CN105975730B - Multiple tuned mass damper Vibration Absorption Designing method for steel arch-gate - Google Patents
Multiple tuned mass damper Vibration Absorption Designing method for steel arch-gate Download PDFInfo
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- CN105975730B CN105975730B CN201610413784.XA CN201610413784A CN105975730B CN 105975730 B CN105975730 B CN 105975730B CN 201610413784 A CN201610413784 A CN 201610413784A CN 105975730 B CN105975730 B CN 105975730B
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Abstract
For the multiple tuned mass damper Vibration Absorption Designing method of steel arch-gate, include the following steps:(1)Dynamic characteristics is carried out to steel arch-gate using FInite Element and dynamic response is analyzed;(2)Simulation water pressure influences the dynamic characteristics of steel arch-gate;(3)Modal strain energy analysis is carried out to steel arch-gate, to determine the optimal installation sites of MTMD;(4)Multiple tuned mass damper is disposed on the support arm of steel arch-gate;(5)According to the actual loading situation of steel arch-gate, number, the frequency distribution range of multiple tuned mass damper and the damping ratio of multiple tuned mass damper of single tuning mass damper in multiple tuned mass damper are determined by optimization.The present invention on the support arm of steel arch-gate by being arranged multiple tuned mass damper, in the case of multiple tuned mass damper Rational Parameters, can effectively reduce support arm or even the response of integrally-built flow induced vibration, reach the purpose of protection agent structure.
Description
Technical field
The invention belongs to the Vibration Absorption Designing technical fields of gate in hydraulic engineering, and more particularly, to steel arch-gate is more
Tuning quality damper vibration damping design method.
Background technology
It is the product that stream swashs load and the coupling of gate dynamic characteristics that gate stream, which swashs load dynamic response,.Streams
In the case that determining, the sharp load of stream can not be changed, adjustment gate dynamic characteristics can effectively reduce structural dynamic response.Arc-shaped steel lock
It slim and graceful Men Yiqi structure type, the advantages that rational stress performance and hoisting capacity are small, is answered extensively in hydro-structure
With.But the flow induced vibration problem of steel arch-gate is more prominent, because flow induced vibration damages in hydro-structure at home and abroad
It happens occasionally.Flow induced gate vibration is determined by hydrodynamic load feature and radial gate vibration characteristic, when hydrodynamic load can not change
When, optimizing the dynamic characteristics of gate becomes unique selection.How to avoid steel-slag sand that stream occurs and swash destruction, gives full play to steel-slag sand
Advantageous feature, scientific research personnel propose different solutions.
The damage -form of gates of segmental shape is made a general survey of, is largely to cause support arm dynamic buckling since support arm generation vibration is excessive,
Or load effect is more than the strength of materials, and then destroy.Single tuning Tuned mass damper(TMD) vibration damping is only to certain first order resonance frequency
Effectiveness in vibration suppression is notable, and because steel-slag sand generally works under water, the natural frequency of vibration is influenced by water pressure, therefore TMD effectiveness in vibration suppression is poor.
Invention content
The present invention provides the multiple-tuned Tuned mass damper for steel arch-gate to solve shortcoming in the prior art
Device Vibration Absorption Designing method, to increase frequency adjustment range, is reached by the way that multiple tuned mass damper is arranged on steel arch-gate
Reduce the purpose of structural dynamic response.
In order to solve the above technical problems, the present invention adopts the following technical scheme that:Multiple-tuned quality for steel arch-gate
Damper vibration damping design method, the steel arch-gate include curved panel, two sunpenders and two support arms, after curved panel
Surface is equipped with several crossbeams along its short transverse uniform intervals, and every crossbeam is arranged along left and right horizontal direction, after curved panel
Surface is equipped with several longerons, the arc-shaped structure of every longeron and the radian phase with curved panel along its width direction uniform intervals
Together, two sunpenders are obliquely installed and are mutually parallel, and one end of two sunpenders is connect with the rear surface of curved panel respectively, Mei Gezhi
Arm includes upper cantilever and lower cantalever, and web member is equipped between upper cantilever and lower cantalever, is included the following steps:
(1)Dynamic characteristics is carried out to steel arch-gate using FInite Element and dynamic response is analyzed, curved panel selects shell
Unit simulation stress, support arm, crossbeam and longeron select beam element to simulate stress, and sunpender selects bar unit to simulate stress
State;
(2)The equivalent mass of water, dynamic characteristics of the simulation water pressure to steel arch-gate are calculated using Westergaard methods
It influences;
(3)Modal strain energy analysis is carried out to steel arch-gate, obtains the value of the support arm modal strain energy of steel arch-gate
For maximum value;
(4)Multiple tuned mass damper is disposed on the support arm of steel arch-gate, multiple tuned mass damper is by several
Single tuning mass damper composes in parallel, and the quality of each single tuning mass damper is identical with damping ratio;
(5)According to the actual loading situation of steel arch-gate, single tuning in multiple tuned mass damper is determined by optimization
Number, the frequency distribution range of multiple tuned mass damper and the damping ratio of multiple tuned mass damper of mass damper,
Optimal control results are obtained after so that steel arch-gate is passed through multiple tuned mass damper vibration damping.
Step(1)In, formula that dynamic characteristics to steel arch-gate and dynamic response analysis use for:, in formula,、WithThe respectively quality of steel arch-gate, damping and stiffness matrix;、With
Respectively displacement, speed and acceleration;Swash load to flow.
Step(2)The middle formula that uses of equivalent mass for calculating water for:, whereinFor the density of water;
It is steel arch-gate under water apart from the depth of the water surface;For library water head.
Step(4)Middle multiple tuned mass damper includes n single tuning mass damper, and n is the natural number more than 0, and n is a
The intrinsic frequency average value of single tuning mass damperFor:,For the frequency of each damper;Frequency band
It is wideFor:;Center frequency ratioFor:, whereinIt is controlled frequency for structure;Multiple-tuned Tuned mass damper
The frequency calculating formula of k-th of single tuning mass damper is in device:。
The single tuning mass damper number for including in the mass ratio of multiple tuned mass damper, multiple tuned mass damper
The maximum displacement value and maximum acceleration value that amount, the damping ratio of multiple tuned mass damper are responded by steel arch-gate flow induced vibration
Damping rate determines that multiple tuned mass damper damping rate is the response of non-control structure and structure after multiple tuned mass damper control
The ratio of the dynamic magnification factor difference of response and the response of non-control structure;Non- control structure is that more tune are not arranged for steel arch-gate
The component of humorous mass damper, including curved panel, crossbeam, longeron and sunpender;The frequency bandwidth of multiple tuned mass damper by
The difference of steel arch-gate frequency determines when steel arch-gate frequency and consideration complete floodage when disregarding fluid matasomatism.
Dynamic magnification factor calculating formula is:, wherein,, wherein:,,,,, in formula:、、WithThe mass ratio of respectively k-th single tuning mass damper, frequency ratio, resistance
Buddhist nun's ratio and controlled structural damping ratio,The ratio of frequency is controlled for driving frequency and structure, wherein:,,,,;In formula:For k-th of single tuning Tuned mass damper in multiple tuned mass damper
The frequency of device,It is controlled frequency for structure,、WithThe quality of respectively k-th single tuning mass damper, damping and
Circular frequency,、WithQuality, damping and the circular frequency of respectively controlled structure,For imposed load circular frequency.
It enables,, then when dynamic characteristics and dynamic response are analyzed
The kinetics equation used for:, calculated to simplify, introduce constant equation, by integral operation
It is converted into algebraic operation, kinetics equation is expressed as:, then enable:, then equation be represented by:, non trivial solution is:;
Transfer matrixExpression formula be:, whereinFor discrete time step;Arc is obtained according to non trivial solution
Displacement, speed and the acceleration of shape steel-slag sand.
Using above-mentioned technical proposal, the present invention has the advantages that:
1, multiple tuned mass damper (MTMD) is arranged in the present invention on the support arm of steel arch-gate, in MTMD Rational Parameters
In the case of, support arm or even the response of integrally-built flow induced vibration can be effectively reduced, achievees the purpose that protect agent structure, avoid
The support arm of steel arch-gate power destruction in the case where stream swashs load action, and then overall structure is caused to be squashed.
2, single tuning mass damper is parallel with one another in multiple tuned mass damper, can realize steel arch-gate stream exciting
Energy passes to multiple tuned mass damper, is consumed energy by multiple tuned mass damper, reduces the vibration of steel arch-gate, protection
Agent structure prevents structure from destroying;Multiple tuned mass damper has monomer mass small, facilitates construction, installation and the spy used
Point.
3, the present invention multiple tuned mass damper is set on the support arm of steel arch-gate, with increase frequency adjustment range,
Achieve the purpose that reduce structural dynamic response, in the case where the sharp load of stream is immutable, passes through the mode to steel arch-gate
Analysis, it is first determined the installation site of multiple tuned mass damper, and fundamental frequency value and structure total quality are found out, so as to true
The parameter of each single tuning mass damper of multimass tuned damper is determined, then to the arc-shaped steel of installation multiple tuned mass damper
Gate carries out Dynamic time history analysis, the results showed that, it can effectively be dropped in the support arm setting multiple tuned mass damper of steel arch-gate
Low structural dynamic response amount avoids being squashed too early for gate structure.
Description of the drawings
Fig. 1 is the structural schematic diagram of steel arch-gate;
Fig. 2 is the structural map of controlled structure and multiple tuned mass damper;
Fig. 3 is that stream swashs load time-histories figure and Fourier amplitude figures;
Fig. 4 is the variation diagram of displacement and acceleration damping rate with mass ratio;
Fig. 5 is the variation of displacement and acceleration damping rate with single tuning mass damper quantity in multiple tuned mass damper
Figure;
Fig. 6 is the variation diagram of displacement and acceleration damping rate with multiple tuned mass damper damping ratio;
Fig. 7 is support arm midpoint comprehensive displacement time-history curves in steel arch-gate.
Specific implementation mode
As shown in figs. 1-7, steel arch-gate includes 1, two sunpender 2 of curved panel and two support arms, table after curved panel 1
Face is equipped with several crossbeams 3 along its short transverse uniform intervals, and every crossbeam 3 is arranged along left and right horizontal direction, after curved panel 1
Surface along its width direction uniform intervals be equipped with several longerons 4, the arc-shaped structure of every longeron 4 and with the arc of curved panel 1
Spend identical, two sunpenders 2 are obliquely installed and are mutually parallel, and one end of two sunpenders 2 connects with the rear surface of curved panel 1 respectively
It connects, each support arm includes upper cantilever 5 and lower cantalever 6, and web member 7 is equipped between upper cantilever 5 and lower cantalever 6;Certain steel arch-gate
As shown in Figure 1, the width and height of steel arch-gate are respectively, the outer arc radius of curved panel 1 is 22m, and two are hung
Spacing between bar 2 is 6.6m, and the thickness of curved panel 1 is 35mm, and curved panel 1 is evenly arranged 9 crossbeams 3, arc along longitudinal direction
Shape panel 1 is transversely evenly arranged 9 longerons 4, and 1 arc length of curved panel is 14.9m, wherein upper cantilever 5 and 1 top of curved panel
Between arc length 3.1m, the arc length 9.4m between upper cantilever 5 and lower cantalever 6, the arc between 1 bottom end of lower cantalever 6 and curved panel
A length of is 2.4m, and the normal pool level 850m of the steel arch-gate, normal filling water head is 58m, check water level 855m, is checked
Head is 59m.
The multiple tuned mass damper Vibration Absorption Designing method for steel arch-gate of the present invention, includes the following steps:
(1)Dynamic characteristics is carried out to steel arch-gate using FInite Element and dynamic response is analyzed, curved panel 1 selects shell
Unit simulation stress, support arm, crossbeam 3 and longeron 4 select beam element to simulate stress, and sunpender 2 selects bar unit simulation
Stress;The formula used for:, in formula,、WithThe respectively quality of steel arch-gate, damping
And stiffness matrix;、WithRespectively displacement, speed and acceleration;Swash load to flow;It enables,, then the kinetics equation that is used when dynamic characteristics and dynamic response are analyzed for:, calculated to simplify, introduce constant equation, convert integral operation to algebraic operation, power
Equation is learned to be expressed as:, then enable:, then square
Journey is represented by:, non trivial solution is:;Transfer matrixExpression formula be:, whereinFor discrete time step;The displacement of steel arch-gate, speed are obtained according to non trivial solution and are added
Speed;
(2)Simulation water pressure influences the dynamic characteristics of steel arch-gate, using Westergaard methods(Additional mass method)
Calculate water equivalent mass, the formula used for:, whereinFor the density of water;It is steel arch-gate in water
The lower depth apart from the water surface;For library water head;
(3)Modal strain energy analysis is carried out to steel arch-gate, obtains the value of the support arm modal strain energy of steel arch-gate
For maximum value;
(4)Multiple tuned mass damper is disposed on the support arm of steel arch-gate(MTMD), multiple tuned mass damper by
Several single tuning mass dampers(TMD)It composes in parallel, the quality of each single tuning mass damper is identical with damping ratio;It is more
Tuned mass damper includes n single tuning mass damper, and n is the natural number more than 0, n single tuning mass damper
Intrinsic frequency average valueFor:,For the frequency of each damper;Frequency bandwidthFor:;
Center frequency ratioFor:, whereinIt is controlled frequency for structure;K-th of single tuning quality in multiple tuned mass damper
The frequency calculating formula of damper is:;
(5)According to the actual loading situation of steel arch-gate, single tuning in multiple tuned mass damper is determined by optimization
Number, the frequency distribution range of multiple tuned mass damper and the damping ratio of multiple tuned mass damper of mass damper,
Optimal control results are obtained after so that steel arch-gate is passed through multiple tuned mass damper vibration damping.
The single tuning mass damper number for including in the mass ratio of multiple tuned mass damper, multiple tuned mass damper
The maximum displacement value and maximum acceleration value that amount, the damping ratio of multiple tuned mass damper are responded by steel arch-gate flow induced vibration
Damping rate determines that multiple tuned mass damper damping rate is structure after the response of non-control structure and multiple tuned mass damper control
The ratio of the dynamic magnification factor difference of response and the response of non-control structure;Non- control structure is that more tune are not arranged for steel arch-gate
The component of humorous mass damper, including curved panel, crossbeam, longeron and sunpender;The frequency bandwidth of multiple tuned mass damper by
The difference of steel arch-gate frequency determines when steel arch-gate frequency and consideration complete floodage when disregarding fluid matasomatism;Power
Amplification coefficient calculating formula is:, wherein,, wherein:,,,,, in formula:、、WithThe mass ratio of respectively k-th single tuning mass damper, frequency ratio, resistance
Buddhist nun's ratio and controlled structural damping ratio are the ratio that driving frequency and structure are controlled frequency, wherein:,,,,;In formula:For k-th of single tuning Tuned mass damper in multiple tuned mass damper
The frequency of device,It is controlled frequency for structure,、WithThe quality of respectively k-th single tuning mass damper, damping and
Circular frequency,、WithQuality, damping and the circular frequency of respectively controlled structure,For imposed load circular frequency.
By to steel arch-gate carry out model analysis, obtained water and it is anhydrous when fundamental frequency be respectively 5.67Hz and
6.58Hz;Steel arch-gate overall quality is 340504Kg, under normal circumstances, multiple tuned mass damper quality and overall structure
Mass ratio is taken as 1 ~ 5%, in order to determine the quantity of TMD and the damping of MTMD in the MTMD mass ratioes of steel arch-gate, MTMD
Than carrying out dynamic response analysis to steel arch-gate, being determined by displacement and acceleration dynamic magnification factor damping rate;Displacement and plus
Speed power amplification coefficient damping rate is as shown in Figure 4 with the change curve of mass ratio;Displacement and acceleration dynamic magnification factor subtract
Rate of shaking is as shown in Figure 5 with MTMD quantity change curves;Displacement and acceleration dynamic magnification factor damping rate are with variation of damping ratio song
Line is as shown in Figure 6.As seen from Figure 4, when the mass ratio of MTMD is 2%, displacement and acceleration dynamic magnification factor damping rate
It tends towards stability, excessive MTMD mass can influence structure partial load effect in addition, therefore take steel arch-gate MTMD mass ratioes
It is 2%.By dynamic magnification factor displacement and acceleration with quantity change curve Fig. 5 of TMD in MTMD it is found that when TMD quantity between
Effect is best at 6 ~ 10, it is contemplated that support arm has 4 bearing beams, takes 8 TMD.It will be appreciated from fig. 6 that excessive MTMD damps ratio
Displacement and acceleration dynamic magnification factor damping rate is caused all to tend to reduce, the reason is that the damping ratio that TMD is provided makes itself to resonate
Reaction reduces, to which the more multiagent that cannot dissipate is controlled structural vibration energy, therefore MTMD damping ratios take it is 5% more suitable.This
Sample determines the quantity and damping ratio of TMD in the mass ratio of MTMD dampers, MTMD by Fig. 4 ~ 6.That is MTMD mass is about
6800Kg;There are four beams to constitute for support arm, TMD should on each beam mean allocation, as 4 multiple, therefore take 8 TMD;Each
The damping ratio of TMD takes 5%, and each TMD structural parameters are as shown in table 1.Support arm midpoint comprehensive displacement time-history curves as shown in fig. 7,
It is arranged before MTMD and is arranged the maximum comprehensive displacement, comprehensive speed and comprehensive acceleration reduced value such as table 2 at MTMD back arms midpoint
It is shown.
Table 1:
Table 2:
The present embodiment is not to be made any form of restriction to shape, material, the structure etc. of the present invention, every according to this hair
Bright technical spirit belongs to the technology of the present invention side to any simple modification, equivalent change and modification made by above example
The protection domain of case.
Claims (7)
1. for the multiple tuned mass damper Vibration Absorption Designing method of steel arch-gate, the steel arch-gate includes arcwall face
Plate, two sunpenders and two support arms, curved panel rear surface are equipped with several crossbeams, every crossbeam along its short transverse uniform intervals
It is arranged along left and right horizontal direction, curved panel rear surface is equipped with several longerons, every longeron along its width direction uniform intervals
Arc-shaped structure and identical as the radian of curved panel, two sunpenders are obliquely installed and are mutually parallel, one end of two sunpenders
It is connect respectively with the rear surface of curved panel, each support arm includes upper cantilever and lower cantalever, is set between upper cantilever and lower cantalever
There is web member, it is characterised in that:Include the following steps:
(1)Dynamic characteristics is carried out to steel arch-gate using FInite Element and dynamic response is analyzed, curved panel selects shell unit
Stress is simulated, support arm, crossbeam and longeron select beam element to simulate stress, and sunpender selects bar unit to simulate stress shape
State;
(2)The equivalent mass of water, dynamic characteristics shadow of the simulation water pressure to steel arch-gate are calculated using Westergaard methods
It rings;
(3)Modal strain energy analysis is carried out to steel arch-gate, show that the value of the support arm modal strain energy of steel arch-gate is most
Big value;
(4)Multiple tuned mass damper is disposed on the support arm of steel arch-gate, multiple tuned mass damper is by several dullnesses
Humorous mass damper composes in parallel, and the quality of each single tuning mass damper is identical with damping ratio;
(5)According to the actual loading situation of steel arch-gate, single tuning quality in multiple tuned mass damper is determined by optimization
Number, the frequency distribution range of multiple tuned mass damper and the damping ratio of multiple tuned mass damper of damper, make arc
Shape steel-slag sand after multiple tuned mass damper vibration damping by obtaining optimal control results.
2. the multiple tuned mass damper Vibration Absorption Designing method according to claim 1 for steel arch-gate, feature
It is:Step(1)In, formula that dynamic characteristics to steel arch-gate and dynamic response analysis use for:, in formula,、WithThe respectively quality of steel arch-gate, damping and stiffness matrix;、With
Respectively displacement, speed and acceleration;Swash load to flow.
3. the multiple tuned mass damper Vibration Absorption Designing method according to claim 2 for steel arch-gate, feature
It is:Step(2)The middle formula that uses of equivalent mass for calculating water for:, whereinFor the density of water;For
Steel arch-gate is under water apart from the depth of the water surface;For library water head.
4. the multiple tuned mass damper Vibration Absorption Designing method according to claim 3 for steel arch-gate, feature
It is:Step(4)Middle multiple tuned mass damper includes n single tuning mass damper, and n is the natural number more than 0, and n single
The intrinsic frequency average value of tuned mass damperFor:,For the frequency of each damper;Frequency bandwidthFor:;Center frequency ratioFor:, whereinIt is controlled frequency for structure;Multiple tuned mass damper
In the frequency calculating formula of k-th of single tuning mass damper be:。
5. the multiple tuned mass damper Vibration Absorption Designing method according to claim 4 for steel arch-gate, feature
It is:It is the single tuning mass damper quantity that includes in the mass ratio of multiple tuned mass damper, multiple tuned mass damper, more
The maximum displacement value and maximum acceleration value vibration damping that the damping ratio of tuned mass damper is responded by steel arch-gate flow induced vibration
Rate determines that multiple tuned mass damper damping rate is the response of non-control structure and structural response after multiple tuned mass damper control
Dynamic magnification factor difference and non-control structure response ratio;Non- control structure is that multiple-tuned matter is not arranged for steel arch-gate
Measure the component of damper, including curved panel, crossbeam, longeron and sunpender;The frequency bandwidth of multiple tuned mass damper is by disregarding
The difference of steel arch-gate frequency determines when steel arch-gate frequency and consideration complete floodage when fluid matasomatism.
6. the multiple tuned mass damper Vibration Absorption Designing method according to claim 5 for steel arch-gate, feature
It is:Dynamic magnification factor calculating formula is:, wherein,, wherein:,,,,, in formula:、、WithThe mass ratio of respectively k-th single tuning mass damper, frequency ratio, resistance
Buddhist nun's ratio and controlled structural damping ratio,The ratio of frequency is controlled for driving frequency and structure, wherein:,,,,;In formula:For k-th of single tuning Tuned mass damper in multiple tuned mass damper
The frequency of device,It is controlled frequency for structure,、WithThe quality of respectively k-th single tuning mass damper, damping and
Circular frequency,、WithQuality, damping and the circular frequency of respectively controlled structure,For imposed load circular frequency.
7. the multiple tuned mass damper Vibration Absorption Designing method according to claim 5 for steel arch-gate, feature
It is:It enables,, then adopted when dynamic characteristics and dynamic response are analyzed
Kinetics equation is:, calculated to simplify, introduce constant equation, integral operation is turned
Algebraic operation is turned to, kinetics equation is expressed as:, then enable:, then equation be represented by:, non trivial solution is:;
Transfer matrixExpression formula be:, whereinFor discrete time step;Arc is obtained according to non trivial solution
Displacement, speed and the acceleration of shape steel-slag sand.
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CN106271861A (en) * | 2016-10-25 | 2017-01-04 | 北京工业大学 | A kind of two-stage distributed assembly power bump leveller oscillation damping method controlled for thin-walled parts multi-modal time-varying cutting vibration |
CN107368629B (en) * | 2017-06-22 | 2021-06-01 | 北京理工大学 | Method for identifying fluid-solid coupling vibration parameters of pressure reducing valve |
CN107975014B (en) * | 2017-11-30 | 2020-06-26 | 西安理工大学 | Device and method for actively controlling parameter vibration of hydraulic arc steel gate |
CN108487198B (en) * | 2018-05-09 | 2020-09-01 | 天津大学前沿技术研究院有限公司 | Vibration reduction method for special vibration form of radial hydraulic gate |
CN110046467B (en) * | 2019-05-08 | 2022-06-07 | 水利部交通运输部国家能源局南京水利科学研究院 | Gate earthquake response analysis method considering gate water seal mechanical characteristic effect |
CN110359469B (en) * | 2019-07-29 | 2023-10-13 | 中铁二院工程集团有限责任公司 | Damping slide-resistant pile structure and design method |
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CN101886375A (en) * | 2010-07-15 | 2010-11-17 | 张占飞 | Steel rolling cylinder gate |
CN102031751A (en) * | 2010-12-23 | 2011-04-27 | 湖南大学 | Big-tonnage cantilever type horizontal tuned mass damper for regulating eddy-current damping |
CN104500632A (en) * | 2014-12-02 | 2015-04-08 | 华北水利水电大学 | Tuned mass damper for vibration-damping experiment of structure model and design method |
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Publication number | Priority date | Publication date | Assignee | Title |
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CN101886375A (en) * | 2010-07-15 | 2010-11-17 | 张占飞 | Steel rolling cylinder gate |
CN102031751A (en) * | 2010-12-23 | 2011-04-27 | 湖南大学 | Big-tonnage cantilever type horizontal tuned mass damper for regulating eddy-current damping |
CN104500632A (en) * | 2014-12-02 | 2015-04-08 | 华北水利水电大学 | Tuned mass damper for vibration-damping experiment of structure model and design method |
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