A multi-cable high-frequency vortex-induced vibration reduction method and a multi-tuned mass damper

Abstract

The present application relates to a multi-cable high-frequency vortex-induced vibration damping method and a multiple tuned mass damper. A number of MTMD devices are connected to the cable through connecting rods. The MTMD device includes a first-stage TMD component, and the first-stage TMD component includes a damper. The damper includes a mass member and a first stiffness connecting member, and the first stiffness connecting member has a bending main frequency f1 and a torsional main frequency f2. A number of MTMD devices are designed and manufactured according to the vibration damping requirements so as to have multiple main frequencies. Thus, when in use, each MTMD device can have multiple adjustable main frequencies, and then an appropriate number and appropriate installation height can be selected and installed on the cable, so as to adapt to the broadband vibration control of the cable and effectively damp the vibration of double cables or multiple cables.

Description

Technical Field

[0001] The present application relates to the field of vibration reduction technology, and in particular to a multi-cable high-frequency vortex-induced vibration reduction method and a multi-tuned mass damper. Background Art

[0002] At present, suspension bridges are widely used in bridge projects across rivers, canyons and straits due to their excellent structural form, large span capacity and beautiful appearance. At present, suspension bridges are striding into the 2000m era. For example, the main span of the 1915 Çanakkale Bridge in Turkey, which has been opened to traffic, is 2023m. The main bridge of the Shiziyang Channel, which is being planned in China, is 2180m, and the main span of the cross-river section of the Zhanggao Channel is 2300m. With the increase of the span of the suspension bridge, the length of the sling also increases. The sling is thin and long, with low damping and many vibration modes. Under the excitation of complex wind loads, complex multi-modal vibration problems are prone to occur, and they become more obvious with the increase of span. The main span of the Xihoumen Bridge is 1650m, and the sling is a straddle-type steel wire rope sling. Its vibration form is mainly low-order large-scale vibration, and even cable-touching phenomenon occurs. The low-frequency large-scale vibration is controlled by installing a rigid divider, but high-frequency micro-amplitude vibration still occurs.

[0003] In some related technologies, the double or multi-cable design generally used in large-span suspension cables has more complex and diverse vibration modes than single cables (such as the same phase vibration mode and opposite phase vibration mode of parallel double cables). The existing single vibration reduction measures cannot control all possible vibration forms. The continuous vibration of the cable may not only cause fatigue and corrosion at the anchor end of the cable, seriously affecting the service life and maintenance cost of the cable, but also cause pedestrians to question the safety of the bridge, so effective vibration reduction methods should be adopted. Therefore, solving the problem of large vibration of the cables of large-span suspension bridges is a very urgent engineering issue. Summary of the invention

[0004] The embodiments of the present application provide a multi-cable high-frequency vortex-induced vibration reduction method and a multi-tuned mass damper to solve the problem that the existing single vibration reduction measure in the related art cannot effectively reduce vibration for double cables or multiple cables.

[0005] In a first aspect, a multi-tuned mass damper is provided, comprising:

[0006] A connecting rod with sling clamps at both ends;

[0007] A plurality of MTMD devices, comprising a first-stage TMD assembly, the first-stage TMD assembly comprising a damper, the damper comprising:

[0008] - a mass member, which includes a connecting tube b, the two ends of which are respectively connected to a first mass block a provided with an opening and a second mass block c provided with a water hole;

[0009] - A first stiffness connecting member, one end of which is connected to the connecting rod, the other end of which passes through the connecting tube b and the first mass block a and is coaxially connected to the second mass block c. The first stiffness connecting member has a bending main frequency and a torsional main frequency.

[0010] In some embodiments, the MTMD device further comprises a first vibration damping frame, and the first-stage TMD assembly is disposed in the first vibration damping frame to form a second-stage TMD assembly.

[0011] In some embodiments, the MTMD device further includes a second vibration damping frame, and the second-stage TMD assembly is disposed in the second vibration damping frame to form a third-stage TMD assembly.

[0012] In some embodiments, the first vibration damping frame includes a first rigid connector and two second rigid connectors; two ends of the first rigid connector are respectively connected to the two second rigid connectors, and are connected to the connecting rod through the second rigid connectors; the first rigid connector is connected to the first rigid connector;

[0013] The second vibration damping frame includes a second rigid connector and two third rigid connectors connected to the connecting rod; both ends of the second rigid connector are vertically connected to the third rigid connector; and the second rigid connector is connected to the two second rigid connectors.

[0014] In some embodiments, the second rigid connection member has a bending main frequency and reverse frequency , , , and The calculation formula is:

[0015] , , , ;

[0016] in, is the bending stiffness of the first stiffness connector, is the torsional stiffness of the first stiffness connection, , and are the mass of the second mass block, the mass of the first mass block and the mass of the connecting cylinder respectively; is the bending stiffness of the second stiffness connector, is the torsional stiffness of the second stiffness connection, is the mass of the first rigid connector;

[0017] The third stiffness connection has an additional bending frequency and reverse frequency , and its calculation formula is:

[0018] , ;

[0019] in, is the bending stiffness of the third stiffness connector, is the torsional stiffness of the third stiffness connector, is the mass of the second rigid connector.

[0020] In a second aspect, a multi-cable high-frequency vortex-induced vibration reduction method is provided, which comprises the following steps:

[0021] Conduct actual measurement and analysis on the vibration characteristics of the sling to determine the target value of the main vibration frequency of the sling after damping and vibration reduction;

[0022] According to the target value of the main frequency of vibration, a multiple tuned mass damper is manufactured and installed on the sling; wherein the multiple tuned mass damper adopts the multiple tuned mass damper as claimed in claim 1, and the manufacturing of the multiple tuned mass damper includes the following steps:

[0023] - establishing data models of multiple MTMD devices, and optimizing the damping ratios of the data models of the multiple MTMD devices to obtain optimized damping ratios;

[0024] - Input bending frequency and reverse frequency , and applying the optimized damping ratio to the corresponding data model of the MTMD device to obtain the simulated vibration main frequency after the data model of the MTMD device performs damping and vibration reduction on the sling;

[0025] - Filter out the data model of the MTMD device corresponding to the simulated vibration main frequency not greater than the vibration main frequency target value and the corresponding optimized parameters as the primary data model;

[0026] - Using all the primary data models, establish a data model of a multiple tuned mass damper with multiple different main frequencies;

[0027] -Manufacture a multiple tuned mass damper according to the data model of the multiple tuned mass damper.

[0028] In some embodiments, the multiple tuned mass dampers are installed on the suspension cables by performing the following steps:

[0029] Obtain the initial damping parameters and design vibration mode participation coefficients of the sling;

[0030] Simulate the actual damping parameters and actual vibration mode participation coefficients of the slings after installing several MTMD devices at different positions;

[0031] The actual damping parameters and actual modal participation factors of the sling are analyzed and compared with the initial damping parameters and design modal participation factors to obtain the best installation position.

[0032] In some embodiments, the data model of the MTMD device is:

[0033]

[0034] in, , , are the mass, damping and stiffness matrices of a single cable, is the external force on the structure, , , are the mass, damping and stiffness coefficients of the i-th first-stage TMD component, respectively; , , are the structural displacement vector, the structural displacement at the installation location of the first-stage TMD component, and the displacement of the i-th first-stage TMD component, respectively; =1,...,n; t is the excitation time.

[0035] In some embodiments, data models of multiple MTMD devices are established, and the damping ratios of the data models of the multiple MTMD devices are optimized. The specific steps of obtaining the optimized damping ratios are:

[0036] Obtain the inertial mass of the first-stage TMD component and the mass ratio of the first-stage TMD component to the sling, and use the first-stage TMD component with obvious vibration measured by the sling to obtain the inertial mass of the first-stage TMD component and the mass ratio of the first-stage TMD component to the sling. Taking the order frequency as the object and the optimal displacement control effect as the goal, the dynamic amplification coefficient curve of the first-order TMD component and the target displacement with external excitation is obtained through analysis;

[0037] According to the curve of the dynamic amplification factor changing with external excitation, the optimized intermediate damping ratio of the first-stage TMD component is obtained;

[0038] The additional damping parameter of the kth order main frequency of the sling is calculated according to the first formula;

[0039] The additional damping logarithmic attenuation rate diagram of the cable corresponding to the damping vibration reduction target is obtained by using the additional damping parameter of the kth order main frequency of the cable and the second formula;

[0040] The optimal damping ratio of the first-stage TMD component is obtained by analyzing the logarithmic decay rate diagram of the additional damping corresponding to the damping vibration reduction target of the sling.

[0041] In some embodiments, the first formula is:

[0042] ;

[0043] in, is the k-th order dynamic amplification factor of the sling at resonance, is the logarithmic decay rate of the k-th order modal damping of the sling;

[0044] The second formula is:

[0045]

[0046] In the above formula, g is the ratio of the external excitation frequency to the controlled structure frequency, , , is the i-th TMD to the The mass ratio, damping ratio and frequency ratio of the order mode, is the mode participation coefficient of the i-th TMD to the k-th mode; =1,...,n; i=1,...,n; is the k-order modal damping ratio of the structure, j is an imaginary unit (j 2 =-1).

[0047] The beneficial effects of the technical solution provided by this application include:

[0048] The embodiment of the present application provides a multi-tuned mass damper. Since a plurality of MTMD devices are connected to a connecting rod, the MTMD device includes a first-stage TMD component, and the first-stage TMD component includes a mass member and a first stiffness connecting member; wherein the mass member includes a connecting tube, and the two ends of the connecting tube are respectively connected to a first mass block provided with an opening, and a second mass block provided with a water hole; one end of the first stiffness connecting member is connected to the connecting rod, and the other end is penetrated by the connecting tube and the first mass block, and is coaxially connected to the second mass block, so that the MTMD device has a bending main frequency and a torsional main frequency, and the bending main frequency and the torsional main frequency can be adjusted according to the specific mass of the mass member. The damping ratio is designed according to the vibration reduction requirements of the sling, so that each MTMD device can have multiple adjustable main frequencies, and a suitable number and a suitable installation height are selected to be installed on the sling, so as to adapt to the broadband vibration control of the sling, so as to effectively reduce the vibration of double slings or multiple slings. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0050] Figure 1A schematic diagram of the structure of the second-stage TMD component provided in an embodiment of the present application;

[0051] Figure 2 A schematic diagram of the structure of the first-stage TMD component provided in an embodiment of the present application;

[0052] Figure 3 The bending vibration mode of the first-stage TMD component provided in the embodiment of the present application;

[0053] Figure 4 The torsional vibration mode of the first-stage TMD component provided in the embodiment of the present application;

[0054] Figure 5 A schematic diagram of the overall structure of two MTMD devices provided in an embodiment of the present application;

[0055] Figure 6 A schematic diagram of the structure of multiple MTMD devices provided in an embodiment of the present application installed on a double sling;

[0056] Figure 7 A curve diagram showing the dynamic amplification factor D of the first-stage TMD component and target displacement as a function of external excitation provided in an embodiment of the present application;

[0057] Figure 8 A diagram of additional damping parameters of the sling at each main frequency under different damping ratios of the first-stage TMD assembly provided in an embodiment of the present application;

[0058] Fig. 9 A graph showing the logarithmic attenuation rate of damping provided to the main frequency vibrations of the sling by the single effect and the coordinated work of the multiple first-stage TMDs provided in the embodiment of the present application;

[0059] Fig.10 The variation trend diagram of the 5-20Hz damping logarithmic attenuation rate δ of the 92# sling after the MTMD devices of four main frequencies are uniformly installed in the embodiment of the present application;

[0060] Fig.11 A variation trend diagram of the 5-20Hz damping logarithmic attenuation rate δ of the 92# sling after the MTMD devices of four main frequencies with different installation positions provided in the embodiment of the present application are installed;

[0061] Fig.12 A schematic diagram of the k-th order modal effective cable length of a sling provided in an embodiment of the present application.

[0062] In the figure: 1, connecting rod; 2, sling clamp; 3, first vibration damping frame; 300, second rigidity connecting member; 301, first rigid connecting member; 4, damper; 400, mass member; 401, first rigidity connecting member; 5, second vibration damping frame; 500, third rigidity connecting member; 501, second rigid connecting member; a, first mass block; b, connecting tube; c, second mass block. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0064] The embodiments of the present application provide a multi-cable high-frequency vortex-induced vibration reduction method and a multi-tuned mass damper to solve the problem that the existing single vibration reduction measure in the related art cannot effectively reduce vibration for double cables or multiple cables.

[0065] See also Figure 1-Figure 6 A multiple tuned mass damper comprises: a connecting rod 1 and a plurality of MTMD devices, each of which comprises a first-stage TMD component, and the first-stage TMD component comprises a damper 4.

[0066] The damper 4 includes a mass member 400 and a first stiffness connecting member 401, wherein the mass member 400 includes a connecting tube b, and the two ends of the connecting tube b are respectively connected to a first mass block a provided with an opening and a second mass block c provided with a water hole. The provision of the water hole prevents rainwater from being deposited inside the damper, causing corrosion and affecting the durability of the damper 4.

[0067] One end of the first rigidity connector 401 is connected to the connecting rod 1, and the other end is provided with a connecting tube b and the first mass block a, and is coaxially connected to the second mass block c. The first rigidity connector 401 can be directly cast and connected to the second mass block c, or can be connected by bolts, anchors, etc.; the second mass block c is made of a low melting point metal such as aluminum or zinc-aluminum alloy; the first rigidity connector 401 has a bending main frequency and reverse frequency The first rigidity connecting member 401 may be a steel strand, a steel rod or a steel pipe.

[0068] Bending frequency and reverse frequency It can be adjusted according to the size of the first mass block a, the second mass block c and the first rigidity connector 401. Rigidity refers to its elastic modulus E, and stiffness refers to EA, where A is the cross-sectional area.

[0069] Through the above structure, several MTMD devices are connected to the connecting rod 1, and then installed on the sling through the sling clamps 2 at both ends of the connecting rod 1. Figure 3 and Figure 4 , MTMD device has a bending frequency and reverse frequency , and bend the main frequency and reverse frequency The damping ratio can be adjusted according to the specific mass of the mass member 400. Each MTMD device can have two adjustable main frequencies. The two adjustable main frequencies of each MTMD device can be different. The MTMD devices can be arranged in a single set or in two sets symmetrically up and down. The damping ratio of the bending main frequency and the torsional main frequency can be adjusted according to the specific mass of the mass member. The damping ratio is designed according to the vibration reduction requirements of the sling, so that each MTMD device can have multiple adjustable main frequencies, thereby adapting to the broadband vibration control of the sling, so as to effectively reduce the vibration of double slings or multiple slings.

[0070] In some preferred embodiments, the following settings are made to increase the adjustable main frequency of the MTMD device:

[0071] The MTMD device also includes a first vibration damping frame 3, in which the first-stage TMD assembly is arranged to form a second-stage TMD assembly; the first vibration damping frame 3 includes a first rigid connector 301 and two second rigid connectors 300; both ends of the first rigid connector 301 are respectively connected to the two second rigid connectors 300, and are connected to the connecting rod 1 through the second rigid connectors 300; the first rigid connector 401 is connected to the first rigid connector 301.

[0072] The second rigidity connecting member 300 has a bending main frequency and reverse frequency , , , and The calculation formula is:

[0073] , , , ;

[0074] in, is the bending stiffness of the first stiffness connecting member 401, is the torsional stiffness of the first stiffness connecting member 401, , and are the mass of the second mass block c, the mass of the first mass block a and the mass of the connecting tube b respectively; is the bending stiffness of the second stiffness connecting member 300, is the torsional stiffness of the second stiffness connecting member 300, is the mass of the first rigid connector 301.

[0075] Therefore, by adding the first vibration-damping frame 3, the multiple tuned mass damper has two-stage TMD components and four adjustable main frequencies, which is more suitable for broadband vibration control of the sling.

[0076] In some preferred embodiments, the MTMD device also includes a second vibration damping frame 5, and the second-level TMD assembly is arranged in the second vibration damping frame 5 to form a third-level TMD assembly; the second vibration damping frame 5 includes a second rigid connector 501 and two third rigid connectors 500 connected to the connecting rod 1; both ends of the second rigid connector 501 are vertically connected to the third rigid connector 500; the second rigid connector 501 is connected to the two second rigid connectors 300.

[0077] The third rigidity connecting member 500 has an additional bending main frequency and reverse frequency , and its calculation formula is:

[0078] , ;

[0079] in, is the bending stiffness of the third stiffness connecting member 500, is the torsional stiffness of the third stiffness connecting member 500, is the mass of the second rigid connecting member 501.

[0080] Thus, by adding the second vibration-damping frame 5, the multi-tuned mass damper has three-level TMD components and six adjustable main frequencies, which is more suitable for broadband vibration control of the sling. Thus, by combining multiple sets of TMD components with different control main frequencies into an MTMD device, broadband control is achieved, and full coverage of the main frequency of the sling vibration is achieved. On the basis of different main frequencies covering a certain frequency range, they work together to achieve coverage of the main frequency vibration of the sling.

[0081] The present application also proposes a multi-cable high-frequency vortex-induced vibration reduction method, which comprises the following steps:

[0082] S1, conduct actual measurement and analysis on the vibration characteristics of the sling to determine the target value of the main vibration frequency of the sling after damping and vibration reduction;

[0083] S2, according to the target value of the main frequency of vibration, a multiple tuned mass damper is manufactured and installed on the sling; wherein the multiple tuned mass damper is as shown above, and the specific steps of manufacturing the multiple tuned mass damper are as follows:

[0084] S200, establishing data models of multiple MTMD devices, and optimizing the damping ratios of the data models of the multiple MTMD devices to obtain optimized damping ratios; the data models of the MTMD devices are:

[0085]

[0086] in, , , are the mass, damping and stiffness matrices of a single cable, is the external force on the structure, , , are the mass, damping and stiffness coefficients of the i-th first-stage TMD component, respectively; , , are the structural displacement vector, the structural displacement at the installation location of the first-stage TMD component, and the displacement of the i-th first-stage TMD component, respectively; =1,...,n; t is the excitation time.

[0087] S201, input bending frequency and reverse frequency , and applying the optimized damping ratio to the corresponding data model of the MTMD device to obtain the simulated vibration main frequency after the data model of the MTMD device performs damping and vibration reduction on the sling;

[0088] S202, screening out the data model of the MTMD device corresponding to the simulated vibration main frequency not greater than the vibration main frequency target value and the corresponding optimized parameters as the primary data model;

[0089] S203, using all the primary data models, establishing a data model of a multiple tuned mass damper with multiple different main frequencies;

[0090] S204, manufacturing a multiple tuned mass damper according to the data model of the multiple tuned mass damper.

[0091] Through the above steps, a multiple tuned mass damper that meets the cable vibration reduction requirements can be obtained and installed, thereby reducing the vibration of multiple cable high-frequency vortex excitation. A specific embodiment is given below to explain the above steps in detail:

[0092] S1 Step

[0093] The Nansha Bridge was selected as the analysis object. The Nansha Bridge includes two main channel bridges, namely the Nizhou Waterway Bridge with a main span of 1,688 meters and the Dasha Waterway Bridge with a main span of 1,200 meters. During the construction, the long suspension cables over 60 meters all experienced obvious vibrations. Through actual measurement and analysis, its main characteristics are as follows:

[0094] ① The vibration of the sling is mainly medium and high frequency. The measured frequency coverage range of different slings is 5~20Hz. Table 1 below is a statistical table of the vibration frequency, corresponding order and vibration acceleration amplitude of typical slings.

[0095]

[0096] Table 1

[0097] ② The vibration mode combination of the double (triple) cables in parallel at each suspension point is complex. After adding a rigid vibration damping frame every 40m, the cables still experience synchronous vibration and asynchronous vibration along the bridge, and synchronous and asynchronous vibration in the transverse direction of the bridge.

[0098] ③ The suspension cables are arranged vertically, and the wind-induced vibration is mainly manifested as vortex-induced vibration. The damping logarithmic attenuation rate δ required to control the vortex-induced vibration reaches 1%~1.5%.

[0099] Since each suspension point has two or three cables in parallel, the modal is complex after combination. If we focus on controlling a single cable independently, the combined vibration mode of the parallel cables will also be controlled. Therefore, the damping and vibration reduction target of the Nansha Bridge cable is determined as follows: by installing the MTMD device, the modal logarithmic attenuation rate δ of the 5-20Hz vibration of a single cable is greater than 1.5%.

[0100] S200 Steps

[0101] The inertial mass of the first-stage TMD component and the mass ratio of the first-stage TMD component to the sling are obtained, and the first-order frequency of the sling with obvious vibration is taken as the object, and the displacement control effect is optimized. The dynamic amplification coefficient of the first-stage TMD component and the target displacement is analyzed with the external excitation change curve;

[0102] According to the curve of the dynamic amplification coefficient changing with external excitation, the optimized intermediate damping ratio of the first-stage TMD component is obtained; the additional damping parameters of the k-th order main frequency of the sling are calculated according to the first formula; the additional damping logarithmic attenuation rate diagram of the sling corresponding to the damping vibration reduction target is obtained by using the additional damping parameters of the k-th order main frequency of the sling and the second formula; according to the additional damping logarithmic attenuation rate diagram of the sling corresponding to the damping vibration reduction target, the optimal damping ratio of the first-stage TMD component is obtained through analysis.

[0103] According to the above provided embodiments, the single cable of the 92# suspension cable of the Dasha Waterway Bridge is selected as the analysis object, and its basic parameters are shown in the following Table 2:

[0104]

[0105] Table 2

[0106] According to the classic TMD vibration reduction theory, the damping ratio provided by TMD for the structure increases with the increase of mass ratio; therefore, the inertial mass of a single first-stage TMD component is designed to be m=5kg. For the mass ratio of the first-stage TMD component of the 92# sling, =0.42%. Taking the 18th frequency (17.33Hz) of the 92# sling with obvious vibration as the object and the optimal displacement control effect as the goal, the dynamic amplification coefficient D of the first-level TMD component and the target displacement with external excitation is obtained, as shown in Figure 7 shown.

[0107] from Figure 7 It can be seen that the optimal damping ratio after optimization is =4%, the optimal frequency is 17.3Hz. Under this optimal parameter, the controlled target of the sling has two equal peak values ​​of the dynamic amplification factor of 21.8, and the first-stage TMD component has two equal peak values ​​of the dynamic amplification factor of 244.8. According to the first formula, the additional damping parameter δ of the 18th order (17.33Hz) main frequency of the sling is calculated to be 14.4%.

[0108] The actual vibration of the sling has multiple main frequencies. Under the optimal parameters of the first-level TMD component mentioned above, the additional damping parameter of the 18th-order main frequency of the sling and the second formula are used to solve the additional damping logarithmic attenuation rate δ of the 92# sling in the range of 5~20Hz as follows: Figure 8 As shown in the figure, since the sling has multiple main frequency vibrations, it is necessary to improve the control effect of a single TMD component on multiple main frequencies. Figure 7 The optimal damping ratio and the control effect comparison curve after the damping ratio is increased are also listed.

[0109] from Figure 8It can be seen that when the optimal damping ratio ξ=0.04 is used as the optimization target for the minimum displacement under the single controlled frequency of the sling, the damper 4 has the best additional damping effect on the 17.33Hz main frequency of the sling, but the additional damping effect on the adjacent main frequencies decreases rapidly, and its effective control frequency range is narrow; when the damping ratio is increased to 10%, the additional damping effect of the first-stage TMD component on the 17.33Hz vibration decreases, while the additional damping effect on the adjacent main frequencies increases, and the effective control range becomes wider; when the damping ratio is increased from 10% to 15%, it still has the above-mentioned change trend, but the controlled main frequency is weakened more, while the improvement of the adjacent frequencies is not obvious. Considering that the damping ratio provided by the steel strand in the actual structure of the first-stage TMD component is about 10%, 10% is selected as the optimal damping ratio of the first-stage TMD component for controlling the sling. In addition, the frequency coverage range of a single first-stage TMD component is limited. In order to fully cover the vibration of 5~20Hz, multiple MTMD devices with main frequencies are required.

[0110] The first formula used in step S200 is:

[0111] ;

[0112] in, is the k-th order dynamic amplification factor of the sling at resonance, is the logarithmic decay rate of the k-th order modal damping of the sling;

[0113] The second formula is:

[0114]

[0115] In the above formula, g is the ratio of the external excitation frequency to the controlled structure frequency, , , is the i-th TMD to the The mass ratio, damping ratio and frequency ratio of the order mode, is the mode participation coefficient of the i-th TMD to the k-th mode; =1,...,n; i=1,...,n; is the k-order modal damping ratio of the structure, j is an imaginary unit (j 2 =-1).

[0116] In steps S201 and S202, the reason for the operation is that the full coverage of the main frequency of the cable vibration is achieved by working together on the basis that different main frequencies each cover a certain frequency range; therefore, through multiple trials, in order to effectively suppress the 5~20Hz vibration of a single cable, multiple groups of MTMD devices with different main frequencies are required to achieve full coverage of the main frequency of the cable vibration. and reverse frequency It is selected based on empirical values, so multiple trial calculations are required, and the simulated vibration main frequency is compared with the vibration main frequency target value, so as to obtain multiple MTMD devices that can effectively suppress the 5-20Hz vibration of a single sling, where the vibration main frequency target value is the vibration frequency after installing multiple MTMD devices.

[0117] In this embodiment, there are four MTMD devices, whose frequencies are f1 = 6.5 Hz, f2 = 9.5 Hz, f3 = 13.5 Hz and f4 = 18 Hz respectively. The single effect and coordinated work of the four first-stage TMD components provide the damping logarithmic attenuation rate δ of each main frequency vibration of the sling as shown in Fig. 9 As shown, from Figure 8 and Fig. 9 It can be seen that the frequency coverage range of the four first-stage TMD components is wide at high orders and narrow at low orders. Through the collaborative working scheme of the four first-stage TMD components, the purpose of multi-modal vibration coverage of the sling is achieved.

[0118] It should be understood that in the above-mentioned embodiment, four first-stage TMD components are used, and the first-stage TMD components have a bent main frequency. and reverse frequency , to achieve the corresponding effect, two second-stage TMD components are sufficient; similarly, only one third-stage TMD component is sufficient. The MTMD device has a bending main frequency and a torsional main frequency, and the bending main frequency and the torsional main frequency can be adjusted according to the specific mass of the mass part. The damping ratio is designed according to the vibration reduction requirements of the sling, so that each MTMD device can have multiple adjustable main frequencies, and select a suitable number and a suitable installation height to be installed on the sling, so as to adapt to the broadband vibration control of the sling, so as to effectively reduce the vibration of double slings or multiple slings.

[0119] In some preferred embodiments, the following description is given on how to select a suitable installation height:

[0120] When the MTMD device is at the maximum k-order vibration mode, the vibration mode participation coefficient is 1. In order to play a better role, the damper should be installed at the maximum of each vibration mode as much as possible. However, for the vibration mode characteristics of the sling, the vibration mode participation coefficients corresponding to different vibration modes at the same position are different; therefore, in the actual sling damping vibration reduction, the damper is installed at a fixed position, and the vibration mode participation coefficients for each vibration mode are different; to install the multi-tuned mass damper on the sling, the following steps are required:

[0121] The initial damping parameters and design modal participation coefficients of the sling are obtained; the actual damping parameters and actual modal participation coefficients of the sling after several MTMD devices are installed at different positions are simulated; the actual damping parameters and actual modal participation coefficients of the sling are analyzed and compared with the initial damping parameters and design modal participation coefficients to obtain the optimal installation position.

[0122] The specific implementation steps are:

[0123] When MTMD is installed on the beam end sling Department ( is the distance between the installation position of the damper 4 and the hinge point of the suspension cable at the beam end), the total length of the suspension cable is L, then the k-th order vibration mode participation coefficient of the damper 4 is:

[0124]

[0125] is the mode participation coefficient of the i-th TMD for the k-th mode, L is the length of the sling, and k is the vibration order.

[0126] According to the field measurement, the initial damping parameter δ of the sling is set to 0.6%. After installing the MTMD devices with four main frequencies, the change trend of the 5~20Hz damping logarithmic attenuation rate δ of the 92# sling is as follows: Fig.10 and Fig.11 shown.

[0127] Fig.10 In the figure, the MTMD devices are installed on the same sling, and the installation position ratios are 2.5%, 3.8%, and 5%, respectively. The corresponding maximum vibration mode participation coefficients appear at 19.6 Hz (20th order), 12.7 Hz (13th order), and 9.6 Hz (10th order). The three layout schemes are as follows:

[0128] ① Under the installation position ratio of 2.5%, the effect of the high-frequency part is better, and the low- and medium-order part is worse. 5~7Hz is lower than the target value of 0.015, which does not meet the requirements;

[0129] ②For the 5% installation position, the effect of medium and low frequencies is better, and 16~20Hz is lower than the target value of 0.015, which does not meet the requirements.

[0130] ③At the installation position ratio of 3.8%, the damping parameters in the middle frequency range are better, and the effects of low and high frequencies become worse, but both can meet the target value requirement of 0.015.

[0131] Fig.11In the experiment, 6.5Hz and 9.5Hz MTMD devices were installed at a position ratio of 6.5%, and 13.5Hz and 18Hz MTMD devices were installed at a position ratio of 2.9%. The DMTMD was formed by combining them. The damping parameter δ corresponding to each order frequency was greater than 0.03. Therefore, it can be proved that the comprehensive performance of each order is better than the effect of installing the four main frequencies at the same position.

[0132] In some preferred embodiments, the cables of the suspension bridge, except for the longest cables close to the bridge towers, are of the same model and have basically the same cable force. The only difference is the cable length. For the parameter design of MTMD devices with different cable lengths, it is necessary to study the scope of application of the above theoretical analysis and whether each cable needs to be optimized and analyzed separately.

[0133] The kth frequency of the sling is given by the formula:

[0134]

[0135] f k is the k-order vibration frequency of the sling, L is the length of the sling, k is the vibration order of the sling, H is the force of the sling, and m is the linear density of the sling.

[0136] definition is the effective cable length of the kth mode of the sling, and its physical meaning is as follows Fig.12 As shown, the above formula is transformed into The expression is:

[0137]

[0138] L is the length of the cable, k is the vibration order of the cable, H is the cable force, and m is the cable line density. It can be seen that when the models of cables of different lengths are the same, the cable forces are close, and the controlled frequency ranges are the same, their modal effective lengths are close, and the installation positions xd of the MTMD devices are also close. Therefore, when the MTMD devices are used for vibration reduction of suspension bridge cables, the same type of MTMD devices can be used under the premise of the same target control frequency range, and the design, parameters and installation positions are uniformly designed. Therefore, if the adjacent cables are of the same model, close cable forces and the same controlled frequency range, but different lengths, the same multiple tuned mass damper is used.

[0139] In the description of the present application, it should be noted that the terms "upper", "lower", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. Unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be a connection between the two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to the specific circumstances.

[0140] It should be noted that, in this application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0141] The above description is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest range consistent with the principles and novel features applied for herein.

Claims

1. A multi-cable high-frequency vortex-induced vibration reduction method, characterized in that: It includes the following steps: Conduct actual measurement and analysis on the vibration characteristics of the sling to determine the target value of the main vibration frequency of the sling after damping and vibration reduction; According to the target value of the main frequency of vibration, a multiple tuned mass damper is manufactured and installed on the sling; The multiple tuned mass damper comprises: a connecting rod (1), both ends of which are provided with sling clamps (2); a plurality of MTMD devices, the MTMD devices comprising a first-stage TMD component, a first vibration damping frame (3) and a second vibration damping frame (5); the first-stage TMD component is arranged in the first vibration damping frame (3) to form a second-stage TMD component; the second-stage TMD component is arranged in the second vibration damping frame (5) to form a third-stage TMD component; the first-stage TMD component comprises a damper (4), and the damper (4) comprises: - a mass member (400), comprising a connecting tube (b), wherein two ends of the connecting tube (b) are respectively connected to a first mass block (a) provided with an opening and a second mass block (c) provided with a water hole; - a first rigidity connecting member (401), one end of which is connected to the connecting rod (1), the other end of which passes through the connecting tube (b) and the first mass block (a), and is coaxially connected to the second mass block (c), the first rigidity connecting member (401) having a bending main frequency and reverse frequency ; The above manufacturing of the multiple tuned mass damper includes the following steps: - establishing data models of multiple MTMD devices, and optimizing the damping ratios of the data models of the multiple MTMD devices to obtain optimized damping ratios; - Input bending frequency and reverse frequency , and inputting the optimized damping ratio into the data model of the corresponding MTMD device to obtain the simulated vibration main frequency after the data model of the MTMD device performs damping and vibration reduction on the sling; - Filter out the data model of the MTMD device corresponding to the simulated vibration main frequency not greater than the vibration main frequency target value and the corresponding optimized parameters as the primary data model; - Using all the primary data models, establish a data model of a multiple tuned mass damper with multiple different main frequencies; -Manufacture a multiple tuned mass damper according to the data model of the multiple tuned mass damper.

2. The multi-cable high-frequency vortex-induced vibration reduction method according to claim 1, characterized in that: The first vibration damping frame (3) comprises a first rigid connection member (301) and two second rigid connection members (300); two ends of the first rigid connection member (301) are respectively connected to the two second rigid connection members (300), and are connected to the connecting rod (1) via the second rigid connection members (300); the first rigid connection member (401) is connected to the first rigid connection member (301); The second vibration damping frame (5) comprises a second rigid connector (501) and two third rigid connectors (500) connected to the connecting rod (1); both ends of the second rigid connector (501) are vertically connected to the third rigid connector (500); and the second rigid connector (501) is connected to the two second rigid connectors (300).

3. The multi-cable high-frequency vortex-induced vibration reduction method according to claim 2, characterized in that: The second rigidity connecting member (300) has a bending main frequency and reverse frequency , , , and The calculation formula is: ， ， ， ； in, is the bending stiffness of the first stiffness connecting member (401), is the torsional stiffness of the first stiffness connecting member (401), , and are the mass of the second mass block (c), the mass of the first mass block (a) and the mass of the connecting tube (b); is the bending stiffness of the second stiffness connecting member (300), is the torsional stiffness of the second stiffness connecting member (300), is the mass of the first rigid connecting member (301); The third stiffness connecting member (500) has an additional bending main frequency and reverse frequency , and its calculation formula is: ， ； in, is the bending stiffness of the third stiffness connecting member (500), is the torsional stiffness of the third stiffness connecting member (500), is the mass of the second rigid connecting member (501).

4. The multi-cable high-frequency vortex-induced vibration reduction method according to claim 1, characterized in that: To install the multi-tuned mass damper on the sling, the following steps are required: Obtain the initial damping parameters and design vibration mode participation coefficients of the sling; Simulate the actual damping parameters and actual vibration mode participation coefficients of the slings after installing several MTMD devices at different positions; The actual damping parameters and actual modal participation factors of the sling are analyzed and compared with the initial damping parameters and design modal participation factors to obtain the best installation position.

5. The multi-cable high-frequency vortex-induced vibration reduction method according to claim 1, characterized in that: The data model of the MTMD device is: in, , , are the mass, damping and stiffness matrices of a single cable, is the external force on the structure, , , are the mass, damping and stiffness coefficients of the i-th first-stage TMD component, respectively; , , are the structural displacement vector, the structural displacement at the installation location of the first-stage TMD component, and the displacement of the i-th first-stage TMD component, respectively; =1,...,n; t is the excitation time.

6. The multi-cable high-frequency vortex-induced vibration reduction method according to claim 1, characterized in that: The data models of multiple MTMD devices are established, and the damping ratios of the data models of the multiple MTMD devices are optimized. The specific steps of obtaining the optimized damping ratios are as follows: Obtain the inertial mass of the first-stage TMD component and the mass ratio of the first-stage TMD component to the sling, and use the first-stage TMD component with obvious vibration measured by the sling to obtain the inertial mass of the first-stage TMD component and the mass ratio of the first-stage TMD component to the sling. Taking the kth order frequency as the object and the optimal displacement control effect as the goal, the dynamic amplification coefficient of the first-stage TMD component and the target displacement is analyzed to obtain the curve of the change of external excitation; according to the curve of the change of the dynamic amplification coefficient with external excitation, the optimized intermediate damping ratio of the first-stage TMD component is obtained; the additional damping parameter of the kth order main frequency of the sling is calculated according to the first formula; the additional damping logarithmic attenuation rate diagram of the sling corresponding to the damping vibration reduction target is obtained by using the additional damping parameter of the kth order main frequency of the sling and the second formula; according to the additional damping logarithmic attenuation rate diagram of the sling corresponding to the damping vibration reduction target, the optimal damping ratio of the first-stage TMD component is obtained; The first formula is: ； in, is the k-th order dynamic amplification factor of the sling at resonance, is the logarithmic decay rate of the k-th order modal damping of the sling; The second formula is: In the above formula, g is the ratio of the external excitation frequency to the controlled structure frequency, , , is the i-th TMD to the The mass ratio, damping ratio and frequency ratio of the order mode, is the mode participation coefficient of the i-th TMD to the k-th mode; =1,...,n; i=1,...,n; is the k-order modal damping ratio of the structure, j is an imaginary unit, 2 =-1.

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