length remains to be tested.

[0004] In conclusion, there is an urgent need for a new vibration reduction and control system that can effectively control the wind-induced vibration of long suspension cables in suspension bridges while reducing the risk of device detachment. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a vibration reduction system for the cable ends of long suspension cables of suspension bridges, which can effectively control wind vibration at the upper end of long suspension cables exceeding 200m.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A vibration reduction system for the cable ends of a long suspension bridge includes a vibration reduction bracket and two sets of cable end damping components.

[0008] The main cable of the suspension bridge is connected to the steel beams of the bridge deck through several sets of long suspension cables, each set of long suspension cables consisting of two parallel suspension cables.

[0009] The vibration damping support includes main cable clamps, ring tie rods, and vertical support rods.

[0010] The main cable clamp is locked on the outside of the main cable; the ring tie rod is horizontally and coaxially sleeved on the outer circumference of one of the long suspenders directly below the main cable, and the ring tie rod is connected to the main cable clamp through several vertical support rods.

[0011] Two sets of cable end damping vibration reduction components are symmetrically arranged in the inner cavity of the annular tie rod, and the two ends of each set of cable end damping vibration reduction components are connected to the corresponding sling and the annular tie rod respectively.

[0012] Each cable end damping vibration reduction assembly includes two cable end dampers arranged in a V-shape or L-shape.

[0013] The vibration damping bracket also includes auxiliary connecting rods, which are used to connect the middle parts of several vertical support rods to form a whole.

[0014] The average value of the projections of all vertical support rods onto the vertical plane is called the cable end damper installation height 'a'. h Then a h The calculation formula is:

[0015] a h =2lζ h

[0016] in:

[0017] ζ h =ζ d -ζ l -ζ s

[0018]

[0019] In the formula, ζ h ζ is the minimum design damping ratio for the cable end vibration reduction system. d Design the damping ratio for the sling; ζ l Design the damping ratio for the beam end damper; ζ s The inherent damping ratio of the sling; a l 1 is the height of the beam end damper from the ground; l is the length of the sling.

[0020] The damping ratio ζ is designed for the cable end vibration reduction system. h While keeping the same as before, the manufacturing cost F of the cable end vibration damping system can be reduced by decreasing the mass M of the vibration damping bracket.

[0021] By constructing a function of the manufacturing cost F of the cable end vibration damping system with respect to the mass M of the vibration damping bracket, the optimal design parameters of the cable end vibration damping system are obtained. These parameters include the unit mass price w1 of the ring tie rod material, its material density ρ1, the cross-sectional area A1 of the ring tie rod, and the shape function C1 of the ring tie rod; the unit mass price w2 of the auxiliary connecting rod material, its material density ρ2, the cross-sectional area A2 of the auxiliary connecting rod, and the shape function C2 of the auxiliary connecting rod; the unit mass price w3 of the vertical support rod material, its material density ρ3, the cross-sectional area A3 of the vertical support rod, and the total length L3 of all vertical support rods; the mass M of the vibration damping bracket includes the mass M1 of the ring tie rod, the mass M2 of the auxiliary connecting rod, and the mass M3 of the vertical support rod. Therefore, the functional expression of the manufacturing cost F of the cable end vibration damping system with respect to the mass M of the vibration damping bracket is:

[0022] min F = {w1M1, w2M2, w3M3}

[0023] in:

[0024]

[0025]

[0026] M3=ρ3A3L3

[0027] In the formula, ds represents the length of the integral infinitesimal segment of curve C1 or C2 in the line integral.

[0028] In addition, the manufacturing cost F of the cable end vibration damping system must meet the following 7 constraints during the solution process:

[0029]

[0030] In the formula, σ1, σ2 and σ3 are the stresses in the ring tie rod, auxiliary connecting rod and vertical support rod, respectively;

[0031] [σ1], [σ2] and [σ3] are the allowable material stresses of the ring tie rod, auxiliary connecting rod and vertical support rod, respectively;

[0032] ε1, ε2 and ε3 are the strains in the annular tie rod, auxiliary connecting rod and vertical support rod, respectively;

[0033] [ε1], [ε2] and [ε3] are the allowable material strains of the ring tie rod, auxiliary connecting rod and vertical support rod, respectively;

[0034] disp represents the deformation of the cable end vibration damping system, lim represents the deformation limit of the cable end vibration damping system, and is a set value.

[0035] The elevation angle γ between the plane containing the two cable end dampers in each cable end damping vibration reduction assembly and the horizontal plane ranges from 0 to 6°. The specific calculation formula is as follows:

[0036]

[0037] In the formula: f s，max G represents the maximum static damping force when a single cable end damper is started, which is the design value; G is the self-weight of a single cable end damper.

[0038] It also includes anti-detachment devices, which include a ring tie rod anti-detachment flexible cable and a cable end damper anti-detachment flexible cable; each sling is connected to the ring tie rod through symmetrically arranged ring tie rod anti-detachment flexible cables; each cable end damper is connected to the main cable clamp through a cable end damper anti-detachment flexible cable.

[0039] The present invention has the following beneficial effects:

[0040] 1. This invention forms a stable spatial structure through supporting hangers, curved rigid tie beams, and auxiliary connecting rods, which can provide sufficient stiffness in the longitudinal and transverse directions of the bridge, thereby providing effective support for the damper; at the same time, the structure has an aesthetically pleasing shape that meets the requirements of modern bridge aesthetics.

[0041] 2. The damper in this invention is installed at a lower height than the cable end connector at the curved tie beam, which can effectively avoid the internal piston of the damper getting stuck due to gravity.

[0042] 3. The damper in this invention is arranged based on the vibration damping bracket and the sling, and uses a flexible cable to prevent it from falling off as a safety measure. This not only facilitates the installation, maintenance and replacement of the damper, but also reduces the risk of the damper falling off after failure.

[0043] 4. The anti-fall-off device in this invention can reduce the risk of accidental fall-off of the vibration damping bracket.

[0044] 5. The present invention adopts a multi-parameter joint optimization scheme, which can improve the overall working efficiency of the vibration reduction system. That is, under the premise that the damping ratio of the cable end vibration reduction system remains unchanged, the manufacturing cost can be reduced by reducing the mass of the vibration reduction bracket. Attached Figure Description

[0045] Figure 1 This is a three-dimensional simulation diagram of a long suspension cable end vibration reduction system for a suspension bridge according to the present invention.

[0046] Figure 2 This is a front view of a long suspension cable end vibration reduction system for a suspension bridge according to the present invention.

[0047] Figure 3 for Figure 2 Cross-sectional view at point 1-1.

[0048] Figure 4 This is a side view of a long suspension cable end vibration reduction system for a suspension bridge according to the present invention.

[0049] Among them are:

[0050] 1. Vertical support rod; 2. Ring tie rod; 3. Connecting steel plate; 4. Auxiliary connecting rod; 5. Cable end connector; 6. Cable end damper; 7. Suspension cable; 8. Anti-fall device; 9. Main cable; 10. Main cable clamp. Detailed Implementation

[0051] The present invention will now be described in further detail with reference to the accompanying drawings and specific preferred embodiments.

[0052] In the description of this invention, it should be understood that the terms "left side," "right side," "upper part," "lower part," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. "First," "second," etc., do not indicate the importance of the components, and therefore should not be construed as a limitation of this invention. The specific dimensions used in this embodiment are only for illustrating the technical solution and do not limit the scope of protection of this invention.

[0053] like Figures 1 to 4 As shown, a long cable end vibration reduction system for a suspension bridge includes a vibration reduction bracket, two sets of cable end damping vibration reduction components, and an anti-fall-off device 8.

[0054] The main cable of the suspension bridge is connected to the steel beams of the bridge deck through several sets of long suspension cables, each set of long suspension cables including two parallel suspension cables 7.

[0055] The vibration damping support includes a main cable clamp 10, a ring tie rod 2, a vertical support rod 1, and an auxiliary connecting rod 4.

[0056] The main cable clamp is locked on the outside of the main cable; the ring tie rod is horizontally and coaxially sleeved on the outer periphery of one of the long suspenders directly below the main cable. The ring tie rod is connected to the main cable clamp through several vertical support rods. In this invention, the ring tie rod is preferably connected to the main cable clamp through 4 vertical support rods.

[0057] Two sets of cable end damping vibration reduction components are symmetrically arranged in the inner cavity of the annular tie rod, and the two ends of each set of cable end damping vibration reduction components are connected to the corresponding sling and the annular tie rod respectively.

[0058] Each set of cable end damping vibration reduction components includes two cable end dampers 6 arranged in a V-shape or L-shape. The outer end of each cable end damper 6 is preferably installed on the inner wall of the annular tie rod through a connecting steel plate 3, and the inner end of each cable end damper is preferably fixedly sleeved on the outer periphery of the corresponding sling.

[0059] The auxiliary connecting rod is used to connect the middle parts of several vertical support rods to form a whole.

[0060] The anti-detachment device includes a ring tie rod anti-detachment flexible cable and a cable end damper anti-detachment flexible cable; each sling is connected to the ring tie rod through symmetrically arranged ring tie rod anti-detachment flexible cables; each cable end damper is connected to the main cable clamp through a cable end damper anti-detachment flexible cable.

[0061] The average value of the projections of all vertical support rods onto the vertical plane is called the cable end damper installation height 'a'. h Then a h The calculation formula is:

[0062] a h =2lζ h

[0063] in:

[0064] ζ h =ζ d -ζ l -ζ s

[0065]

[0066] In the formula, ζ h ζ is the minimum design damping ratio for the cable end vibration reduction system. d Design the damping ratio for the sling; ζ l Design the damping ratio for the beam end damper; ζ s The inherent damping ratio of the sling; a l 1 is the height of the beam end damper from the ground; l is the length of the sling.

[0067] The damping ratio ζ is designed for the cable end vibration reduction system. h While keeping the same as before, the manufacturing cost F of the cable end vibration damping system can be reduced by decreasing the mass M of the vibration damping bracket.

[0068] By constructing a function of the manufacturing cost F of the cable end vibration damping system with respect to the mass M of the vibration damping bracket, the optimal design parameters of the cable end vibration damping system are obtained. These parameters include the unit mass price w1 of the ring tie rod material, its material density ρ1, the cross-sectional area A1 of the ring tie rod, and the shape function C1 of the ring tie rod; the unit mass price w2 of the auxiliary connecting rod material, its material density ρ2, the cross-sectional area A2 of the auxiliary connecting rod, and the shape function C2 of the auxiliary connecting rod; the unit mass price w3 of the vertical support rod material, its material density ρ3, the cross-sectional area A3 of the vertical support rod, and the total length L3 of all vertical support rods; the mass M of the vibration damping bracket includes the mass M1 of the ring tie rod, the mass M2 of the auxiliary connecting rod, and the mass M3 of the vertical support rod. Therefore, the functional expression of the manufacturing cost F of the cable end vibration damping system with respect to the mass M of the vibration damping bracket is:

[0069] min F = {w1M1, W2M2, w3M3}

[0070] in:

[0071]

[0072]

[0073] M3=ρ3A3L3

[0074] In the formula, ds represents the length of the integral infinitesimal segment of curve C1 or C2 in the line integral.

[0075] For M1 and C1, the shape of the ring tie rod is used as the determining factor.

[0076] For ring-shaped tie rods with a circular curve shape, Therefore, the mass M1 = πρ1A1d1, where d1 is the diameter of the ring rod.

[0077] For a ring-shaped tie rod with a curved shape that is square, Mass M1 = 4ρ1A1a1, where a1 is the side length of the ring rod.

[0078] For elliptical ring rods, it is necessary to add an optimization variable, eccentricity e1.

[0079] For M2 and C2, the shape of the auxiliary tie rod is used as the reference for M1 and C1.

[0080] In addition, the manufacturing cost F of the cable end vibration damping system must meet the following 7 constraints during the solution process:

[0081]

[0082] In the formula, σ1, σ2 and σ3 are the stresses in the ring tie rod, auxiliary connecting rod and vertical support rod, respectively;

[0083] [σ1], [σ2] and [σ3] are the allowable material stresses of the ring tie rod, auxiliary connecting rod and vertical support rod, respectively;

[0084] ε1, ε2 and ε3 are the strains in the annular tie rod, auxiliary connecting rod and vertical support rod, respectively;

[0085] [ε1], [ε2] and [ε3] are the allowable material strains of the ring tie rod, auxiliary connecting rod and vertical support rod, respectively;

[0086] disp represents the deformation of the cable end vibration damping system, lim represents the deformation limit of the cable end vibration damping system, and is a set value.

[0087] Furthermore, the displacement balance constraints and load balance constraints of the long suspension cable end vibration reduction system are set as follows:

[0088]

[0089] In the formula, u i For boundary displacement vectors, σ represents the boundary constraint displacement; ij For the surface stress on the boundary, n j Let be the outer normal vector of the surface. This is the boundary load, representing the reaction force of the damping force at the damper connection nodes. The boundary includes: the connection nodes between the vertical support rod and the main cable, the connection nodes between the vertical ring tie rod and the damper, and the windward side of the vertical support rod.

[0090] The elevation angle γ between the plane containing the two cable end dampers in each cable end damping vibration reduction assembly and the horizontal plane ranges from 0 to 6°. The specific calculation formula is as follows:

[0091]

[0092] In the formula: f s，max G represents the maximum static damping force when a single cable end damper is started, which is the design value determined by the damper model designed by the damper manufacturer; G is the self-weight of a single cable end damper.

[0093] The damper is set at an elevation angle to reduce the jamming effect of the piston inside the cable end damper caused by gravity. Under relatively small wind loads, because the component of the wind load does not reach the maximum static damping force required for damper activation, the damper will not function, reducing its efficiency. This phenomenon is called jamming. Let the maximum static damping force required for damper activation be f. s，max The damper model is designed and determined by the damper manufacturer. Therefore, when When the wind is still, the damper is in dynamic equilibrium, so a small wind load is enough to activate the damper.

[0094] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A vibration damping system for the cable ends of long suspension cables in a suspension bridge, characterized in that: Includes vibration damping brackets and two sets of cable end damping vibration reduction components; The main cable of the suspension bridge is connected to the main beam of the bridge deck through several sets of long suspension cables, each set of long suspension cables including two or more parallel suspension cables; The vibration damping support includes main cable clamps, ring tie rods, and vertical support rods; The main cable clamp is locked and installed on the outside of the main cable; the ring tie rod is horizontally and coaxially sleeved on the outer circumference of one of the long suspenders directly below the main cable, and the ring tie rod is connected to the main cable clamp through several vertical support rods; Two sets of cable end damping vibration reduction components are symmetrically arranged in the inner cavity of the annular tie rod, and the two ends of each set of cable end damping vibration reduction components are connected to the corresponding sling and the annular tie rod respectively. Each set of cable end damping vibration reduction components includes two cable end dampers arranged in a V-shape or L-shape. The elevation angle γ between the plane containing the two cable end dampers in each cable end damping vibration reduction assembly and the horizontal plane ranges from 0 to 6°. The specific calculation formula is as follows: ； In the formula: G represents the maximum static damping force when a single cable end damper is started, which is the design value; G is the self-weight of a single cable end damper.

2. The suspension bridge long cable end vibration reduction system according to claim 1, characterized in that: The vibration damping bracket also includes auxiliary connecting rods, which are used to connect the middle parts of several vertical support rods to form a whole.

3. The suspension bridge long cable end vibration reduction system according to claim 1, characterized in that: The average value of the projections of all vertical support rods onto the vertical plane is called the cable end damper installation height. ,but The calculation formula is: ； in: ； ； In the formula, This is the minimum design damping ratio for the cable end vibration reduction system; Design the damping ratio for the slings; Design the damping ratio for the beam end damper; The inherent damping ratio of the sling; The height of the beam end damper from the ground; This refers to the length of the sling.

4. The suspension bridge long cable end vibration reduction system according to claim 2, characterized in that: The damping ratio is designed for the cable end vibration reduction system. While keeping the overall mass unchanged, reduce the mass of the vibration damping bracket. This reduces the manufacturing cost of the cable end vibration damping system. .

5. The suspension bridge long cable end vibration reduction system according to claim 4, characterized in that: Cost of constructing a cable end vibration damping system Regarding the quality of vibration damping brackets The function is used to obtain the optimal design parameters for the cable end vibration reduction system; among which, the design parameters for the cable end vibration reduction system include the unit mass price of the ring tie rod material. Material density Circular tie rod cross-sectional area Circular tie rod shape function Price per unit mass of auxiliary connecting rod materials Material density Cross-sectional area of ​​auxiliary connecting rod Auxiliary link shape function Price per unit weight of vertical support rod materials Material density , cross-sectional area of ​​vertical support rod and the total length of all vertical support rods Vibration damping bracket quality For the mass of the ring tie rod auxiliary connecting rod mass and the mass of the vertical support rod The manufacturing cost of the cable end vibration damping system is then... Regarding the quality of vibration damping brackets The function expression is: ； in: ； ； ； In the formula, ds represents the curve in the line integral. or The length of the integral infinitesimal segment; in addition, the manufacturing cost of the cable end vibration damping system. The following seven constraints must be satisfied during the solution process: ； In the formula, , and These are the stresses within the ring-shaped tie rod, auxiliary connecting rod, and vertical support rod, respectively. , and These are the allowable material stresses for the ring-shaped tie rod, auxiliary connecting rod, and vertical support rod, respectively. , and These are the strains within the ring-shaped tie rod, auxiliary connecting rod, and vertical support rod, respectively. , and The allowable strain of the materials for the ring tie rod, auxiliary connecting rod, and vertical support rod are respectively. This refers to the deformation of the cable end vibration damping system. Here is the deformation limit for the cable end vibration damping system, and here is the set value.

6. The suspension bridge long cable end vibration reduction system according to claim 1, characterized in that: It also includes anti-detachment devices, which include a ring tie rod anti-detachment flexible cable and a cable end damper anti-detachment flexible cable; each sling is connected to the ring tie rod through symmetrically arranged ring tie rod anti-detachment flexible cables; each cable end damper is connected to the main cable clamp through a cable end damper anti-detachment flexible cable.

Images