AU2021105110A4

AU2021105110A4 - Stay Cable Combined Vibration Damping Device and Method

Info

Publication number: AU2021105110A4
Application number: AU2021105110A
Authority: AU
Inventors: Guoqiang Jing; Dongchao Li; Pengfei Liu; Changfei MA; Nengjun SHENG; Bo Wang; Xiang Wang; Zehao WANG; Zhengxing Wang; Xiaobo Wu; Haiwei Zhao
Original assignee: China Railway Major Bridge Engineering Group Co Ltd MBEC; China Railway Bridge Science Research Institute Ltd
Current assignee: China Railway Major Bridge Engineering Group Co Ltd MBEC; China Railway Bridge Science Research Institute Ltd
Priority date: 2020-09-30
Filing date: 2021-08-09
Publication date: 2021-09-30
Anticipated expiration: 2029-08-09
Also published as: CN112227180A; CN112227180B

Abstract

The present invention relates to the technical field of structural vibration control, in particular to a stay cable combined vibration damping device and method, and the method comprises the following steps: determining fundamental vibrational frequency of a stay cable according to parameters of the stay cable; determining installation position of an external damper according to vibration damping requirements of the stay cable; determining vibration stationary point frequency of the stay cable at the installation position of the external damper according to the fundamental vibrational frequency of the stay cable and the installation position of the external damper; determining control frequency of a tuned mass damper to be installed according to the stationary point frequency of the stay cable at the installation position of the external damper of the stay cable; and installing the external damper according to the installation position of the external damper, and installing the tuned mass damper on the stay cable between an anchor point and the external damper. The present invention can solve the problem in the prior art that the stationary point cannot effectively damp the vibration frequency adjacent to the corresponding vibration frequency due to the fact that the external damper is installed at the vibration stationary point, and solve the problem that the external damper of the stay cable has poor control effect on high-frequency vibration of the stay cable. -1- 1/1 3 2 11 12 13 4 Fig. 1 21 23 22 24 23 Fig. 2

Description

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Specification Stay Cable Combined Vibration Damping Device and Method

Field of the Invention The present invention relates to the technical field of structural vibration control, in particular to a stay cable combined vibration damping device and method.

Background of the Invention With the development of science and technology, the research and development of new materials and technologies, the span of cable-stayed bridges has been continuously broken, and the number of cable-stayed bridges with a main span of more than 1,000 m has also been increasing, which has also led to the increasing application of super-long stay cables ( "External Viscous Fluid Damper for Stay Cables" with standard number of JT/T 1038-2016 stipulates that stay cables longer than 450 m are super-long stay cables). Compared with stay cables which have normal length, the flexibility of the super-long stay cables will be larger and the damping will be greatly reduced, therefore, different types of vibration will be more likely to occur under the excitation of dynamic loading. A large number of engineering examples show that the super-long stay cables are prone to fatigue failure, which is because the super-long stay cables of the cable-stayed bridge often have large and violent vibrations even in light rain and low wind conditions. The fatigue damage of the super-long stay cables often causes damage to stay cable protective sleeves, thereby accelerating the corrosion of the stay cables. In severe cases, the stay cable may lose most of the bearing capacity or failure, thereby seriously affecting the safety of the entire bridge. For the vibration control of the super-long stay cable, there are usually external dampers, internal dampers or a combination of both, however, when the external damper is adopted, the installation position of the required damper is relatively high, which will cause the installation position of the external damper to be a vibration stationary point (the vibration displacement herein is 0), at this time, the external damper of the stay cable cannot perform the vibration damping function, and the damper connector may be damaged if the vibration is serious. In addition, the external damper of the stay cable has limited control effect on the higher-order vibration of the stay cable, and high-frequency vibration easily causes damage to the damper connector of the stay cable and loosening of bolts, which greatly reduces durability thereof.

Summary of the Invention In view of the defects existing in the prior art, the purpose of the present invention is to provide a stay cable combined vibration damping device and method, which can solve the problem in the prior art that the installation position of the required damper is relatively high when the external damper is adopted, causing the installation position of the external damper to be a vibration stationary point, thereby being unable to effectively perform the vibration damping function; at the same time, which can solve the problem that the high-frequency vibration of the stay cable causes damage to the external damper of the stay cable and affects the vibration damping effect. In order to achieve the above purpose, the present invention adopts the following technical solutions. On the one hand, the present invention provides a stay cable combined vibration damping device, comprising: an external damper, which comprises: -a damper cable clamp, which is configured to clamp at a set position of a stay cable, -a dowel bar, one end of which is connected to the damper cable clamp, -a damper, which is installed on a bridge deck and connected to the other end of the dowel bar; and a tuned mass damper, which is installed on the stay cable between an anchor point and the external damper. In order to achieve better wide-frequency control effect and multi-order high frequency vibration control, the tuned mass damper can be a multiple tuned mass damper, which can control the vibration of the stay cable at a plurality of vibration frequencies. On the basis of the above technical solution, the tuned mass damper is installed on a midpoint between the anchor point of the stay cable and the external damper. On the basis of the above technical solution, the external damper is an oil damper, a viscous damper or an eddy current damper, and the tuned mass damper is a multiple tuned mass damper. On the other hand, the present invention also provides a stay cable combined vibration damping method, comprising the following steps: determining fundamental vibrational frequency of the stay cable according to parameters of the stay cable; determining installation position of the external damper according to vibration damping design requirements of the stay cable; determining vibration stationary point frequency of the stay cable at the installation position of the external damper according to the fundamental vibrational frequency of the stay cable and the installation position of the external damper; determining control frequency of the tuned mass damper to be installed according to the vibration stationary point frequency of the stay cable at the installation position of the external damper; and installing the external damper according to the installation position of the external damper, and installing the tuned mass damper on the stay cable between the anchor point and the external damper. On the basis of the above technical solution, determining the fundamental vibrational frequency of the stay cable, specifically comprising: calculating the fundamental vibrational frequency f; of the stay IT cable according to the formula f 1 = , wherein L is the length of the 2Lm stay cable, T is the tensioning force of the stay cable, and m is the linear density of the stay cable. On the basis of the above technical solution, according to the vibration damping design requirements of the stay cable, the installation position of the external damper is determined to be 1%-4% of the length of the stay cable from the anchor point of the bridge deck. On the basis of the above technical solution, determining the vibration stationary point frequency of the stay cable at the installation position of the external damper according to the fundamental vibrational frequency of the stay cable and the installation position of the external damper, specifically comprising: determining an installation position ratio n of the external damper according to the formula n= L ; and 11 determining the vibration stationary point frequency f, of the stay n T cable at the installation position according to the formula, = nm 2L m1 wherein 11 is the distance from the anchor point of the stay cable to the external damper, L is the length of the stay cable, T is the tensioning force of the stay cable, and m is the linear density of the stay cable. On the basis of the above technical solution, determining control frequency of the tuned mass damper to be installed according to the stationary point frequency of the stay cable at the installation position of the external damper, specifically comprising: determining control frequency range of the tuned mass damper according to the vibration stationary point frequency of the stay cable at the installation position of the external damper; and determining the control frequency of the tuned mass damper to be installed according to the control frequency range of the tuned mass damper. On the basis of the above technical solution, the control frequency range of the tuned mass damper is three-order vibration frequencies before and after the vibration stationary point frequency of the stay cable at the installation position of the external damper 1: n-3 T n+3 T

On the basis of the above technical solution, the tuned mass damper adopts a multiple tuned mass damper with steel strands and two mass blocks, the control frequency of the tuned mass damper is determined according to the formulas f=- = 2L n and 2T MLE 2L 'm 1 3EI _n+3 T 27 M2 L 2L m

wherein f is the first control frequency of the tuned mass damper, f is the second control frequency of the tuned mass damper, E is elastic modulus of the steel strand, I is flexural stiffness of the steel strand, M, is the mass of the first mass block, LI is the distance from the first mass block to the cable clamp, M2 is the mass of the second mass block, L 2 is the distance from the second mass block to the cable clamp, and L 2 is smaller than LI, when installing, the second mass block is located above. Compared with the prior art, the present invention has the advantages as follows: when the stay cable combined damping device and method are adopted, a tuned mass damper is installed on the stay cable between the anchor point and the external damper, and the tuned mass damper selects a damper that can meet the wide-frequency control effect within a certain range, which meets the vibration damping requirements of three-order front and after the frequencies around the stationary point of the super-long stay cable, and adopts certain measures to attach the damper to the stay cable. In addition, the tuned mass damper is easy to install, and the combined use of the two dampers can effectively control the stay cable in the full frequency range, thereby solving the problem of damping the vibration of the super-long stay cable. Besides, the present invention is also suitable for the vibration damping requirements of the rod-type structure such as long suspension cables of suspension bridges and long suspension rods of arch bridges.

Description of the Drawings In order to better illustrate the technical solution in the embodiments of the present application, the following will briefly introduce the drawings needed in the description of the embodiments, and it is obvious that the drawings in the following description are part of embodiments of the present application, for those of ordinary skill in the art, other drawings may also be obtained based on these drawings without any creative work. Fig. 1 is a structural schematic diagram of a stay cable combined vibration damping device in the embodiment of the present invention; Fig. 2 is a structural schematic diagram of a tuned mass damper in the embodiment of the present invention. In the figures: 1. external damper; 11. damper cable clamp; 12. dowel bar; 13. damper; 2. tuned mass damper; 21. TMD clamp; 22. steel strand; 23. mass block; 24. steel strand clamp; 3. stay cable; 4. bridge deck.

Detailed Description of the Embodiments In order to make the purpose, 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 in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a 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 a person of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application. The present invention will be further described below in detail with reference to the drawings in combination with the embodiments. Fig. 1 is a structural schematic diagram of a stay cable combined vibration damping device in the embodiment of the present invention. As shown in Fig. 1, the present invention provides a stay cable combined vibration damping device, comprising: an external damper 1, which comprises: a damper cable clamp 11, which is clamped at a set position of a stay cable 3; a dowel bar 12, one end of which is connected to the damper cable clamp 11; and a damper 13, which is installed on a bridge deck 4 and connected to the other end of the dowel bar 12. The stay cable combined vibration damping device further comprises a tuned mass damper 2, which is installed on the stay cable 3 between an anchor point and the external damper 1. When the stay cable combined damping device is adopted, the tuned mass damper 2 is installed on the stay cable 3 between the anchor point and the external damper 1, and the tuned mass damper 2 selects a damper that can meet the wide-frequency control effect within a certain range, which meets the vibration damping requirements of three-order front and after the frequencies around the stationary point of the super-long stay cable, and adopts certain measures to attach the damper to the stay cable 3. In addition, the tuned mass damper 2 is easy to install, and the combined use of the two dampers can effectively control the stay cable 3 in the full frequency range, thereby solving the problem of damping the vibration of the super-long stay cable. Besides, the present invention is also suitable for the vibration damping requirements of the rod-type structure such as long suspension cables of suspension bridges and long suspension rods of arch bridges. In addition, according to the fundamental vibrational frequency of the stay cable, the frequency range of the control effect that can be achieved by the external damper of the stay cable and the damage to the external damper of the stay cable can be checked. For the vibration that exceeds the control frequency range of the stay cable, a multiple tuned mass damper is adopted to control. Similar to stationary point vibration control, the multiple tuned mass damper performs high-frequency vibration control, and a plurality of sets of tuned mass dampers (multiple tuned mass dampers) can be arranged to achieve the effect of wide-frequency control of the stay cable. In some alternative embodiments, the tuned mass damper 2 is installed on a midpoint between the anchor point of the stay cable and the external damper 1. In the embodiment, the tuned mass damper 2 is installed on the midpoint between the anchor point of the stay cable and the external damper 1. The midpoint has the largest vibration amplitude, so the tuned mass damper 2 installed on the midpoint can control vibration more effectively. In some alternative embodiments, the external damper 1 is an oil damper, a viscous damper or an eddy current damper, and the tuned mass damper 2 is a multiple tuned mass damper. The multiple tuned mass damper is adopted to achieve better wide-frequency control effect and multi-order high frequency vibration control, and the tuned mass damper can be the multiple tuned mass damper, to control the vibration of the stay cable at a plurality of vibration frequencies. Fig. 2 is a structural schematic diagram of a tuned mass damper in the embodiment of the present invention. As shown in Fig. 2, in addition, in the embodiment, the tuned mass damper 2 adopts a damping scheme of multiple tuned mass damper with steel strands and mass blocks, and the specific structure comprises four parts: TMD clamps 21, steel strands 22, cylindrical mass blocks 23, and steel strand clamps 24. The present invention further provides a stay cable combined vibration damping method, comprising the following steps. SI: determining fundamental vibrational frequency of the stay cable 3 according to parameters of the stay cable 3.

Preferably, obtaining the fundamental vibrational frequency of the stay cable by calculation according to the formula f1 = 2L m wherein L is the length of the stay cable, T is the tensioning force of the stay cable, and m is the linear density of the stay cable. The fundamental vibrational frequency f, is the first-order vibration frequency.

S2: determining installation position of the external damper 1 according to vibration damping design requirements of the stay cable 3. In the embodiment, according to the vibration damping design requirements of the stay cable 3, the installation position of the external damper 1 is determined to be 1%-4% of the length of the stay cable 3 from the anchor point of the bridge deck. S3: determining vibration stationary point frequency of the stay cable at the installation position of the external damper 1 according to the fundamental vibrational frequency of the stay cable 3 and the installation position of the external damper 1. The vibration stationary point frequency is the vibration frequency with the installation position of the external damper 1 as the stationary point. Preferably, determining the vibration stationary point frequency of the stay cable at the installation position of the external damper 1, specifically comprising: determining an installation position ratio n of the external damper according to the formula n= L; and 11

determining the vibration stationary point frequency f, of the stay cable at the installation position of the external damper 1 according to the formula L= n 2L m

wherein 11 is the distance from the anchor point of the stay cable to the external damper, L is the length of the stay cable, T is the tensioning force of the stay cable, and m is the linear density of the stay cable. fn is the n-th order vibration frequency. In the embodiment, the installation position ratio n of the external damper is rounded to the nearest integer. S4: determining control frequency of the tuned mass damper 2 to be installed according to the vibration stationary point frequency of the stay cable at the installation position of the external damper 1. Preferably, determining the control frequency of the tuned mass damper 2, specifically comprising the following steps. S41: determining the control frequency of the tuned mass damper 2 to be installed according to the vibration stationary point frequency of the stay cable 3 at the installation position of the external damper 1. Preferably, the control frequency range of the tuned mass damper 2 is three-order vibration frequencies before and after the vibration stationary point frequency of the stay cable:

The frequency at the position of the stationary point of the stay cable is the n-th order. The vibration amplitude of the stay cable near the n-3 and n+3 stationary point is very small, and the vibration damping effect of the external damper of the stay cable is not obvious, therefore, the tuned mass damper adopted should cover three-order modes of vibration before and after the n-order, which can improve the vibration damping effect of the entire stay cable. S42: determining the control frequency of the tuned mass damper 2 to be installed according to the control frequency range of the tuned mass damper 2. Preferably, the control frequency of the tuned mass damper 2 is determined according to the formulas I= =3E1 n -3 T 2 ML 2L m 1 3EI n+3 T n d N M2L 2L m'

wherein f is the first control frequency of the tuned mass damper 2, f, is the second control frequency of the tuned mass damper 2, E is elastic modulus of the steel strand, Iis flexural stiffness of the steel strand, M is the mass of the first mass block, LI is the distance from the first mass block to the cable clamp, M 2 is the mass of the second mass block, L 2 is the distance from the second mass block to the cable clamp, and L 2 is smaller than LI, when installing, the second mass block is located above. M, and M2 are determined by the modal mass M of the stay cable, in order to achieve the target logarithmic decrement of the stay cable of 3% (the damping ratio is about 0.5%), the mass ratios pi and t2 (pi=M/M and t2 =M2 /M)should be greater than 0.05%, that is, M, and M 2 are taken as 0.05% of the modal mass of the stay cable. Through determining the mass of the mass block, the model of steel strand for trial use (corresponding to El) is selected, thereby determining L, and L 2 according to the formulas f'= L - [ and 2 MIL 2L m 1 3EI _n+3 T 2 M2 L 2L m

In the embodiment, the frequency of the tuned mass damper 2 is set to be 1.05 times the minimum range and 0.95 times the maximum range, so that the frequency controlled by the tuned mass damper 2 can be wider. S5: installing the external damper according to the installation position of the external damper, and installing the tuned mass damper 2 on the stay cable between the anchor point and the external damper 1. In general, when the stay cable combined damping method is adopted, the tuned mass damper 2 is installed on the stay cable between the anchor point and the external damper 1, and the tuned mass damper 2 selects a damper that can meet the wide-frequency control effect within a certain range, which meets the vibration damping requirements of three-order front and after frequencies around the stationary point of the super-long stay cable, and adopts certain measures to attach the damper to the stay cable. In addition, the tuned mass damper 2 is easy to install, and the combined use of the two dampers can effectively control the stay cable in the full frequency range, thereby solving the problem of damping the vibration of the super-long stay cable. Besides, the present invention is also suitable for the vibration damping requirements of the rod-type structure, such as long suspension cables of suspension bridges and long suspension rods of arch bridges. On the basis of the external damper installed on the stay cable, the multiple tuned mass damper is installed, through the combination of two dampers, the effect of high-frequency vibration control of the stay cable is achieved. The installation position of the multiple tuned mass damper is away from the vibration stationary point of the stay cable. It can solve the problem that the external damper of the stay cable has limited control effect on the high-order vibration of the stay cable, and the high-frequency vibration is easy to cause the damage of the connector of stay cable damper and the loosening of bolts. Therefore, providing tuned mass damper to control the high-order vibration of the stay cable can effectively protect the external damper of the stay cable and achieve good vibration damping effect. The present invention can be suitable for the control of wind-induced vibration and parametric vibration of the stay cable, and same for the vibration control of the rob-type structure, such as suspension cables of suspension bridges and suspension rods of arch bridges. Taking vibration damping control of an super-long stay cable of a large-span cable stay bridge as an example, which has the cable length of 540.9 m, the outer diameter of the stay cable of 0.2 m, the cable force of 6774 kN, the cable weight of 100.8 kg/m per meter, the total cable weight of 54.52 tons, and the inclination angle of 25.39°, the fundamental frequency of the stay cable is calculated to be fl=0.24 Hz, and the installation position ratio of the external damper of the stay cable is ll/L=2.5%, so the vibration order of the stay cable at the stationary point is n=1/2.5%/=40, the vibration frequency fn=40x0.24=9.6 Hz, so the TMD control frequency range is (9.6-3*0.24, 9.6+3*0.24) = (8.88, 10.32) Hz, so the TMD design fundamental frequencies are 8.88 Hz and 10.32 Hz respectively. The 40-order modal mass of the stay cable is 0.5*54.52 tons = 27.26 tons. According to the regulations, the required damping ratio for stay cable vibration control is 3%, and the mass ratio of TMD is 1%o through optimization calculation, so the total mass of the mass blocks is 27.26 kg, and the mass of a single mass block is 13.63 kg. According to the quality and control frequency of a single mass block, the type of the steel strand can be selected, so as to determine the diameter and length of the steel strand. The mass block and the clamp proposed in the embodiment are both made of zinc-aluminum alloy material, and the mass block and the clamp are directly cast on the steel strand. In the description of the present application, it should be noted that the orientation or positional relationship indicated by the terms "upper", "lower", etc. are based on the orientation or positional relationship shown in the drawings, which is only for the convenience of describing the present application and simplifying the description, instead of indicating or implying that the pointed device or element must have a specific orientation, be configured and operated in a specific orientation, therefore it cannot be understood as a limitation of the present application. Unless otherwise clearly specified and limited, the terms "installation", "connected" and "connection" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; further can be a mechanical connection, or an electrical connection; further can be directly connected, or indirectly connected through an intermediate medium, or can be the internal communication between two components. For those of ordinary skill in the art, the specific meanings of the above-mentioned terms in the present application can be understood according to specific circumstances. It should be noted that relational terms such as "first" and "second" are only for distinguishing one entity or operation from another entity or operation in the present application, 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 comprising a series of elements not only comprises those elements, but also comprises those that are not explicitly listed, or further comprises elements inherent to the process, method, article, or device. If there are no more restrictions, the elements defined by the sentence "comprising a..." does not exclude the existence of other same elements in the process, method, article, or device comprising the elements. The above-mentioned are only the embodiments of the present application, so that those skilled in the art can understand or implement the present application. For those skilled in the art, various modifications to these embodiments will be obvious, 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 in this document, but will be subject to the widest scope consistent with the principles and novel features applied herein.

Claims

1. A stay cable combined vibration damping device, comprising: an external damper (1), which comprises: -a damper cable clamp (11), which is configured to clamp at a set position of a stay cable (3), -a dowel bar (12), one end of which is connected to the damper cable clamp (11), -a damper (13), which is installed on a bridge deck (4) and connected to the other end of the dowel bar (12); and a tuned mass damper (2), which is installed on the stay cable (3) between an anchor point and the external damper (1).

2. A stay cable combined vibration damping method using the stay cable combined vibration damping device according to claim 1, comprising the following steps: determining fundamental vibrational frequency of the stay cable (3) according to parameters of the stay cable (3); determining installation position of the external damper (1) according to vibration damping design requirements of the stay cable (3); determining vibration stationary point frequency of the stay cable (3) at the installation position of the external damper (1) according to the fundamental vibrational frequency of the stay cable (3) and the installation position of the external damper (1); determining control frequency of the tuned mass damper (2) to be installed according to the vibration stationary point frequency of the stay cable (3) at the installation position of the external damper (1); and installing the external damper (1) according to the installation position of the external damper (1), and installing the tuned mass damper (2) on the stay cable between the anchor point and the external damper (1).

3. The stay cable combined vibration damping method according to claim 2, wherein determining the vibration stationary point frequency of the stay cable (3) at the installation position of the external damper (1) according to the fundamental vibrational frequency of the stay cable (3) and the installation position of the external damper (1), specifically comprising: determining an installation position ratio n of the external damper according to the formula n= L ; and 11 determining the vibration stationary point frequency f, of the stay cable at the installation position according to the formula f f= nn T 2 L m; wherein li is the distance from the anchor point of the stay cable to the external damper, L is the length of the stay cable, T is the tensioning force of the stay cable, and m is the linear density of the stay cable.

4. The stay cable combined vibration damping method according to claim 2, wherein determining control frequency of the tuned mass damper (2) to be installed according to the stationary point frequency of the stay cable (3) at the installation position of the external damper (1), specifically comprising: determining control frequency range of the tuned mass damper (2) according to the vibration stationary point frequency of the stay cable (3) at the installation position of the external damper (1); and determining the control frequency of the tuned mass damper (2) to be installed according to the control frequency range of the tuned mass damper (2).

5. The stay cable combined vibration damping method according to claim 4, wherein the tuned mass damper (2) adopts a multiple tuned mass damper with steel strands and two mass blocks, the control frequency of the tuned mass damper (2) is determined according to the formulas If= = - and 2T MLE 2L m 1 3EI _n+3 T 2 M2 L2 2L m wherein f is the first control frequency of the tuned mass damper (2), 2f 'is the second control frequency of the tuned mass damper (2), E is elastic modulus of the steel strand, Iis flexural stiffness of the steel strand, M is the mass of the first mass block, LI is the distance from the first mass block to the cable clamp, M 2 is the mass of the second mass block, L 2 is the distance from the second mass block to the cable clamp, and L 2 is smaller than LI, when installing, the second mass block is located above.