CN103952974A - Wind-induced vibration suppression structure of square chamfered bridge tower - Google Patents
Wind-induced vibration suppression structure of square chamfered bridge tower Download PDFInfo
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Abstract
The invention discloses a wind-induced vibration suppression structure of a square chamfered bridge tower. The wind-induced vibration suppression structure disclosed by the invention has the advantage that the galloping safety of the square chamfered bridge tower can be effectively improved. The wind-induced vibration suppression structure comprises the square chamfered bridge tower (10), wherein the square chamfered bridge tower (10) is provided with four chamfering surfaces (11) at corners, the chamfering surfaces (11) are fixedly provided with flow guiding wing plates (20) of which the cross sections are rectangular, and the flow guiding wing plates (20) are vertical to the chamfering surfaces (11) and stretch along vertical central lines of the chamfering surfaces (11).
Description
Technical field
Bridge of the present invention, particularly the square bridge tower wind-induced vibration of a kind of chamfering suppresses structure.
Background technology
Bridge tower is the important component part of bridge, highly can enlarge markedly along with the increase of spanning.For the bridge tower structure in Loads of Long-span Bridges, more blunt when its section form, structure is more soft, and quality is light, when damping is low, under natural wind effect, will easily occur galloping problem.Galloping is one of the wind vibrational of 4 kinds of Main Morphologies of bridge, and other 3 kinds are respectively flutter, buffeting and vortex-induced vibration.Wherein galloping and flutter are all the self-excited vibration with diversity, for example, and galloping mainly occurs in elongated flexible structure (bridge tower), that a kind of beam wind of producing because of air-flow self-priming effect is to significantly vibration, this vibration is found in icing electric wire at first, the ripple of vibrational excitation transmits fast between two electric poles, amplitude can reach 10 times of the diameter of wire, just as flying horse benz, is therefore called galloping.Because galloping and flutter are similar, vibration all has emissivity, and destruction is large, so once occur to cause serious catastrophic effect.Famous old Tacoma suspension bridge (the Old Tacoma Narrows Bridge) wind that for example occurs in the U.S. for 1940 is ruined accident, be exactly that a kind of typical full-bridge by the unstable initiation of flutter destroys disaster, similarly, if there is galloping in bridge tower, also likely cause the destruction of full tower, and then affect the safety of whole bridge.Therefore in Longspan Bridge design, be necessary the galloping problem of its bridge tower paid attention to and study, and for the poor bridge tower structure of galloping stability, find out effective, economic damping measure and have very important significance.
The engineering measure that suppresses bridge wind-induced vibration (comprising bridge tower galloping) can be divided into mechanical measure and aerodynamic countermeasure.Mechanical measure is mainly to improve bridge construction damping by composed of external damping device, thereby reach the object that reduces and suppress wind-induced vibration, gulf, Tokyo rainbow bridge just passes through mechanical measure in bridge tower climbing-form construction---HMD(Hybrid Mass Damper) and damper, the wind-induced vibration that has effectively suppressed bridge tower, but the shortcoming of mechanical measure is to need to safeguard and increase extra engineering cost; Aerodynamic countermeasure is by the profile of appropriate change bridge, to arrange or add some guiding devices to improve flow around body, thereby reach the object that suppresses wind-induced vibration, aerodynamic countermeasure can be eliminated driving source, there is reliable operation, do not need to safeguard, expense is low, the wind of real bridge shake control in application very extensive.
Wind tunnel test be research greatly across very important and irreplaceable means of, tall and slender structure aerodynamic performance, wind tunnel test mainly comprises full-bridge aeroelastic model test (being exactly full tower aerodynamic model test for bridge tower), Segment Model test and tie rod model testing.Comparatively speaking, aerodynamic model test and Segment Model developing test more ripe, study more, application also wider.
For the galloping research of bridge tower, carry out Quan Taqi bullet model wind tunnel test and can directly record the wind vibrational response condition of bridge tower, just can easily directly judge the galloping stability of this bridge tower: if do not observe bridge tower vibration Divergent Phenomenon, illustrate this bridge tower in test wind speeds are in galloping stable state, can there is not galloping; If the beam wind of obviously observing bridge tower is to oscillation phenomenon significantly, and amplitude can increase and increase rapidly with wind speed, just can think that this bridge tower has entered vibration divergent state, and galloping has occurred, and can directly determine the critical wind velocity that bridge tower enters divergent state, i.e. galloping critical wind velocity.But there is any to merit attention, for guaranteeing the similar of the quiet power behavior of bridge tower model structure and prototype (being actual bridge tower), in the design of Quan Taqi bullet model, except needing, meeting geometric profile similar, also should to meet the uniformity of elastic parameter, inertial parameter, weight parameter, sticky parameter and damping parameter and actual bridge tower.
By the slow test of Segment Model, and utilize classical Den Hartog(Deng Hatuo) certainly Chang Chizhen theory can further investigate the galloping performance of bridge tower equally, but Segment Model must meet the similar of profile and prototype in design, and model geometric scaling factor should not be less than 1:100, guarantee Segment Model Static Test Results and prototype consistent.According to the force balance device in wind-tunnel, can record bridge tower Segment Model suffered mean resistance F under system of wind axes
dwith average lift F
l, just can calculate the resistance coefficient C of bridge tower under system of wind axes according to following formula
dwith lift coefficient C
l:
In formula: l representative model length; The width of B representative model windward side; V represents incoming flow wind speed, is provided with special measuring wind speed instrument in wind-tunnel; ρ represents the density of air.According to Den Hartog galloping mechanism, the galloping stability of bridge tower can be judged by following formula:
Wherein, s is called galloping force coefficient.If s >=0, bridge tower, in stable state, there will not be galloping unstable phenomenon; If s < 0, may there is galloping in bridge tower, and now, according to Chang Chizhen theory certainly, can derive the critical wind velocity that bridge tower is about to enter galloping divergent state:
In formula, m represents bridge tower linear mass; ζ is that bridge tower beam wind is to the damping ratio of vibration; ω is the circular frequency of bridge tower vibration; ρ, B meaning are the same, represent respectively atmospheric density and bridge tower windward side width; S is galloping force coefficient.By bridge tower galloping critical wind velocity v
crexpression formula can find out: negative s less (absolute value that is s is larger), bridge tower galloping critical wind velocity v
crvalue also less, the possibility that galloping occurs is also just larger, i.e. bridge tower galloping stability is poorer; Otherwise, negative s larger (absolute value that is s is less), bridge tower galloping stability is better, and (this is also very easy to understand, consider ultimate limit state: if negative s increases gradually, until increase to, be no longer less than 0, according to Den Hartog criterion, no longer may there is galloping in bridge tower now, and galloping stability is also just best certainly).
With only pillar bridge tower of the square sectional form of chamfering, there is the advantages such as good looking appearance, structure are slim and graceful, easy construction, application to some extent in actual bridge, but the galloping critical wind velocity of the square bridge tower of chamfering is lower, has serious galloping safety issue.Take across footpath, be arranged as 152.4m+304.8m+152.4m (by foot unit conversion) certain at the two rope faces three of a double tower of building, across steel box girder stayed-cable bridge, be abroad example, its both sides bridge tower is only pole structure of chamfering square-section.Wherein be positioned at the bridge tower overall height 157.3m (516 feet) in west side, upper king-post strut is 18 feet * 18 feet of prismatic 5.5m * 5.5m(), bevel edge length of side 0.3m(1 foot wherein); Middle king-post is changed to Ta Liang land from bottom, anchor-hold district linearity, is of a size of 6.4 * 6.4m(21 foot * 21 foot), chamfering length of side 1.2m(4 foot); Then linear change, to tower basal cross section, is of a size of 9.3 * 9.3m(30.5 foot * 30.5 foot), chamfering length of side 4.1m(13.5 foot).By carrying out the full tower aeroelastic model wind tunnel test of west side bridge tower, find that the galloping critical wind velocity of this bridge tower only has 30m/s in 0.5% structural damping ratio situation, this wind speed is not too high, sometimes can meet by land.And take the Section model wind tunnel test that west side bridge tower upper king-post strut typical section is prototype, same further to confirm that the galloping force coefficient s value of bridge tower under some wind angle shows as negative, illustrate that bridge tower has the possibility of generation galloping unstability at these wind angle places; And the s value of bridge tower minimum has reached-6.5, compare with some easy s values that galloping structure occurs of listing in < < highway bridge wind force proofing design standard > >, the s(-6.5 of the square bridge tower of chamfering) also calculated and done very little numerical value, be in close proximity in the normal s value that the H type cross section structure of galloping can occur under wind speed of meeting.In a word, do not add the square bridge tower galloping of the chamfering stability extreme difference of any engineering measure, have serious galloping safety problem.
Summary of the invention
Technical problem to be solved by this invention is to provide the square bridge tower wind-induced vibration of a kind of chamfering and suppresses structure, effectively to improve the galloping safety of the square bridge tower of chamfering.
The technical solution adopted for the present invention to solve the technical problems is as follows:
The square bridge tower wind-induced vibration of a kind of chamfering of the present invention suppresses structure, comprise the square bridge tower of chamfering with four bight fillet surfaces, feature is: described fillet surface is installed with the rectangular wing plate of cross section, and guide vanes is perpendicular to fillet surface, and extends along the vertical center line of fillet surface.
The invention has the beneficial effects as follows, can significantly improve the galloping critical wind velocity of the square bridge tower of chamfering, increase bridge tower at galloping unsteady wind to the galloping force coefficient value between angular region, can effectively improve the galloping safety of the square bridge tower of chamfering, and then the safety that has improved bridge construction; Simple in structure, be easy to construction
Accompanying drawing explanation
Fig. 1 is the sectional schematic diagram that the square bridge tower wind-induced vibration of a kind of chamfering of the present invention suppresses structure;
Fig. 2 is the plan view (part) that the square bridge tower wind-induced vibration of a kind of chamfering of the present invention suppresses guide vanes in structure;
Fig. 3 a-Fig. 3 e is that abroad certain is building large general arrangement and typical section dimensional drawing across cable stayed bridge west side bridge tower, wherein Fig. 3 a is the elevation of bridge tower, Fig. 3 b is the side view of bridge tower, Fig. 3 c is king-post B-B cross dimensions figure, Fig. 3 d is king-post C-C cross dimensions figure, Fig. 3 e is king-post D-D cross dimensions figure, and in figure, dimensional units is mm;
Fig. 4 is the definition schematic diagram of wind angle;
Fig. 5 is that the wind-induced vibration displacement root-mean-square value of the square bridge tower of chamfering under each wind angle that do not add any engineering measure is with the change curve of wind speed;
Fig. 6 adds the comparison diagram that the present invention constructs rear bridge tower and do not add any engineering measure bridge tower wind-induced vibration;
Fig. 7 is the change curve of the square bridge tower aerodynamic coefficient of chamfering in 0 °～45 ° wind angle intervals that does not add any engineering measure;
Fig. 8 is the change curve of the square bridge tower galloping of chamfering force coefficient in 0 °～45 ° wind angle intervals that does not add any engineering measure;
Fig. 9 adds aerodynamic coefficient that the present invention constructs rear bridge tower and the do not add any engineering measure bridge tower variation comparison diagram in-20 °～20 ° wind angle intervals;
Figure 10 adds galloping force coefficient that the present invention constructs rear bridge tower and the do not add any engineering measure bridge tower variation comparison diagram in-20 °～20 ° wind angle intervals;
Figure 11 is the variation comparison diagram of aerodynamic coefficient in-20 °～20 ° wind angle intervals that adds different ventilative rate guide vanes bridge towers;
Figure 12 is the variation comparison diagram of galloping force coefficient in-20 °～20 ° wind angle intervals that adds different ventilative rate guide vanes bridge towers.
Member shown in figure, position and corresponding mark: the square bridge tower 10 of chamfering; Fillet surface 11, width L; Guide vanes 20, width h, thickness b, through hole 21a.
The specific embodiment
Below in conjunction with drawings and Examples, the present invention is further described.
With reference to Fig. 1, the square bridge tower wind-induced vibration of chamfering suppresses structure, comprises the square bridge tower 10 of chamfering with four bight fillet surfaces 11.The rectangular wing plate of cross section 20 is installed on described fillet surface 11, and wing plate 20 is perpendicular to fillet surface 11, and extends along fillet surface 11 length directions.
Take that certain is example at the actual bridge tower of a Loads of Long-span Bridges of building below abroad, by the wind-induced vibration of aeroelastic model, test to contrast and add the present invention and construct rear bridge tower and do not add any engineering measure bridge tower wind-induced vibration situation.With reference to Fig. 3, should the main bridge of building bridge be the two rope faces three of a double tower across steel box girder stayed-cable bridge, across footpath, be arranged as 152.4m+304.8m+152.4m, both sides bridge tower is only pole structure of chamfering square-section.With reference to Fig. 3, be wherein positioned at the bridge tower overall height 157.3m in west side, upper king-post strut is uniform section 5.5m * 5.5m, wherein fillet surface width is 0.3m; Middle king-post is changed to Ta Liang land from bottom, anchor-hold district linearity, and sectional dimension is 6.4 * 6.4m, and fillet surface width is 1.2m; Then linear change is to tower basal cross section, and sectional dimension is 9.3 * 9.3m, and fillet surface width is 4.1m.
The above-mentioned west side bridge tower of take is prototype, has made the aeroelastic model of full tower according to the geometry scaling factor of 1:80, and in wind-tunnel, carries out the wind-induced vibration test of gas bullet model.This gas bullet model has met the condition for consistence of geometric parameter, elastic parameter, inertial parameter and weight parameter in design, so can guarantee the consistent of the quiet power behavior of model structure and prototype bridge tower.Because bridge tower section is typical bluff body, sticky parameter condition not obvious to affect its fluidised form of streaming similar, therefore loosened the condition of similarity of sticky parameter; And be to obtain the more significant wind phenomenon of shaking to have adopted less damping, the structural damping ratio of bridge tower model is adjusted to 0.5%.
Because wind angle is an important parameter that affects bridge tower galloping performance, so carried out the wind-induced vibration test of bridge tower in 0 °, 5 °, 30 °, 45 ° ,-5 ° and-15 ° of six kinds of wind angle situations.Wherein the definition of wind angle as shown in Figure 4: incoming flow wind is defined as to 0 ° of wind angle perpendicular to the bevel edge of chamfering square-section; And incoming flow wind is defined as to 45 ° of wind angles perpendicular to the right-angle side in cross section.Before test in bridge tower top layout acceleration transducer, this sensor can record the acceleration root-mean-square value of tower top wind-induced vibration, accordingly and then can extrapolate the displacement root-mean-square value of tower top wind-induced vibration under each wind speed.
Fig. 5 is that under different wind angles, tower top displacement root-mean-square value is with the situation of change of wind speed, and in figure, wind speed, displacement are all scaled to actual bridge tower by similarity criterion.Can find out that the bridge tower that do not add any engineering measure has occurred oscillating divergent phenomenon under 0 °, 5 ° and-5 ° and wind angle.Especially under the effect of 0 ° of wind angle incoming flow, tower top displacement is when the wind speed of 30m/s, just there is very precipitous growth trend (root-mean-square value of displacement has just increased to 700mm left and right by 50mm left and right in very little wind speed limit increase), and continue to increase with wind speed, the vibration of tower top is always very violent, in test wind speeds are, maximum displacement root-mean-square value can reach 900mm, and this amplitude is very large.Can think that significant galloping phenomenon has appearred in bridge tower under 0 ° of wind angle, and the critical wind velocity that enters galloping divergent state only has 30m/s, this air speed value is not very too high, sometimes can meet by land, obviously can not meet the requirement of the general wind force proofing design of structure.So do not add, the square bridge tower galloping of the chamfering of any engineering measure critical wind velocity is low, galloping poor stability, has serious galloping safety problem.
For effectively suppressing the wind-induced vibration of the square bridge tower of chamfering, improve bridge tower galloping stability.At the upper king-post strut of bridge tower, partly add wind of the present invention and shake and suppress structure, with reference to Fig. 1, on four bight fillet surfaces of upper king-post strut, the square-section guide vanes that width equates with fillet surface width, thickness is fillet surface width 1/10 is installed respectively.Then carried out adding the wind-induced vibration test of the posttectonic bridge tower of the present invention under 0 ° of the poorest wind angle of galloping stability.Result as shown in Figure 6, adds the present invention and constructs the Oscillation Amplitude of later bridge tower under the effect of 0 ° of wind angle incoming flow and be obviously inhibited: below 50m/s wind speed, substantially do not observed the significantly phenomenon of wind-induced vibration; Only have and increase to 50m/s when above when wind speed, bridge tower vibration is aggravation gradually, has the trend that enters divergent state, but that its vibration severe degree also will relax when not adding any measure is many.The galloping critical wind velocity value that shows the square bridge tower of chamfering, more than can the 30m/s when not adding any measure being promoted to and adding the posttectonic 50m/s of the present invention, this wind speed is very high, can meet the requirement of general structure wind force proofing design completely.
In a word, aeroelastic model evidence the present invention of full tower structure can effectively suppress the wind-induced vibration of the square bridge tower of chamfering, and can significantly promote the galloping critical wind velocity of bridge tower, improves bridge tower galloping safety.
For further utilizing Den Hartog certainly galloping performance and the improve effect of the present invention's structure to galloping stability of the square bridge tower of Chang Chizhen theoretical evaluation chamfering, the upper king-post strut typical section (referring to Fig. 3) of above-mentioned west side bridge tower of take is again prototype, according to the geometry scaling factor of 1:40, has made Segment Model.Consider the real size (2.4m wide * 2.0m is high) of carrying out Section model wind tunnel test section section, the length of Segment Model has been taken as to 2.0m.Bridge tower Segment Model in design, make in strict guarantee its geometric shape and prototype similar, so both aerodynamic coefficients can meet coherence request.
First with 1 ° of angle for a change step-length carried out the slow test of bridge tower Segment Model within the scope of 0 °～45 ° wind angles, wherein the definition mode of wind angle and consistent (referring to Fig. 3) in aerodynamic model test, can record bridge tower at the resistance coefficient C of each wind angle
dwith lift coefficient C
l(Fig. 7), obviously find C
lin 0 °～6 ° wind angle intervals, having a descending branch (is dC
l/ (d α) < 0), galloping force coefficient s is likely negative value.According to formula s=dC
l/ (d α)+C
dfurther make the change curve (Fig. 8) at galloping force coefficient box haul angle, find out that s is less than 0(due to C in 0 °～5 ° wind angle intervals
dimpact, s at place, 6 ° of angles for just), and at 0 ° of wind angle place, reach minimum, approximate-6.5.Illustrate that the square bridge tower of chamfering exists the possibility of galloping unstability in 0 °～5 ° wind angle intervals, and minimum at the galloping critical wind velocity at 0 ° of wind angle place.By Segment Model slow test and according to the Den Hartog theoretical income analysis result of Chang Chizhen certainly, meet completely with the experimental phenomena drawing by aeroelastic model.
If continue to install the present invention's structure on bridge tower Segment Model, on four fillet surfaces of Segment Model, add the guide vanes (with reference to Fig. 1) of square-section, and the situation during with aerodynamic model test is identical, guide vanes width is taken as to the value equating with fillet surface width and wing plate width is taken as to 1/10 of fillet surface width, then carried out adding the present invention and constructed later bridge tower Segment Model slow test.Because the galloping unsteady wind of the square bridge tower of chamfering is to concentrating between angular region near 0 ° of angle, think and more intuitively embody the impact on bridge tower aerodynamic coefficient and galloping performance of the present invention structure, for the slow test that adds the present invention and construct rear bridge tower, all in-20 °～20 ° wind angle intervals, carry out.Aerodynamic coefficient result of the test (Figure 10) shows: when not adding any engineering measure, add the posttectonic bridge tower resistance coefficient of the present invention C
dvalue becomes large, lift coefficient C
lat the downward trend of descending branch mitigation (the i.e. negative dC that obviously becomes
lit is large that the value of/(d α) becomes).According to C
d, C
lchange curve further make add the present invention construct before and after the variation comparison diagram of bridge tower galloping force coefficient s, referring to Fig. 9.Can find out, in-5 °～5 ° wind angle intervals of the square bridge tower galloping of chamfering unstable (being s < 0), add structure of the present invention and can make bridge tower s value be increased, wherein at the worst 0 ° of wind angle place of bridge tower galloping, increase trend particularly evident: s value-6.5 having increased to and add the present invention posttectonic-1.2 when not adding any measure.So according to Den Hartog galloping mechanism, the present invention's structure can effectively improve the galloping critical wind velocity of bridge tower.This confirms the present invention's structure again can play significant improvement effect to the galloping stability of the square bridge tower of chamfering.
With reference to Fig. 2, on the plate face of described guide vanes 20, be evenly equipped with through hole 21a.The gross area of described each through hole 21a is the ventilative rate of 40%～60%(with the ratio of the plate face gross area of guide vanes 20).On guide vanes in afore-mentioned test, all do not offer through hole 21a, its ventilative rate is 0%.
For the structure of guide vanes 20 in further research the present invention structure is on the square bridge tower galloping of chamfering improved stability effect with affect rule, the guide vanes 20 that is 40%, 60% by its ventilative rate is respectively arranged on rear bridge tower Segment Model, in-20 °～20 ° wind angle intervals, carry out slow test, and comparing by result of the test and while adding 0% ventilative rate wing plate above, obviously find resistance coefficient C
dvalue with the increase of the ventilative rate of wing plate, reduce; Lift coefficient C
lin the downward trend of descending branch, with ventilative rate, increase and become gradually precipitous.Only from C
d, C
lchange curve on just can be according to formula s=dC
l/ (d α)+C
dsubstantially judging s can diminish with the increase of ventilative rate, for the affect rule of the ventilative rate of wing plate on the square bridge tower galloping of chamfering stability is described more intuitively, continue to make the galloping force coefficient s comparison diagram of bridge tower after additional three kinds of ventilative rate guide vanes, as shown in figure 12.Can find out, within the wind angle interval (-5 °～5 °) of galloping unstability very easily appears in bridge tower, the obvious increase of understanding with the ventilative rate of wing plate of s value reduces, and the worst 0 ° of wind angle place of the galloping of take is example: when ventilative rate is as 0% time, s value equals-1.2; When ventilative rate is 40%, s value is reduced to-2.0; And ventilative rate is while increasing to 60%, s value is reduced to-3.2 especially; But a bit merit attention in addition, add after three kinds of ventilative rate wing plates the s value of bridge tower and all will significantly be greater than while not adding any measure-6.5.Visible, the guide vanes of three kinds of ventilative rates all can improve the square bridge tower galloping of chamfering critical wind velocity, improve the galloping stability of bridge tower, and guide vanes can weaken with the increase of the ventilative rate of wing plate the effect of improving of bridge tower galloping performance, but it is evident that, the construction costs of the present invention's structure, weight and the increase that the influence degree of original structure characteristic properties is understood equally with the ventilative rate of wing plate diminish.So, in practical engineering application, can consider above because usually choosing the ventilative rate of optimum of wing plate in the present invention's structure.
Claims (4)
1. the square bridge tower wind-induced vibration of chamfering suppresses structure, comprise the square bridge tower of chamfering (10) with four bight fillet surfaces (11), feature is: described fillet surface (11) is installed with the rectangular guide vanes of cross section (20), guide vanes (20) is perpendicular to fillet surface (11), and extends along the vertical center line of fillet surface (11).
2. the square bridge tower wind-induced vibration of a kind of chamfering as claimed in claim 1 suppresses structure, it is characterized in that: on the plate face of described guide vanes (20), be evenly equipped with through hole (21a).
3. the square bridge tower wind-induced vibration of a kind of chamfering as claimed in claim 2 suppresses structure, it is characterized in that: the ratio of the plate face gross area of the gross area of described each through hole (21a) and guide vanes (20) is 40%～60%.
4. the square bridge tower wind-induced vibration of a kind of chamfering as described in claims 1 to 3 any one suppresses structure, it is characterized in that: the width (h) of described guide vanes (20) equates with the width (L) of fillet surface (11), the thickness (b) of guide vanes (20) is 1/10 of fillet surface (11) width (L).
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| CN108221642A (en) * | 2018-01-08 | 2018-06-29 | 长安大学 | Improve the pneumatic structure of bridge H-type bluff body wind induced structural vibration performance |
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| CN104894968A (en) * | 2015-06-23 | 2015-09-09 | 东南大学 | Bridge tower for large-span bridge capable of resisting strong wind/typhoons |
| CN104894968B (en) * | 2015-06-23 | 2016-06-29 | 东南大学 | A kind of Longspan Bridge bridge tower resisting strong/typhoon |
| CN108221642A (en) * | 2018-01-08 | 2018-06-29 | 长安大学 | Improve the pneumatic structure of bridge H-type bluff body wind induced structural vibration performance |
| CN111441234A (en) * | 2020-03-27 | 2020-07-24 | 中南大学 | Deformable air nozzle for inhibiting wind-induced vibration of bridge |
| CN111441234B (en) * | 2020-03-27 | 2021-04-20 | 中南大学 | Deformable air nozzle for inhibiting wind-induced vibration of bridge |
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Application publication date: 20140730 |