A multi-directional broadband tuned mass damper and design method

Abstract

The application relates to a multidirectional broadband tuning mass damper and a design method thereof. First damping structures and second damping structures are arranged on a rigid damping frame. The first damping structures have one control main frequency, and the second damping structures have two control main frequencies. The control main frequencies of the second damping structures are greater than the control main frequency of the first damping structures. Under the synergistic effect, the second damping structures mainly effectively widen the control range of high frequencies, and the multiple first damping structures control one low-frequency control main frequency in a one-to-one mode, so that the full frequency is controlled. The extension directions of the first damping structures and the second damping structures on the rigid damping frame are the same, and the isotropic mass and stiffness distribution characteristics are ensured. Furthermore, when different control frequency ranges are used, the number and distribution form of the first damping structures and the second damping structures, and the corresponding mass ratio and damping ratio can be designed in advance, so that different control requirements can be adapted.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vibration reduction, and in particular to a multi-directional broadband tuned mass damper and a design method. BACKGROUND

[0002] Suspender is the main connecting and force transmitting component of stiffening girder and main cable of suspension bridge. With the increasing span of suspension bridge, the characteristics of thin and long, small damping and multiple vibration modes of suspender become more and more obvious. Under the action of external wind load and traffic load, various forms of vibration such as vortex-induced vibration, wake galloping and parametric vibration are easy to occur. The suspender of long-span suspension bridge is usually vertically arranged in parallel by double suspender or multiple suspender. Compared with single cable, the vibration is more complex and diverse. From the vibration mode, there are relative motion modes between suspender and synchronous motion modes between suspender. From the frequency, the suspender may have combined vibration of multiple frequencies with different external excitations. The continuous vibration of suspender not only may cause fatigue and corrosion of suspender anchoring end, seriously affect the service life and maintenance cost of suspender, but also may cause doubts about the safety of bridge by pedestrians. Therefore, effective measures should be taken to control the vibration of suspender.

[0003] In some related technologies, for different forms of suspender vibration, the following structural control measures are taken for the built long-span suspension bridge. For example, the aerodynamic measure of winding spiral line, the external damper of suspender, the rigid vibration reduction frame, the external pendulum lever damper, the impact mass damper and the pendulum type tuned mass damper. The scheme of using rigid vibration reduction frame for vibration reduction has the advantages of simple structure, economical price, small landscape influence and good control effect on wake galloping; however, the rigid vibration reduction frame is only effective for the relative motion between strands, and cannot effectively control the vibration of multiple suspender in the same phase. Therefore, generally, damping vibration reduction measures are added on the basis of the original rigid vibration reduction frame to effectively suppress the vibration of suspender, but there are still the following problems:

[0004] The additional damping vibration reduction measure is generally to set a tuned mass damper. The tuned mass damper adjusts its frequency by changing its mass or stiffness, so that it is close to the frequency of the main structure. When the main structure vibrates, the vibration of the main structure is amplified and transmitted to the substructure through resonance principle, and the vibration energy is dissipated through the damping device of the tuned mass damper. Although the control frequency range can be effectively widened by increasing the damping ratio and mass ratio, the range of low frequency vibration is limited, and long suspender broadband damping vibration reduction cannot be achieved. SUMMARY

[0005] The embodiments of the present application provide a multi-directional broadband tuned mass damper and a design method to solve the problem that although the control frequency range can be effectively widened by increasing the damping ratio and mass ratio in the related technology, the range of low frequency vibration is limited.

[0006] In a first aspect, a multi-directional broadband tuned mass damper is provided, which includes a rigid damping frame, two ends of the rigid damping frame being configured to be connected with a sling, a plurality of first damping structures and second damping structures being arranged on the rigid damping frame and spaced along a length direction of the rigid damping frame, the first damping structures and the second damping structures having the same extension direction.

[0007] Each of the first damping structures has one control main frequency, each of the second damping structures has two control main frequencies, and the control main frequencies of the second damping structures are greater than the control main frequency of the first damping structures.

[0008] In some embodiments, the number of the first damping structures and the second damping structures is plural.

[0009] The control main frequencies of the first damping structures are different from each other, the two control main frequencies of each of the second damping structures are different from each other, and the two control main frequencies of the second damping structures are different from each other.

[0010] In some embodiments, the first damping structures and the second damping structures are arranged on the rigid damping frame in descending or ascending order of the control main frequencies.

[0011] In some embodiments, one second damping structure is arranged between two adjacent first damping structures, or,

[0012] The length direction of the rigid damping frame is provided with a first region and a second region, all the first damping structures being arranged in the first region, and all the second damping structures being arranged in the second region.

[0013] In some embodiments, the first damping structure includes a first steel strand and a first mass block, one end of the first steel strand being connected with the rigid damping frame through a connecting block, and the other end of the first steel strand being connected with the first mass block.

[0014] The control main frequency of the first damping structure is determined by the following formula:

[0015] wherein, is the stiffness of the first steel strand, is the mass of the first mass block (201).

[0016] In some embodiments, the first mass block is provided with a first pouring hole, and the portion of the first steel strand extending into the first pouring hole is connected with the first mass block through a first pouring alloy.

[0017] In some embodiments, the second damping structure includes a second steel strand, a second mass block, a first rigid pipe and a third mass block.

[0018] The second mass is coaxially connected with the third mass through the first rigid pipe; the second mass is provided with a through hole; one end of the second steel strand is connected with the third mass through the through hole, and the other end is connected with the rigid damping frame through the connecting block;

[0019] The formula for controlling the two main frequencies of the second damping structure is:

[0020] ;

[0021] ; wherein, is the stiffness of the second steel strand, is the mass of the third mass, is the mass of the second mass; is the mass of the first rigid pipe; T is the torsional stiffness of the second steel strand.

[0022] In some embodiments, the third mass is provided with a second pouring hole; the part of the second steel strand located in the second pouring hole is connected with the third mass through the second pouring alloy.

[0023] In some embodiments, the second damping structure includes a second rigid pipe and a third steel strand; the bottom of the second rigid pipe is provided with a sealing bottom plate;

[0024] The third steel strand extends into the second rigid pipe and is connected with the second rigid pipe through a fifth mass; the outer side of the second rigid pipe is coaxially fixedly connected with a fourth mass.

[0025] In some embodiments, the second damping structure includes a second rigid pipe and a third steel strand; the bottom of the second rigid pipe is provided with a sealing bottom plate;

[0026] The third steel strand extends into the second rigid pipe and is connected with the second rigid pipe through a fifth mass; the outer side of the second rigid pipe is coaxially fixedly connected with a fourth mass; the diameter of the sealing bottom plate is equal to the outer diameter of the fourth mass, and the sealing bottom plate is connected with the bottom of the fourth mass through a third rigid pipe.

[0027] In some embodiments, the fifth mass is a third pouring alloy for pouring and connecting the second rigid pipe and the third steel strand.

[0028] In some embodiments, the fifth mass is provided with a plurality of water holes arranged along the length direction of the third steel strand; the bottom of the water hole penetrates the sealing bottom plate.

[0029] In a second aspect, a design method of a multi-directional broadband tuned mass damper is provided, which includes the following steps:

[0030] Obtaining a target range of control frequency and deriving a plurality of target control main frequencies;

[0031] The target control main frequency is compared with the set control main frequency; if the target control main frequency is less than the set control main frequency, the target control main frequency is taken as a design parameter of the first damping structure; otherwise, the target control main frequency is taken as a design parameter of the second damping structure;

[0032] The number of target control main frequencies less than the set control main frequency is obtained; and the number of target control main frequencies greater than or equal to the set control main frequency is obtained.

[0033] The first damping structure and the second damping structure are manufactured based on the design parameters and the number of the first damping structure and the design parameters and the number of the second damping structure, and are installed on the rigid damping frame.

[0034] In some embodiments, when the installation space on a single rigid damping frame is less than the required installation space of all the first damping structures and the second damping structures, a plurality of same rigid damping frames are additionally arranged to install all the first damping structures and the second damping structures on the sling.

[0035] The technical scheme provided in the application has the following beneficial effects:

[0036] The embodiment of the application provides a multi-directional broadband tuned mass damper and a design method thereof. The first damping structure and the second damping structure are arranged on the rigid damping frame, the first damping structure has one control main frequency, the second damping structure has two control main frequencies, all the control main frequencies of the second damping structure are greater than the control main frequency of the first damping structure, and the second damping structure mainly effectively widens the control range of high frequencies in the cooperative action. The first damping structures control one low-frequency control main frequency in one-to-one mode, so that the full frequency is controlled. The extension directions of the first damping structure and the second damping structure on the rigid damping frame are the same, so that the isotropic mass and stiffness distribution characteristics are ensured. In addition, when different control frequency ranges are used, the number and distribution form of the first damping structure and the second damping structure, and the corresponding mass ratio and damping ratio can be designed in advance, so that different control requirements are adapted. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to more clearly illustrate the technical scheme in the embodiments of the application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0038] Figure 1 The fixed mass ratio of the damping structure in the related art is shown in the schematic diagram of the sling optimization damping parameter under different damping ratios.

[0039] Figure 2 Optimized damping parameter diagram of the damping structure in the related art under different mass ratios at a fixed damping ratio;

[0040] Figure 3 The first damping structure and the second damping structure provided in the embodiments of the present application can realize the damping reduction target of the sling in the full modal range of 0-30 Hz;

[0041] Figure 4 The diagram shows the connection of the multi-directional broadband tuned mass damper provided in the embodiments of the present application and the sling;

[0042] Figure 5 The diagram shows the structure of the multi-directional broadband tuned mass damper provided in the embodiments of the present application;

[0043] Figure 6 The diagram shows the structure of another multi-directional broadband tuned mass damper provided in the embodiments of the present application;

[0044] Figure 7 The diagram shows the first form of the second damping structure provided in the embodiments of the present application;

[0045] Figure 8 The diagram shows the second form of the second damping structure provided in the embodiments of the present application;

[0046] Figure 9 The diagram shows the second damping structure provided in the embodiments of the present application;

[0047] Figure 10 The diagram shows the first damping structure provided in the embodiments of the present application;

[0048] Figure 11 The diagram shows the free decay vibration time curve of the mass block of the first damping structure provided in the embodiments of the present application;

[0049] Figure 12 The diagram shows the free decay vibration time curve of the mass block of the second damping structure provided in the embodiments of the present application;

[0050] Figure 13 The diagram shows the dynamic amplification factor of the mass block of the first damping structure provided in the embodiments of the present application;

[0051] Figure 14 The diagram shows the dynamic amplification factor of the mass block of the second damping structure provided in the embodiments of the present application.

[0052] In the figure: 1, rigid damping frame; 2, first damping structure; 200, first steel strand; 201, first mass block; 202, first pouring alloy; 3, second damping structure; 300, second mass block; 301, first rigid pipe; 302, third mass block; 303, second steel strand; 304, second rigid pipe; 305, third steel strand; 306, fourth mass block; 307, third rigid pipe; 308, sealing bottom plate; 309, second pouring alloy; 310, water hole; 311, fifth mass block; 4, connecting block. DETAILED DESCRIPTION

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0054] For the reason why the present application is only improved for the rigid damping frame, refer to the following description:

[0055] The Japanese Akashi Strait Bridge cable adopts a winding spiral line aerodynamic measure, which requires special theoretical analysis and wind tunnel test verification before the damping effect is implemented, has poor applicability to cables of different sizes and spacings, is inconvenient to install and high in cost when applied to the bridge in operation; the Great Belt Bridge in Denmark is installed with a cable external damper, which needs to be laid with a special support and has high requirements for the support stiffness and installation height, and has a great impact on the bridge landscape; the Xihumen Bridge in China adopts a rigid damping frame scheme, which effectively controls the collision between the cables and suppresses the wake-induced vibration of the cables, but needs to be reasonably designed for the spacing between the rigid damping frames, and cannot provide damping for the cables, and has limited control effect on the same direction movement and out-of-plane vibration of the cables; the Nansha Bridge, Niaozhou Waterway Bridge, and Dasha Waterway Bridge in China respectively adopt three kinds of dampers, namely, external pendulum lever damper, impact mass damper, and pendulum type tuned mass damper, but the use conditions and cable control frequency range of various dampers are limited.

[0056] Therefore, the rigid damping frame is taken as the research object. The following describes the effects and defects of the rigid damping frame. When the double cables have opposite-phase in-plane vibration modes or out-of-plane vibration modes, the rigid damping frame installed at the n-division point of the double cables can effectively constrain the displacement of the two ends of the cable, which is equivalent to providing a rigid constraint to the cable, changing the effective vibration length of the cable from L to L / n, and changing the frequency of the cable to n times the original frequency, thereby effectively reducing the probability of cable vibration. However, when the frequency of the external wind load approaches the natural frequency of the cable, the double cables may have the same-phase in-plane vibration mode or out-of-plane vibration. At this time, the displacement and velocity of the beam end of the damping frame installed at the n-division point are consistent, and the damping frame does not play a role and does not change the vibration characteristics of the original cable. In addition, since the damping frame is a purely rigid element, it cannot provide structural damping for the double cables. Once the cable is excited by external excitation, the vibration state will continue for a long time before slowly decaying. Long-term vibration will cause fatigue damage to the cable body, anchor head, and rigid damping frame.

[0057] To overcome the defects of the rigid damping frame, a tuned mass damper (TMD) is generally used to increase damping. The following describes the problems discovered by analyzing a long-cable broadband vibration bridge:

[0058] The long-cable broadband vibration bridge is the Guangxi Longmen Bridge. The Guangxi Longmen Bridge is a double-tower single-span suspension bridge with a main span of 1098 m. The steel box girder of the main span extends 50 m to each side of the side span, with a rise-to-span ratio of 1:10. The center distance between the main cables in the transverse direction of the bridge is 33.8 m. The bridge uses parallel steel wire cables with an outer hot-extruded double-layer HDPE sheath. Two cables are provided at each suspension point, and the standard interval of the cables in the longitudinal direction of the bridge is 12.8 m. The cable material is φ5.0 mm zinc-aluminum alloy plated high-strength steel wire with a standard tensile strength of ≥1770 MPa. Among them, the ordinary cable has a specification of 91-5 and a cable diameter of 69 mm; the tower-side reinforced cable has a specification of 241-5 and a cable diameter of 105 mm. There are 56 suspension points with a cable length of more than 50 m on the bridge, and the longest cable is 128.564 m long. The Longmen Bridge is located on the coast of the Maoxian Sea, where there are 2-5 typhoons per year, and the wind is frequent. Long cables are prone to wind-induced vibration, and appropriate damping measures should be taken.

[0059] The fundamental frequency of vibration of the suspension cables over 50m in length on the Longmen Bridge is 1.0~2.0Hz. The initial damping ratio of the parallel wire suspension cables is approximately 0.16% (logarithmic attenuation rate of approximately 1%), and the required damping ratio for vibration control is 0.5% (logarithmic attenuation rate greater than 3%). The vibration control frequency of the suspension cables is 0~30Hz. To address the shortcomings of rigid vibration damping frame schemes, tuned mass dampers (TMDs) are used to achieve broadband damping vibration reduction for suspension cables over 50m in length. TMDs adjust their own frequency by changing their mass or stiffness to approximate the frequency of the main structure. When the main structure vibrates, the vibration is amplified and transmitted to the substructure through resonance, and this vibration energy is dissipated through their own damping device, achieving rapid attenuation of the main structure's vibration.

[0060] To meet the vibration reduction target of the long suspension cables of the Longmen Bridge, based on the classical TMD (Modal Mass Ratio) vibration reduction theory, parameter optimization was performed by progressively increasing the modal mass ratio μ of the TMD to the suspension cables. The corresponding optimal frequency ratio of the TMD to the suspension cables, the optimal damping ratio of the TMD, and the equivalent damping ratio ξD of the suspension cables are shown in Table 1. Table 1 shows that the additional damping ratio provided by the TMD to the structure increases with the increase of the modal mass ratio. Under the optimal TMD parameters, a very small mass ratio (0.01%) is sufficient to meet the vibration reduction requirements of the suspension cables (damping ratio greater than 0.5%).

[0061] Table 1. Optimization Results of Sling-TMD Optimal Parameters

[0062] Tab.1 Optimal parameter optimization results of TMD - hangers

[0063]

[0064] Note: Equivalent damping ratio of sling = Initial damping ratio of sling (0.16%) + Additional damping ratio of TMD.

[0065] To achieve broadband control of the suspension cables of the Longmen Bridge, two parameters were optimized: the TMD damping ratio and the modal mass ratio of a single TMD to the suspension cable. The modal mass ratio of a single TMD to the suspension cable was set to 0.50%, and the TMD damping ratios were optimized to ξT1=4.32% (optimal damping ratio), ξT2=7.00%, ξT3=10.00%, and ξT4=13.00%, respectively. The results are shown in the attached figure. Figure 1 As shown. By Figure 1 It can be seen that the smaller the TMD damping ratio, the narrower the coverage range of the adjacent main frequency, which is not suitable for multi-mode control of the sling; after increasing the TMD damping ratio to 10%, the frequency coverage range increases, and it can reach 83%~115% of the control of the main frequency; while further increasing the damping ratio, the overall effect is not obvious.

[0066] Taking the TMD damping ratio as 10%, and the single TMD and sling modal mass ratio as 0.1%, 0.5% and 1.0% respectively, the single TMD and sling modal mass ratio is optimized, and the results are shown in Figure 2 . As shown in Figure 2 , when the TMD damping ratio is 10%, if the mass ratio is too small (such as 0.1%), the overall vibration reduction target requirement cannot be met; the greater the mass ratio, the wider the coverage range near the main frequency, but the control cost is also greater.

[0067] According to the above analysis and description, we find that by increasing the TMD damping ratio and mass ratio, the control frequency range can be effectively widened, but the range of low frequency vibration is limited.

[0068] Therefore, based on the above description, we have the following settings:

[0069] A multi-directional wide-frequency tuned mass damper, comprising a rigid damping frame 1, the two ends of the rigid damping frame 1 in the length direction are used to connect with the sling; the rigid damping frame 1 is provided with a plurality of first damping structures 2 and second damping structures 3 distributed along the length direction, the extension directions of the first damping structures 2 and the second damping structures 3 are the same; wherein a single first damping structure 2 has one control main frequency; a single second damping structure 3 has two control main frequencies; all control main frequencies of the second damping structure 3 are greater than the control main frequency of the first damping structure 2.

[0070] Under the synergistic effect, the second damping structure 3 mainly effectively widens its control range of high frequency, and the plurality of first damping structures 2 control one low frequency control main frequency one by one, thereby controlling the full frequency, and the extension directions of the first damping structures 2 and the second damping structures 3 on the rigid damping frame 1 are the same, which ensures the isotropic mass and stiffness distribution characteristics; in addition, when different control frequency ranges are used, the number and distribution form of the first damping structure 1 and the second damping structure 3, as well as the corresponding mass ratio and damping ratio, can be designed in advance, so as to adapt to different control requirements. The first damping structure 1 and the second damping structure 3 are isotropic pendulum tuned mass dampers (PTMD). The extension direction can be explained as follows: Figure 4 , the extension direction is to extend along a straight line from top to bottom. The first damping structure 2 is not randomly set, and its control main frequency and number need to be designed according to the needs.

[0071] In some preferred embodiments, according to different vibration reduction requirements, the number of the first damping structure 2 and the second damping structure 3 is also different, and the following several forms are given:

[0072] The first damping structure 2 is one in number, and the second damping structure 3 is one in number.

[0073] The first damping structure 2 and the second damping structure 3 are multiple in number; the control main frequencies of the multiple first damping structures 2 are different; the two control main frequencies of each second damping structure 3 are different, and the two control main frequencies of the multiple second damping structures 3 are different.

[0074] The first damping structure 2 and the second damping structure 3 have the following arrangement modes:

[0075] Arrangement mode one: the first damping structure 2 and the second damping structure 3 are arranged on the rigid damping frame 1 according to the control main frequencies from large to small or from small to large.

[0076] Arrangement mode two: one second damping structure 3 is arranged between every two adjacent first damping structures 2. Figure 5 and Figure 6 .

[0077] Arrangement mode three: the rigid damping frame 1 has a first region and a second region in the length direction, all the first damping structures 2 are arranged in the first region, and all the second damping structures 3 are arranged in the second region.

[0078] In some preferred embodiments, referring to Figure 10 , the first damping structure 2 comprises a first steel strand 200 and a first mass block 201; one end of the first steel strand 200 is connected to the rigid damping frame 1 through the connecting block 4, and the other end is connected to the first mass block 201; the formula of the control main frequency of the first damping structure 2 is:

[0079] , wherein, is the stiffness of the first steel strand 200, is the mass of the first mass block 201.

[0080] In order to facilitate connection, the first mass block 201 is provided with a first pouring hole, and the part of the first steel strand 200 extending into the first pouring hole is connected to the first mass block 201 by pouring the first pouring alloy 202.

[0081] In some preferred embodiments, referring to Figure 9 , the second damping structure 3 comprises a second steel strand 303, a second mass block 300, a first rigid pipe 301, and a third mass block 302;

[0082] The second mass 300 is coaxially connected with the third mass 302 through the first rigid pipe 301; the second mass 300 is provided with a through hole; one end of the second steel strand 303 is connected with the third mass 302 through the through hole, and the other end is connected through the connecting block 4 and the rigid damping frame 1; the two control main frequency formulas of the second damping structure 3 are:

[0083]

[0084] ; wherein, the rigidity of the second steel strand 303, the mass of the third mass 302, the mass of the second mass 300; the mass of the first rigid pipe 301; the third mass 302 is provided with a second pouring hole; the part of the second steel strand 303 located in the second pouring hole is connected with the third mass 302 through the second pouring alloy 309; this structure is the PTMD structure in the related art; T is the torsional stiffness of the second steel strand 303.

[0085] Of course, the present application also proposes a new structure, which can be specifically referred to Figure 7 and Figure 8 , as follows:

[0086] New structure one: as Figure 8 , the second damping structure 3 includes the second rigid pipe 304 and the third steel strand 305; the bottom of the second rigid pipe 304 is provided with a sealing bottom plate 308; the third steel strand 305 extends into the second rigid pipe 304 and is connected with the second rigid pipe 304 through the fifth mass 311; the outer side of the second rigid pipe 304 is coaxially fixedly connected with the fourth mass 306.

[0087] New structure two: as Figure 7 , the second damping structure 3 includes the second rigid pipe 304 and the third steel strand 305; the bottom of the second rigid pipe 304 is provided with a sealing bottom plate 308; the third steel strand 305 extends into the second rigid pipe 304 and is connected with the second rigid pipe 304 through the fifth mass 311; the outer side of the second rigid pipe 304 is coaxially fixedly connected with the fourth mass 306; the diameter of the sealing bottom plate 308 is equal to the outer diameter of the fourth mass 306, and the sealing bottom plate 308 is connected with the bottom of the fourth mass 306 through the third rigid pipe 307.

[0088] ​The above two ways change the position of the fifth mass block 311, and change the mass ratio by changing the mass of the fifth mass block 311. In addition, the fifth mass block 311 is a third casting alloy for connecting the second rigid pipe 304 and the third steel wire 305. This structure gives the fifth mass block 311 a new function, that is, it can change its mass according to the casting amount. Since the casting amount is relatively easy to control, compared with directly replacing the entire second damping structure 3, when changing the mass ratio, the casting method can be used for change, so that there is no need to design a new second damping structure 3.

[0089] Further, the fifth mass block 311 is provided with a plurality of water holes 310 arranged along the length direction of the third steel wire 305; the bottom of the water hole 310 is provided with a sealing bottom plate 308, which makes the second damping structure 3 have the function of draining water and avoiding the corrosion caused by rainwater.

[0090] The application also provides a design method of a multi-directional broadband tuning mass damper, which comprises the following steps:

[0091] Obtaining a target range of control frequency and a plurality of target control main frequencies;

[0092] Comparing the plurality of target control main frequencies with the set control main frequency; if the target control main frequency is less than the set control main frequency, the target control main frequency is taken as the design parameter of the first damping structure 2; otherwise, it is taken as the design parameter of the second damping structure 3;

[0093] Obtaining the number of target control main frequencies less than the set control main frequency; obtaining the number of target control main frequencies greater than or equal to the set control main frequency;

[0094] Manufacturing the first damping structure 2 and the second damping structure 3 based on the design parameters and the number of the first damping structure 2 and the design parameters and the number of the second damping structure 3, and installing them on the rigid damping frame 1.

[0095] When the installation space on a single rigid damping frame 1 is less than the required installation space of all the first damping structure 2 and the second damping structure 3, a plurality of same rigid damping frames 1 are additionally arranged to install all the first damping structure 2 and the second damping structure 3 on the sling. It can be understood that the distance between two slings is limited, resulting in a limited length of the rigid damping frame 1, which cannot install all the first damping structure 2 and the second damping structure 3, so the same rigid damping frame 2 can be used to install the remaining first damping structure 2 and the second damping structure 3, which can be referred to Figure 4 .

[0096] The following gives a structure suitable for realizing broadband control of the girder bridge sling by using the above structure and design method, which is described as follows:

[0097] To achieve broadband damping vibration reduction for long suspension cables, taking a long suspension cable with a fundamental frequency of 1 Hz as an example, for the low-order vibration modes (1.0, 2.0, 3.0 Hz), three TMDs with corresponding control frequencies (1.0, 2.0, 3.0 Hz), small mass ratios (μs=0.1%), and small damping ratios (ξTs=2%) are selected for one-to-one control. For the high-order vibration modes (4 Hz and above), six TMDs with large mass ratios (μb=0.5%) and large damping ratios (ξTb=10%) are used for coordinated control, with corresponding control frequencies of 4.5, 7.0, 10.0, 14.0, 20.0, and 27.0 Hz. These control frequencies are used as design parameters.

[0098] The corresponding number of first damping structures 2 is three, and the number of second damping structures 3 is three. Simulation models of the first damping structures 2 and the second damping structures 3 are established based on the design parameters and quantities. The PTMD control frequency is adjusted by adjusting the arrangement of the mass blocks and the size of the steel strands. The control frequency is then verified to meet the requirements. After the requirements are met, actual manufacturing is carried out.

[0099] Simulation tests were conducted after actual manufacturing. To achieve the low and high damping ratio characteristics of the PTMD, a low-order single-frequency PTMD with low damping ratio and low mass ratio was designed using 7×φ4 mm (nominal diameter 12 mm) galvanized steel strand, and a high-order dual-frequency PTMD with high damping ratio and high mass ratio was designed using 19×φ3.2 mm (nominal diameter 16 mm) galvanized steel strand. The PTMDs were fixed to a 1-ton electric vibrator using movable clamps (for easy adjustment of the steel strand length and frequency). Accelerometers were placed at the hammer's center of gravity, the center of gravity of the annular mass block, and the end of the vibrator to test vibration characteristics. The free decay vibration time history curves of the 7×φ4 mm and 19×φ3.2 mm galvanized steel strand PTMDs and the dynamic amplification factor of the PTMDs at different frequencies were tested. The results are as follows: Figure 11 , Figure 12 As shown, the damping ratio can be further calculated from the free decay vibration time history curve. (See attached diagram.) Figure 11 - Appendix Figure 14 It can be seen that the PTMD damping ratio of 7-wire steel strand is 2%; the PTMD damping ratio of 19-wire steel strand is 10%, and it has two control frequencies, namely 7.0 Hz and 14.0 Hz. The control frequency range with a power amplification factor greater than 2 reaches 80%~130% of the control frequency, which can realize wide-frequency vibration control of the sling.

[0100] Additionally, refer to Figure 3As shown, through the synergy of three first damping structures 2 and three second damping structures 3, it has 3 small damping ratio, small mass ratio TMD and 6 large damping ratio, large mass ratio, which can realize the whole modal damping vibration reduction target of the sling 0~30 Hz.

[0101] The above, through the numerical method and model test verify its feasibility, Longmen Bridge adopts the damping scheme of dispersing multiple PTMD on the basis of strengthening the original rigid damping frame, integrating the rigid damping frame rigid connection and PTMD tuning damping function, realizing the wideband damping vibration reduction of the long sling of the bridge. The above can also be understood that the original rigid damping frame can also be strengthened, for example, thickening the thickness of the clamping plate of the rigid damping frame, lengthening the clamping length of the clamping plate at both ends; PTMD with different control frequencies are dispersed on the rigid damping frame according to the principle of maximum vibration mode participation.

[0102] The above technology can be applied to the vibration control of the cable-stayed cable, the arch bridge suspender, the lamp post, the super-long power transmission line, the high-speed railway contact net and other slender members, and the vertical vibration control of the footbridge and the highway bridge, the transverse vibration control of the heavy-load railway bridge and the wind turbine tower.

[0103] In the description of the present application, it should be noted that the orientation or position relationship indicated by the terms "upper", "lower" and the like is based on the orientation or position relationship shown in the drawings, and is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. Unless otherwise specified and limited, the terms "mounting", "connecting", "connecting" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication between two elements inside. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0104] It should be noted that, in the present application, the relational terms such as "first" and "second", and the like, are used solely to distinguish one entity or action from another, without necessarily requiring or implying any actual relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0105] The foregoing is merely illustrative of the principles of the application and various modifications can be made by those skilled in the art without departing from the spirit and scope of the application. The above embodiments are illustrative, and not restrictive, of the scope of the application.

Claims

1. A multi-directional broadband tuned mass damper, comprising a rigid damping frame (1), the ends of the rigid damping frame (1) in the length direction thereof being used for connecting with a sling, characterized in that: a plurality of first damping structures (2) and second damping structures (3) are arranged on the rigid damping frame (1) and spaced along the length direction thereof, the first damping structures (2) and the second damping structures (3) have the same extension direction; wherein a single first damping structure (2) has one control main frequency; a single second damping structure (3) has two control main frequencies; all the control main frequencies of the second damping structures (3) are greater than the control main frequency of the first damping structures (2) ; the second damping structure (3) comprises a second steel strand (303), a second mass block (300), a first rigid pipe (301) and a third mass block (302) ; the second mass block (300) is coaxially connected with the third mass block (302) through the first rigid pipe (301) ; the second mass block (300) is provided with a through hole; one end of the second steel strand (303) is connected with the third mass block (302) through the through hole, and the other end is connected with the rigid damping frame (1) through a connecting block (4) ; the formulae of the two control main frequencies of the second damping structure (3) are as follows: f 1 = 1 2 π k 1 m 1 and f 2 = 1 2 π k 2 m 2, wherein k 1 and k 2 are the stiffness of the first rigid pipe (301) and the second steel strand (303) respectively, and m 1 and m 2 are the masses of the second mass block (300) and the third mass block (302) respectively. 2.The multi-directional broadband tuned mass damper according to claim 1, characterized in that: the number of the first damping structures (2) and the second damping structures (3) is plural; the control main frequencies of the plural first damping structures (2) are different; the two control main frequencies of each second damping structure (3) are different, and the two control main frequencies of the plural second damping structures (3) are different. 3.The multi-directional broadband tuned mass damper according to claim 1 or 2, characterized in that: the first damping structures (2) and the second damping structures (3) are arranged on the rigid damping frame (1) according to the control main frequencies from large to small or from small to large. 4.The multi-directional broadband tuned mass damper according to claim 2, characterized in that: one second damping structure (3) is arranged between every two adjacent first damping structures (2) ; or, the length direction of the rigid damping frame (1) is provided with a first region and a second region, all the first damping structures (2) are arranged in the first region, and all the second damping structures (3) are arranged in the second region. 5.The multi-directional broadband tuned mass damper according to claim 1, characterized in that: the first damping structure (2) comprises a first steel strand (200) and a first mass block (201) ; one end of the first steel strand (200) is connected with the rigid damping frame (1) through a connecting block (4), and the other end is connected with the first mass block (201) ; the formula of the control main frequency of the first damping structure (2) is as follows: f = 1 2 π k m, wherein k is the stiffness of the first steel strand (200), and m is the mass of the first mass block (201). 6.The multi-directional broadband tuned mass damper according to claim 5, characterized in that: the first mass block (201) is provided with a first pouring hole, and the part of the first steel strand (200) extending into the first pouring hole is pouring-connected with the first mass block (201) through a first pouring alloy (202). ； ; wherein, is the stiffness of the second steel strand (303), is the mass of the third mass (302), is the mass of the second mass (300); is the mass of the first rigid tube (301); T is the torsional stiffness of the second steel strand (303). ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ wherein, is the stiffness of the first steel strand (200), is the mass of the first mass (201). ​ ​ 7. The multi-directional broadband tuned mass damper of claim 1, wherein: the third mass block (302) is provided with a second pouring hole; and the second steel strand (303) is connected to the third mass block (302) by a second pouring alloy (309) in the second pouring hole.

8. The multi-directional broadband tuned mass damper of claim 1, wherein: the second damping structure (3) comprises a second rigid tube (304) and a third steel strand (305); and the second rigid tube (304) is provided at its bottom with a sealing bottom plate (308). the third steel strand (305) extends into the second rigid tube (304) and is connected to the second rigid tube (304) by a fifth mass block (311); and the outer side of the second rigid tube (304) is coaxially fixedly connected to a fourth mass block (306).

9. The multi-directional broadband tuned mass damper of claim 1, wherein: the second damping structure (3) comprises a second rigid tube (304) and a third steel strand (305); and the second rigid tube (304) is provided at its bottom with a sealing bottom plate (308). the third steel strand (305) extends into the second rigid tube (304) and is connected to the second rigid tube (304) by a fifth mass block (311); and the outer side of the second rigid tube (304) is coaxially fixedly connected to a fourth mass block (306); and the diameter of the sealing bottom plate (308) is equal to the outer diameter of the fourth mass block (306), and the sealing bottom plate (308) is connected to the bottom of the fourth mass block (306) by a third rigid tube (307).

10. The multi-directional broadband tuned mass damper of claim 8 or 9, wherein: the fifth mass block (311) is a third pouring alloy for pouring and connecting the second rigid tube (304) and the third steel strand (305).

11. The multi-directional broadband tuned mass damper of claim 8 or 9, wherein: the fifth mass block (311) is provided with a plurality of water passing holes (310) arranged along the length direction of the third steel strand (305); and the bottom of the water passing hole (310) penetrates the sealing bottom plate (308).

12. A method of designing a multi-directional broadband tuned mass damper as claimed in claim 1, wherein, It comprises the following steps: obtaining a target range of control frequencies and deriving a plurality of target control main frequencies; comparing the plurality of target control main frequencies with a set control main frequency; if the target control main frequency is less than the set control main frequency, the target control main frequency is taken as a design parameter of the first damping structure (2); otherwise, as a design parameter of the second damping structure (3); obtaining the number of target control main frequencies less than the set control main frequency; obtaining the number of target control main frequencies greater than or equal to the set control main frequency; manufacturing the first damping structure (2) and the second damping structure (3) based on the design parameters and the number of the first damping structure (2) and the design parameters and the number of the second damping structure (3), and installing them on the rigid damping frame (1).

13. The design method of the multi-directional broadband tuned mass damper of claim 12, wherein: When the installation space on a single rigid damping frame (1) is less than the required installation space of all the first damping structures (2) and the second damping structures (3), a plurality of identical rigid damping frames (1) are additionally arranged to install all the first damping structures (2) and the second damping structures (3) on the sling.

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