CN111796611A - Control method for multi-mode vibration of inhaul cable - Google Patents
Control method for multi-mode vibration of inhaul cable Download PDFInfo
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- CN111796611A CN111796611A CN202010691140.3A CN202010691140A CN111796611A CN 111796611 A CN111796611 A CN 111796611A CN 202010691140 A CN202010691140 A CN 202010691140A CN 111796611 A CN111796611 A CN 111796611A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D19/00—Control of mechanical oscillations, e.g. of amplitude, of frequency, of phase
- G05D19/02—Control of mechanical oscillations, e.g. of amplitude, of frequency, of phase characterised by the use of electric means
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- E—FIXED CONSTRUCTIONS
- E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
- E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
- E01D11/00—Suspension or cable-stayed bridges
- E01D11/04—Cable-stayed bridges
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- E—FIXED CONSTRUCTIONS
- E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
- E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
- E01D19/00—Structural or constructional details of bridges
- E01D19/16—Suspension cables; Cable clamps for suspension cables ; Pre- or post-stressed cables
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Abstract
The invention provides a damper and Tuned Mass Damper (TMD) combination scheme for comprehensively controlling low-order wind and rain vibration and high-order vortex vibration of a stay cable and an optimization design method thereof. The method comprises the following steps: designing the position and parameters of the damper according to the additional damping requirement of the modal vibration with the cable frequency below 3.0 Hz; determining a mode in which high-order vortex-induced vibration of the cable is easy to occur according to the position of the damper, wherein the damper is close to a stagnation point of vibration when the cable vibrates in the same type; and determining the installation position and parameters of the TMD according to the mode which is easy to generate the high-order vortex vibration. The method is beneficial to eliminating the hidden danger of high-order vortex vibration of a common inhaul cable-damper system, and TMD has no influence on the optimization parameters and the vibration reduction effect of the damper. The TMD installation position is close to the cable end damper, the installation, maintenance and replacement are convenient, and the method is suitable for vibration treatment of the newly built structural cable and the existing structural cable.
Description
Technical Field
The invention belongs to the field of cable structures, and relates to a vibration control technology of a cable structure, in particular to a multi-mode vibration control technology of a cable-stayed bridge.
Background
The guy cable has the characteristics of light weight, large axial bearing capacity and high rigidity, so that the guy cable is widely applied to the field of structural engineering, including a cable-stayed bridge, a suspension bridge, a suspender arch bridge, a mast tower structure anchored by a cable and the like. Taking a typical cable-stayed bridge as an example, it is widely constructed worldwide, especially in china, due to its aesthetic and economic advantages. In 2019, the built cable-stayed bridge with more than 500 m span in the world has 55 seats, and China has 36 seats; the span cable-stayed bridge with more than 500 meters under construction has 47 seats, and China has 38 seats.
Vibration control of cable stayed bridge cables is one of the problems that must be solved when constructing such bridges. The stay cable vibrates mainly because of small transverse rigidity, low fundamental frequency and low self damping, and the stay cable vibrates in multiple mechanisms and modes under the excitation of external wind, rain and the like. According to different vibration mechanisms, cable vibration can be divided into wind and rain vibration, vortex-induced vibration, parameter vibration and the like. The long-term vibration of the stay cable easily causes the fatigue problem of the stay cable, and if the stay cable is light, a small amount of the stay cable is damaged locally, and if the stay cable is heavy, the whole structure of the bridge is damaged; meanwhile, the vibration of the inhaul cable easily causes public panic, and the social influence is large.
In order to control the vibration of the cable, a number of measures have been applied in practical engineering, which mainly include: (1) the pneumatic appearance of the inhaul cable is changed; (2) installing a mechanical damper at the cable end; (3) and adopting vibration reduction measures such as connecting an auxiliary cable with an adjacent inhaul cable. Practice proves that the method for installing the damper at the cable end can effectively control the vibration of various different types of inhaul cables and has the characteristic of broad spectrum. The cable end damper is relatively convenient to install, maintain and replace, and therefore, the cable end damper is widely applied to engineering.
The design of the existing cable end damper usually aims at the first few orders of modes (usually the modes with cable vibration frequency within the range of 0-3 Hz), and the design method is feasible for controlling the most frequently occurring cable wind and rain vibration. However, when the stay cable generates some high-order vibrations, the damper is located at the modal shape stagnation point to cause the reduction, even failure, of the vibration reduction effect, and as the length of the stay cable increases and the installation height of the damper increases, the stay cable often generates obvious high-order vortex-induced vibrations in the actual engineering. Effectively controlling the high-order vortex-induced vibration of the stay cable becomes an urgent practical need.
For the problem that the inhaul cable high-order vibration occurs because the damper is positioned at the modal vibration mode node, corresponding control measures are still lacked at home and abroad. At present, the general inhaul cable vortex-induced vibration is most often subjected to an aerodynamic method, namely the pneumatic shape of the inhaul cable is changed. The actual measurement result shows that the method has poor control effect on the inhaul cable high-order vortex vibration, and the method has the problem of difficult installation on the bridge in the operation stage. In addition, a method for controlling the stay cable high-order vortex vibration damper is installed at the tower end, and the problems of difficult installation and maintenance and the like exist; the addition of a damper at the beam end affects the optimal parameters and damping effect of the damper. Therefore, an effective and feasible high-order vortex vibration control method is urgently needed to realize multi-mode control of low-order wind and rain vibration and high-order vortex vibration of the stay cable.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, an object of the present invention is to provide a method for controlling multi-modal vibration of a cable, which can be implemented directly in design, and can also perform cable vibration treatment on the existing cable structure, and has the advantages of convenience and economy.
In order to achieve the purpose, the invention adopts the technical scheme that:
a control method for multi-mode vibration of a stay cable is characterized in that a damper and a tuned mass damper are adopted for combined control, the damper aims at a mode that the stay cable is prone to wind and rain vibration, and the tuned mass damper aims at a high-order mode that the stay cable is prone to vortex-induced vibration.
Further, the position and parameters of the damper are optimally designed according to the low-order mode of the cable, and the first 5-order mode or the mode with the cable vibration frequency below 3.0Hz is considered.
The higher order modes of the cable for which the TMD is aimed are determined by the installation location of the damper, and the TMD may be installed inside or outside the damper, preferably outside the damper.
The frequency of the TMD is determined according to the frequency of the targeted cable high-order mode.
The mass, stiffness and damping parameters of the TMD are determined optimally for a cable-damper system.
The TMD has less influence on the damper, and the optimization of the damper is not influenced by the installation of the TMD.
The influence of the cable sag effect on the optimization parameters and the damping effect of the damper is considered; the TMD is optimally designed aiming at a high-order mode, and the sag does not influence the vibration suppression effect of the TMD.
The method comprises the following steps: designing the position and parameters of the damper according to the additional damping requirement of the modal vibration with the cable frequency below 3.0 Hz; determining a mode in which high-order vortex-induced vibration of the cable is easy to occur according to the position of the damper, wherein the damper is close to a stagnation point of vibration when the cable vibrates in the same type; and determining the installation position and parameters of the tuned mass damper according to the mode which is easy to generate the high-order vortex vibration.
Further, the damper-TMD combination method for realizing multi-mode vibration control of the stay cable comprises the following steps:
the method comprises the following steps: according to the parameters of the cable, the cable frequency is calculated to determine the modal order to be controlled, and the modal order is generally the modal with the cable vibration frequency below 3 Hz. And optimizing damping parameters of the damper and determining the installation position of the damper by taking the requirement of restraining wind and rain vibration of the stay cable as a target.
Step two: after the installation position of the damper is determined, the method adopts1The distance from the damper to the adjacent cable end is shown and the cable length is indicated by L. Considering the position of the damper close to the vibration mode node when the inhaul cable generates high-order vortex vibration, the order n of the mode of the order is approximately equal to L/L1(taking the nearest integer). Optimally TMD is mounted at a distance damper l1At/2, it can be installed inside or outside the damper, preferably outside the damper. And (3) carrying out optimization design of the TMD aiming at the nth-order modal vibration of the inhaul cable, namely determining the installation quality, the rigidity and the damping parameters of the TMD so as to meet the damping requirement of vortex vibration control.
Due to the adoption of the technical scheme, the beneficial effects obtained by the invention at least comprise:
1) aiming at the multi-mode vibration problem of cable low-order wind and rain vibration and high-order vortex vibration, the damper and the TMD are adopted to work cooperatively, the multi-mode vibration control of the stay cable is realized, and the defect of the conventional cable-damper system on the control effect of the stay cable high-order vortex vibration is particularly overcome.
2) The damper and the TMD are both arranged near the beam end of the inhaul cable, and the installation, maintenance and replacement are convenient. Particularly, the method has great advantages for the condition that the bridge inhaul cable generates high-order vortex vibration in the operation stage.
3) The TMD mounts the damper outboard and for the guy high order design, it has little effect on the damper, i.e., the TMD does not cause a loss of damper contribution at low order modes.
4) Optimally, the TMD is arranged at the outer side of the damper, and the TMD can more efficiently control high-order vortex vibration, and the damping effect of the TMD on the high order is not limited by the damper.
Drawings
Fig. 1 is a schematic view of the technical scheme of the invention, wherein 1 is a guy cable, 2 is a damper, and 3 is a TMD.
FIG. 2 is a schematic diagram of an analytical model of the Sleeper-damper-TMD system of the present invention.
FIG. 3 is a flow chart of the optimal design method of the present invention.
Fig. 4 is a diagram of the multi-step modal additional damping effect of the implemented rear stay.
FIG. 5a is a graph of the relationship between the damping of the 36 th order vibrational mode and the TMD damping coefficient of the system.
FIG. 5b is a plot of a cable multimode damping with damper only installed versus TMD and damper installed simultaneously.
Detailed Description
The invention will be further described with reference to examples of embodiments shown in the drawings.
As shown in fig. 1, the present invention firstly provides a damper and TMD combined control method, which is optimized for multi-modal vibration of a cable. Firstly, a cable-damper-TMD system analysis model is established by considering sag effect, and a system complex characteristic frequency equation is obtained.
The cable-viscous damper-TMD system with sag is shown in fig. 2. The inhaul cable is horizontally placed, the chord length is L, the horizontal tension is H, the mass per unit length is m, and the axial rigidity is EA. The damper with damping coefficient of c is arranged at the anchoring end l of the left cable1At the location.
Stiffness, damping and mass of TMD are respectively kd、cd、mdDenotes ωdIs the TMD natural vibration circle frequency, and xi is the TMD damping ratio. TMD has the stiffness and damping parameters
cd＝2mdωdξ. TMD is installed at anchoring end l on the right side of the pitch cable3At the location. High-order vortex vibration of the stay cable-damper system often occurs in the long cable, and the bending rigidity of the concerned long cable is negligible. Defining a frequency ratio
Defining fundamental frequency when the guy cable is not provided with a damper and TMD, and omega is frequency of the guy cable-damper-TMD system
Obtaining a complex frequency characteristic equation of the inhaul cable-damper-TMD system through theoretical derivation
Θ+2Ξ1ξ1+2Ξ2ξ2+4Λξ1ξ2In the formula (0) (1),
wherein the content of the first and second substances,
is a complex wave number, alpha is an intermediate variable, lambda2And characterizing the cable sag for an Irvine parameter. The complex nonlinear equation (1) is solved by a numerical method, and the complex frequency omega of the nth-order mode of the system can be obtainednAnd corresponding complex wave number betan. Further, the cable modal damping ratio ζ can be obtained from the formula (2)n,
FIG. 3 is a flow chart of the present invention, which comprises the following steps:
firstly, determining the order of controlling the inhaul cable by the damper according to the parameters of the inhaul cable, and recording the order as 1 st order to Nth order; xi (xi)2When the damper is mounted only on the cable, a modal damping curve is obtained by using the equations (1) and (2) as 0. After the installation position of the damper is given, the abscissa corresponding to the intersection point of the 1 st order modal damping curve and the Nth order modal damping curve of the inhaul cable is the damping parameter of the optimized damper, and the corresponding ordinate is the minimum value of the N-order modal damping before the inhaul cable is under the damping parameter. And continuously optimizing the installation position of the damper to ensure that the minimum value of the front N-order modal damping meets the requirement value of inhaul cable vibration reduction, and further obtaining the final optimized damping parameter and installation position of the damper.
Secondly, optimizing the installation position of the damper according to the first step (keeping the distance between the position and the adjacent anchoring point as l)1) Further, the modal order of the inhaul cable high-order vortex vibration which is easy to appear is n ≈ L/L1(the most similar integer is taken), and the frequency f corresponding to the nth order of the inhaul cable can be calculated according to the frequency fn(ii) a Considering the damper's restriction on the damping effect of the TMD, the TMD is preferentially installed outside the damper; mounting the TMD at a greater amplitude contributes to an increase in its damping contribution, and optimally, mounting the TMD at a distance l from the damper1At the/2 position. Further, TMD parameter optimization is performed: considering that the mass of the TMD is smaller than that of the stay cable modal mass, the optimal frequency of the TMD can be fTMD＝fn. Drafting the practical mass of TMD, dampingAnd (3) substituting the device parameters, the TMD mass and the rigidity coefficient into formulas (1) and (2) to optimize the damping coefficient of the TMD, and verifying whether the vortex vibration order modal damping meets the requirement of controlling vortex vibration. If not, adjusting the TMD quality, and then optimizing the TMD damping until meeting the requirements.
A typical case is used to verify the effectiveness of the method of the present invention.
The first step is as follows: and determining the parameters of the guy cable. The cable parameters in this example are shown in table 1.
TABLE 1 Cable parameters
| Cable length (m) | Rice weight (kg/m) | Cable force (kN) | Cross sectional area (mm)2) | Elastic model (GPa) | Inclination angle (°) | Sag parameter |
| 547 | 91 | 6241 | 151 | 200 | 23 | 1.97 |
The second step is that: parameters of the damper are determined. The embodiment adopts a viscous damper to design aiming at the low-order vibration mode of the stay cable. The design requires that the damper performs parameter optimization on the front five-order vibration of the cable, namely the damping ratio of the front five-order mode is not less than 0.48% (the corresponding logarithmic attenuation rate is not less than 3%); the efficiency coefficient of the damper was taken to be 50%, assuming a damping ratio of 0.032% when the damper was not installed. Xi (xi)2The calculation of the modal damping of the cable-damper system is performed using equation (2) at 0 (without considering the influence of the TMD). The abscissa corresponding to the intersection point of the 1 st order modal damping curve and the 5 th order modal damping curve of the inhaul cable is an optimized damping parameter of the damper, and the corresponding ordinate is the minimum value of the front 5 th order modal damping of the inhaul cable under the damping parameter. And continuously optimizing the installation position of the damper to ensure that the minimum value of the first 5-order modal damping meets the damping ratio of not less than 0.48 percent. Under the aim, the minimum installation height of the damper is optimally determined to be l12.8%, the damping coefficient is 140kn.s/m, as shown in fig. 4.
The third step: the higher order modes that need to be controlled are determined. Depending on the position of the damper, i.e. the overall length of the cable in this example12.8 percent of/L; it can be obtained that the mode order of the cable, in which high-order vortex-induced vibrations tend to occur, is the 36 th (1/2.8% rounded) order.
The fourth step: parameters and control effects of the TMD are determined. The TMD is designed for high-order vortex vibration such that the vortex vibration order modal damping ratio is not less than 0.32% (i.e., the logarithmic decrement is not less than 2%). The efficiency coefficient of the damper is taken to be 50%. The mounting position of TMD is selected as2and/L is 1.4 percent. Considering that the mass of TMD is not too large, 25kg is selected for calculation in this example. The characteristic frequency of TMD is defined as fd＝f36. Inputting the optimized damping parameters of the damper and the characteristic frequency and the quality of the TMD by using the formula (2), and analyzing to obtain the relation between the damping of the 36 th order vibration of the system and the damping coefficient of the TMD, as shown in FIG. 5 a; from the curve in fig. 5a, the optimal TMD damping coefficient ξ is 0.04.
The fifth step: and (4) checking the multi-stage damping effect of the cable-damper-TMD system. And (3) calculating the damping effect of each step of the guy cable after TMD installation by using the formula (1). FIG. 5b shows the multi-modal damping of the cable with dampers only and dampers and TMD installed simultaneously. The combined method of installing the damper and the TMD can be seen from the figure, so that the modal damping of the cable vortex vibration order is effectively improved, the design requirement is met, the modal damping of the front orders of the cable is not adversely affected, and the requirement of cable wind and rain vibration suppression is met.
The method is beneficial to eliminating the hidden danger of high-order vortex vibration of a common inhaul cable-damper system, and TMD has no influence on the optimization parameters and the vibration reduction effect of the damper. The TMD installation position is close to the cable end damper, the installation, maintenance and replacement are convenient, and the method is suitable for vibration treatment of the newly built structural cable and the existing structural cable.
The embodiments described above are intended to facilitate one of ordinary skill in the art in understanding and using the present invention. It will be readily apparent to those skilled in the art that various modifications to these embodiments may be made, and the generic principles described herein may be applied to other embodiments without the use of the inventive faculty. Therefore, the present invention is not limited to the above embodiments, and those skilled in the art should make improvements and modifications within the scope of the present invention based on the disclosure of the present invention.
Claims (11)
1. A control method for multi-mode vibration of a guy cable is characterized by comprising the following steps: the combined control of the damper and the tuned mass damper is adopted, the damper aims at the mode that the cable is easy to generate wind and rain vibration, and the tuned mass damper aims at the high-order mode that the cable is easy to generate vortex-induced vibration.
2. The control method of the multi-modal vibration of the stay cable according to claim 1, characterized in that: and the position and the parameters of the damper are optimally designed according to the low-order mode of the cable.
3. The control method of the multi-modal vibration of the inhaul cable according to claim 2, characterized in that: the low-order mode is the first 5-order mode or the mode with the cable vibration frequency below 3.0 Hz.
4. The control method of the multi-modal vibration of the stay cable according to claim 1, characterized in that: the tuning mass damper is used for tuning the high-order mode of the cable according to the installation position of the damper.
5. The control method of the multi-modal vibration of the stay cable according to claim 1, characterized in that: the tuned mass damper may be mounted either inside or outside the damper.
6. The control method of the multi-modal vibration of the stay cable according to claim 1, characterized in that: and the frequency of the tuned mass damper is determined according to the frequency of the targeted cable high-order mode.
7. The control method of the multi-modal vibration of the stay cable according to claim 1, characterized in that: the mass, stiffness and damping of the tuned mass damper are determined by optimization for a cable-damper system.
8. The control method of the multi-modal vibration of the stay cable according to claim 1, characterized in that: the design considers the influence of the cable sag effect on the optimization parameters and the damping effect of the damper.
9. The control method for the multi-mode vibration of the stay cable according to claim 1, characterized by comprising the following steps of: designing the position and parameters of the damper according to the additional damping requirement of the modal vibration with the cable frequency below 3.0Hz or the first five-order modal vibration; determining a mode in which high-order vortex-induced vibration of the cable is easy to occur according to the position of the damper, wherein the damper is close to a stagnation point of vibration when the cable vibrates in the same type; and determining the installation position and parameters of the tuned mass damper according to the mode which is easy to generate the high-order vortex vibration.
10. The control method for multi-modal vibration of the stay cable according to claim 1, characterized by comprising:
the method comprises the following steps: calculating the cable frequency according to the cable parameters to determine the modal order to be controlled; optimizing damping parameters of the damper and determining the installation position of the damper by taking the damping requirement for inhibiting wind and rain vibration of the stay cable as a target;
step two: after the installation position of the damper is determined, the method adopts1The distance from the damper to the adjacent cable end is represented, and the length of the cable is represented by L; considering the position of the damper close to the vibration mode node when the inhaul cable generates high-order vortex vibration, the order n of the mode of the order is approximately equal to L/L1Taking the nearest integer; and optimally designing the tuned mass damper aiming at nth order modal vibration of the inhaul cable, and determining the installation mass, the rigidity and the damping parameters of the tuned mass damper so as to meet the damping requirement of vortex vibration control.
11. The control method of the multi-modal vibration of the inhaul cable according to claim 10, wherein: the tuned mass damper is mounted at a distance damper l1And/2, mounted on the outside of the damper.
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| CN116577996A (en) * | 2023-07-06 | 2023-08-11 | 华南理工大学 | Movable active control method for vibration of flexible civil structure |
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| CN116577996B (en) * | 2023-07-06 | 2023-10-20 | 华南理工大学 | Movable active control method for vibration of flexible civil structure |
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