CN105975730A - Multi-tuned mass damper vibration absorption design method for arc-shaped steel gate - Google Patents
Multi-tuned mass damper vibration absorption design method for arc-shaped steel gate Download PDFInfo
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Abstract
A multi-tuned mass damper vibration absorption design method for an arc-shaped steel gate comprises the following steps that 1, a finite element method is adopted for carrying out dynamic characteristic and power response analysis on the arc-shaped steel gate; 2, the influence of water pressure on the dynamic characteristic of the arc-shaped steel gate is simulated; 3, modal strain energy analysis is carried out on the arc-shaped steel gate to determine the optimal mounting position of an MTMD; 4, a multi-tuned mass damper is mounted on a branch arm of the arc-shaped steel gate; 5, according to the actual stress condition of the arc-shaped steel gate, the number of single-tuned mass dampers in the multi-tuned mass damper, the frequency distribution range of the multi-tuned mass damper and the damping rate of the multi-tuned mass damper are determined through optimization. The multi-tuned mass damper is arranged on the branch arm of the arc-shaped steel gate, the flow induced vibration response of the branch arm and even the whole structure can be effectively reduced under the condition that parameters of the multi-tuned mass damper are reasonable, and the aim of protecting the main structure is achieved.
Description
Technical field
The invention belongs to the Vibration Absorption Designing technical field of gate in hydraulic engineering, many particularly for steel arch-gate
Tuning quality damper vibration damping method for designing.
Background technology
It is that stream swashs load and the product of gate dynamic trait coupling that gate stream swashs load dynamic response.At streams
Determine, flow and swash in the case of load can not change, adjust gate dynamic trait and can effectively reduce structural dynamic response.Arc-shaped steel lock
The advantages such as version slim and graceful for Men Yiqi, rational stress performance and hoisting capacity are little, obtain extensively should in hydro-structure
With.But the flow induced vibration problem of steel arch-gate is the most prominent, because flow induced vibration damages at home and abroad in hydro-structure
Happen occasionally.Flow induced gate vibration is determined, when hydrodynamic load cannot change by hydrodynamic load feature and radial gate vibration characteristic
Time, the dynamic trait optimizing gate becomes unique selection.How to avoid steel-slag sand to occur stream to swash to destroy, give full play to steel-slag sand
Advantageous feature, scientific research personnel proposes different solutions.
Making a general survey of the damage-form of gates of segmental shape, major part is owing to support arm occurs vibration excessive, causes support arm dynamic buckling,
Or load effect exceedes 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 works the most under water, the natural frequency of vibration is affected by water pressure, therefore TMD effectiveness in vibration suppression is poor.
Summary of the invention
The present invention is to solve weak point of the prior art, it is provided that for the multiple-tuned Tuned mass damper of steel arch-gate
Device Vibration Absorption Designing method, by arranging multiple tuned mass damper on steel arch-gate, to increase frequency adjustment range, reaches
Reduce the purpose of structural dynamic response.
For solving above-mentioned technical problem, the present invention adopts the following technical scheme that the multiple-tuned quality for steel arch-gate
Damper vibration damping method for designing, described steel arch-gate includes curved panel, two suspension rods and two support arms, after curved panel
Surface is provided with some crossbeams along its short transverse uniform intervals, and every crossbeam is all arranged along left and right horizontal direction, after curved panel
Surface is provided with some longerons, the every the most curved structure of longeron and the radian phase with curved panel along its width uniform intervals
With, two suspension rods are obliquely installed and are parallel to each other, and one end of two suspension rods is connected with the rear surface of curved panel respectively, Mei Gezhi
Arm all includes upper cantilever and lower cantalever, is provided with web member, comprises the following steps between upper cantilever and lower cantalever:
(1) using FInite Element that steel arch-gate carries out dynamic trait and dynamic response analysis, curved panel selects shell unit
Simulation stress, support arm, crossbeam and longeron select beam element simulation stress, suspension rod selection bar unit simulation stress shape
State；
(2) Westergaard method is used to calculate the equivalent mass of water, the simulated water pressure power dynamic trait shadow to steel arch-gate
Ring；
(3) steel arch-gate is carried out modal strain energy analysis, show that the value of the support arm modal strain energy of steel arch-gate is
Big value；
(4) disposing multiple tuned mass damper on the support arm of steel arch-gate, multiple tuned mass damper is dull by several
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
The number of antivibrator, the frequency distribution scope of multiple tuned mass damper and the damping ratio of multiple tuned mass damper, make arc
Shape steel-slag sand obtains optimal control results by after multiple tuned mass damper vibration damping.
In step (1), to the dynamic trait of steel arch-gate and the formula of dynamic response analysis employing it is:, in formula,、WithIt is respectively the quality of steel arch-gate, damping and stiffness matrix；、With
It is respectively displacement, speed and acceleration；Load is swashed for stream.
The formula of the equivalent mass employing calculating water in step (2) is:, whereinDensity for water；
The degree of depth for the steel arch-gate distance water surface under water；For storehouse water head.
In step (4), multiple tuned mass damper includes n single tuning mass damper, and n is the natural number more than 0, n
The natural frequency meansigma methods of single tuning mass damperFor:,Frequency for each antivibrator；Frequency band
WideFor:；Center frequency ratioFor:, whereinFor the controlled frequency of structure；Multiple-tuned Tuned mass damper
In device, the cymometer formula of kth single tuning mass damper is:。
The single tuning mass damper number comprised in the mass ratio of multiple tuned mass damper, multiple tuned mass damper
Amount, the maximum displacement value that responded by steel arch-gate flow induced vibration of the damping ratio of multiple tuned mass damper and maximum acceleration value
Damping rate determines, multiple tuned mass damper damping rate is structure after the response of non-control structure controls with multiple tuned mass damper
The dynamic magnification factor difference of response and the ratio of non-control structure response；Non-control structure is that steel arch-gate is not provided with adjusting more
The component of humorous mass damper, including curved panel, crossbeam, longeron and suspension rod；The frequency bandwidth of multiple tuned mass damper by
When disregarding fluid matasomatism, when steel arch-gate frequency and consideration complete floodage, the difference of steel arch-gate frequency determines.
Dynamic magnification factor calculating formula is:, wherein,,, wherein:,,,,, in formula:、、WithIt is respectively the mass ratio of kth single tuning mass damper, frequency ratio, resistance
Buddhist nun's ratio and controlled structural damping ratio,For the ratio of the controlled frequency of driving frequency and structure, wherein:,,,,；In formula:For kth single tuning Tuned mass damper in multiple tuned mass damper
The frequency of device,For the controlled frequency of structure,、WithBe respectively the quality of kth single tuning mass damper, damping and
Circular frequency,、WithIt is respectively the quality of controlled structure, damping and circular frequency,For imposed load circular frequency.
Order,, then when dynamic trait and dynamic response are analyzed
The kinetics equation used is:, in order to simplify calculating, introduce constant equation, by integral operation
Being converted into algebraic operation, kinetics equation is expressed as:, then make:, then equation is represented by:, non trivial solution is:
；Transfer matrixExpression formula be:, whereinFor discrete time step；Arc is drawn according to non trivial solution
The displacement of shape steel-slag sand, speed and acceleration.
Use technique scheme, there is advantages that
1, the present invention arranges multiple tuned mass damper (MTMD) on the support arm of steel arch-gate, in the feelings of MTMD Rational Parameters
Under condition, can effectively reduce support arm or even the response of integrally-built flow induced vibration, reach to protect the purpose of agent structure, it is to avoid arc
The support arm of steel-slag sand is power destruction under stream swashs load action, and then causes overall structure to be squashed.
2, in multiple tuned mass damper, single tuning mass damper is parallel with one another, can realize steel arch-gate stream exciting
Energy passes to multiple tuned mass damper, multiple tuned mass damper consume energy, and reduces the vibration of steel arch-gate, protection
Agent structure, prevents structural deterioration；It is little that multiple tuned mass damper has monomer mass, convenient construction, the spy installing and using
Point.
3, the present invention arranges multiple tuned mass damper on the support arm of steel arch-gate, with increase frequency adjustment range,
Reduce the purpose of structural dynamic response, in the case of the sharp load of stream is immutable, by the mode to steel arch-gate
Analyze, it is first determined the installation site of multiple tuned mass damper, and obtain fundamental frequency value and structure total quality, in order to really
Determine the parameter of multimass tuned damper each single tuning mass damper, then to the arc-shaped steel installing multiple tuned mass damper
Gate carries out Dynamic time history analysis, and result shows, the support arm at steel arch-gate arranges multiple tuned mass damper and can effectively drop
Low structural dynamic response amount, it is to avoid being squashed too early of gate structure.
Accompanying drawing explanation
Fig. 1 is the structural representation 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 figure；
Fig. 4 is displacement and the acceleration damping rate variation diagram with mass ratio；
Fig. 5 is that displacement and acceleration damping rate are with the variation diagram of single tuning mass damper quantity in multiple tuned mass damper；
Fig. 6 is displacement and the acceleration damping rate variation diagram with multiple tuned mass damper damping ratio；
Fig. 7 is support arm midpoint comprehensive displacement time-history curves in steel arch-gate.
Detailed description of the invention
As shown in figs. 1-7, steel arch-gate includes 1, two suspension rods 2 of curved panel and two support arms, table after curved panel 1
Face is provided with some crossbeams 3 along its short transverse uniform intervals, and every crossbeam 3 is all arranged along left and right horizontal direction, after curved panel 1
Surface is provided with some longerons 4, the every the most curved structure of longeron 4 and the arc with curved panel 1 along its width uniform intervals
Spending identical, two suspension rods 2 are obliquely installed and are parallel to each other, and one end of two suspension rods 2 is respectively with the rear surface of curved panel 1 even
Connecing, each support arm all includes upper cantilever 5 and lower cantalever 6, is provided with web member 7 between upper cantilever 5 and lower cantalever 6；Certain steel arch-gate
As it is shown in figure 1, the width of steel arch-gate and height 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 along being longitudinally evenly arranged 9 crossbeams 3, arc
Shape panel 1 is transversely evenly arranged 9 longerons 4, and curved panel 1 arc length is 14.9m, wherein upper cantilever 5 and curved panel 1 top
Between arc length 3.1m, arc length 9.4m between upper cantilever 5 and lower cantalever 6, the arc between lower cantalever 6 and curved panel 1 bottom
A length of for 2.4m, normal pool level 850m of this steel arch-gate, normal filling water head is 58m, and check water level is 855m, checks
Head is 59m.
The multiple tuned mass damper Vibration Absorption Designing method for steel arch-gate of the present invention, comprises the following steps:
(1) using FInite Element that steel arch-gate carries out dynamic trait and dynamic response analysis, curved panel 1 selects shell unit
Simulating stress, support arm, crossbeam 3 and longeron 4 select beam element to simulate stress, and suspension rod 2 selects bar unit to simulate stress
State；The formula used is:, in formula,、WithBe respectively the quality of steel arch-gate, damping and
Stiffness matrix；、WithIt is respectively displacement, speed and acceleration；Load is swashed for stream；Order,, then the kinetics equation that dynamic trait and dynamic response use when analyzing is:, in order to simplify calculating, introduce constant equation, integral operation is converted into algebraic operation, power
Equation is expressed as:, then make:, then
Equation is represented by:, non trivial solution is:；Transfer matrixExpression formula be:, whereinFor discrete time step；Draw the displacement of steel arch-gate, speed according to non trivial solution and add
Speed；
(2) dynamic trait of steel arch-gate is affected by simulated water pressure power, uses Westergaard method (additional mass method) to calculate
The equivalent mass of water, the formula of employing is:, whereinDensity for water；For steel arch-gate under water away from
The degree of depth from the water surface；For storehouse water head；
(3) steel arch-gate is carried out modal strain energy analysis, show that the value of the support arm modal strain energy of steel arch-gate is
Big value；
(4) disposing multiple tuned mass damper (MTMD) on the support arm of steel arch-gate, multiple tuned mass damper is by some
Individual single tuning mass damper (TMD) composes in parallel, and the quality of each single tuning mass damper is identical with damping ratio；Multiple-tuned
Mass damper includes n single tuning mass damper, and n is the natural number more than 0, n single tuning mass damper intrinsic
Average frequency valueFor:,Frequency for each antivibrator；Frequency bandwidthFor:；Center
Frequency ratioFor:, whereinFor the controlled frequency of structure；Kth single tuning Tuned mass damper in multiple tuned mass damper
The cymometer formula of device is:；
(5) according to the actual loading situation of steel arch-gate, single tuning quality in multiple tuned mass damper is determined by optimization
The number of antivibrator, the frequency distribution scope of multiple tuned mass damper and the damping ratio of multiple tuned mass damper, make arc
Shape steel-slag sand obtains optimal control results by after multiple tuned mass damper vibration damping.
The single tuning mass damper number comprised in the mass ratio of multiple tuned mass damper, multiple tuned mass damper
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 subtract
The rate of shaking determines, multiple tuned mass damper damping rate is structural response after the response of non-control structure and multiple tuned mass damper control
Dynamic magnification factor difference and non-control structure response ratio；Non-control structure is that steel arch-gate is not provided with multiple-tuned quality
The component of antivibrator, including curved panel, crossbeam, longeron and suspension rod；The frequency bandwidth of multiple tuned mass damper is by disregarding stream
During body effect, when steel arch-gate frequency and consideration complete floodage, the difference of steel arch-gate frequency determines；Power augmentation system
Number calculating formula is:, wherein,,,
Wherein:,,,,, in formula:、、WithIt is respectively the mass ratio of kth single tuning mass damper, frequency ratio, damping ratio and controlled structural damping ratio,
For the ratio of the controlled frequency of driving frequency and structure, wherein:,,,,；In formula:For the frequency of kth single tuning mass damper in multiple tuned mass damper,Controlled for structure
Frequency,、WithIt is respectively quality, damping and the circular frequency of kth single tuning mass damper,、WithRespectively
For quality, damping and the circular frequency of controlled structure,For imposed load circular frequency.
By steel arch-gate is carried out model analysis, obtain having water and anhydrous time fundamental frequency be respectively 5.67Hz and
6.58Hz；Steel arch-gate oeverall quality is 340504Kg, generally, and multiple tuned mass damper quality and overall structure
Mass ratio is taken as 1 ~ 5%, in order to determine quantity and the damping of MTMD of TMD in the MTMD mass ratio of steel arch-gate, MTMD
Ratio, carries out dynamic response analysis to steel arch-gate, displacement and acceleration dynamic magnification factor damping rate determine；Displacement and adding
Speed power amplification coefficient damping rate with mass ratio change curve as shown in Figure 4；Displacement and acceleration dynamic magnification factor subtract
Rate of shaking is with MTMD number change curve as shown in Figure 5；Displacement and acceleration dynamic magnification factor damping rate are bent with variation of damping ratio
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
Tending towards stability, the most excessive MTMD mass can affect structure partial load effect, therefore takes steel arch-gate MTMD mass ratio
It is 2%.From dynamic magnification factor displacement and acceleration with the number change curve chart 5 of TMD in MTMD, when TMD quantity between
When 6 ~ 10, effect is best, 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
Causing displacement and acceleration dynamic magnification factor damping rate all to tend to reducing, reason is that the damping ratio that TMD provides makes self to resonate
Reaction reduces, thus the more multiagent controlled structural vibration energy that can not dissipate, thus MTMD damping ratio to take 5% the most suitable.This
Sample determines quantity and the damping ratio of TMD in the mass ratio of MTMD antivibrator, MTMD by Fig. 4 ~ 6.I.e. MTMD mass is about
6800Kg；Support arm has four beams to constitute, TMD should on each beam mean allocation, be the multiple of 4, 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 it is shown in fig. 7,
Before MTMD is set and the maximum comprehensive displacement at MTMD back arm midpoint, comprehensive speed and comprehensive acceleration reduced value such as table 2 are set
Shown in.
Table 1:
Table 2:
The shape of the present invention, material, structure etc. are not made any pro forma restriction by the present embodiment, every according to the present invention's
Any simple modification, equivalent variations and the modification that above example is made by technical spirit, belongs to technical solution of the present invention
Protection domain.
Claims (7)
1., for the multiple tuned mass damper Vibration Absorption Designing method of steel arch-gate, described steel arch-gate includes arcwall face
Plate, two suspension rods and two support arms, curved panel rear surface is provided with some crossbeams, every crossbeam along its short transverse uniform intervals
All arranging along left and right horizontal direction, curved panel rear surface is provided with some longerons, every longeron along its width uniform intervals
The most curved structure and identical with the radian of curved panel, two suspension rods are obliquely installed and are parallel to each other, one end of two suspension rods
Being connected with the rear surface of curved panel respectively, each support arm all includes upper cantilever and lower cantalever, sets between upper cantilever and lower cantalever
There is web member, it is characterised in that: comprise the following steps:
(1) using FInite Element that steel arch-gate carries out dynamic trait and dynamic response analysis, curved panel selects shell unit
Simulation stress, support arm, crossbeam and longeron select beam element simulation stress, suspension rod selection bar unit simulation stress shape
State；
(2) Westergaard method is used to calculate the equivalent mass of water, the simulated water pressure power dynamic trait shadow to steel arch-gate
Ring；
(3) steel arch-gate is carried out modal strain energy analysis, show that the value of the support arm modal strain energy of steel arch-gate is
Big value；
(4) disposing multiple tuned mass damper on the support arm of steel arch-gate, multiple tuned mass damper is dull by several
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
The number of antivibrator, the frequency distribution scope of multiple tuned mass damper and the damping ratio of multiple tuned mass damper, make arc
Shape steel-slag sand obtains optimal control results by after multiple tuned mass damper vibration damping.
Multiple tuned mass damper Vibration Absorption Designing method for steel arch-gate the most according to claim 1, its feature
It is: in step (1), to the dynamic trait of steel arch-gate and the formula of dynamic response analysis employing is:, in formula,、WithIt is respectively the quality of steel arch-gate, damping and stiffness matrix；、With
It is respectively displacement, speed and acceleration；Load is swashed for stream.
Multiple tuned mass damper Vibration Absorption Designing method for steel arch-gate the most according to claim 2, its feature
It is: the formula of the equivalent mass employing calculating water in step (2) is:, whereinDensity for water；For
The degree of depth of the steel arch-gate distance water surface under water；For storehouse water head.
Multiple tuned mass damper Vibration Absorption Designing method for steel arch-gate the most according to claim 3, its feature
Being: in step (4), multiple tuned mass damper includes n single tuning mass damper, n is the natural number more than 0, and n single
The natural frequency meansigma methods of tuned mass damperFor:,Frequency for each antivibrator；Frequency bandwidthFor:；Center frequency ratioFor:, whereinFor the controlled frequency of structure；Multiple tuned mass damper
The cymometer formula of middle kth single tuning mass damper is:。
Multiple tuned mass damper Vibration Absorption Designing method for steel arch-gate the most according to claim 4, its feature
It is: the single tuning mass damper quantity that comprises in the mass ratio of multiple tuned mass damper, multiple tuned mass damper, many
Maximum displacement value that the damping ratio of tuned mass damper is responded by steel arch-gate flow induced vibration and maximum acceleration value vibration damping
Rate determines, multiple tuned mass damper damping rate is structural response after the response of non-control structure controls with multiple tuned mass damper
Dynamic magnification factor difference and non-control structure response ratio；Non-control structure is that steel arch-gate is not provided with multiple-tuned matter
The component of amount antivibrator, including curved panel, crossbeam, longeron and suspension rod；The frequency bandwidth of multiple tuned mass damper is by disregarding
During fluid matasomatism, when steel arch-gate frequency and consideration complete floodage, the difference of steel arch-gate frequency determines.
Multiple tuned mass damper Vibration Absorption Designing method for steel arch-gate the most according to claim 5, its feature
It is: dynamic magnification factor calculating formula is:, wherein,,, wherein:,,,,, in formula:、、WithIt is respectively the mass ratio of kth single tuning mass damper, frequency ratio, resistance
Buddhist nun's ratio and controlled structural damping ratio,For the ratio of the controlled frequency of driving frequency and structure, wherein:,,,,；In formula:For kth single tuning Tuned mass damper in multiple tuned mass damper
The frequency of device,For the controlled frequency of structure,、WithBe respectively the quality of kth single tuning mass damper, damping and
Circular frequency,、WithIt is respectively the quality of controlled structure, damping and circular frequency,For imposed load circular frequency.
Multiple tuned mass damper Vibration Absorption Designing method for steel arch-gate the most according to claim 5, its feature exists
In: order,, then what dynamic trait and dynamic response used when analyzing moves
Mechanical equation is:, in order to simplify calculating, introduce constant equation, integral operation is converted into algebraic operation,
Kinetics equation is expressed as:, then make:,
Then equation is represented by:, non trivial solution is:；Transfer matrixExpression formula be:, whereinFor discrete time step；Draw the displacement of steel arch-gate, speed according to non trivial solution and add
Speed.
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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 |
| CN107368629A (en) * | 2017-06-22 | 2017-11-21 | 北京理工大学 | A kind of pressure-reducing valve solid liquid interation parameter identification method |
| CN107975014A (en) * | 2017-11-30 | 2018-05-01 | 西安理工大学 | Device and control method for hydraulic steel radial gate parametric vibration active control |
| CN108487198A (en) * | 2018-05-09 | 2018-09-04 | 天津大学前沿技术研究院有限公司 | A kind of oscillation damping method of the special vibration mode of arc hydraulic gate |
| CN110046467A (en) * | 2019-05-08 | 2019-07-23 | 水利部交通运输部国家能源局南京水利科学研究院 | A kind of gate seismic response analytical method considering Jeakage through Sluice Sealant mechanical characteristic effect |
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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 |
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| 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 |
| CN107975014A (en) * | 2017-11-30 | 2018-05-01 | 西安理工大学 | Device and control method for hydraulic steel radial gate parametric vibration active control |
| CN108487198A (en) * | 2018-05-09 | 2018-09-04 | 天津大学前沿技术研究院有限公司 | A kind of oscillation damping method of the special vibration mode of arc hydraulic gate |
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| CN110046467A (en) * | 2019-05-08 | 2019-07-23 | 水利部交通运输部国家能源局南京水利科学研究院 | A kind of gate seismic response analytical method considering Jeakage through Sluice Sealant mechanical characteristic effect |
| 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 |
| CN110359469A (en) * | 2019-07-29 | 2019-10-22 | 中铁二院工程集团有限责任公司 | A kind of damping anti-slide pile structure and design method |
| 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 |
| CN113868797B (en) * | 2021-09-28 | 2024-06-11 | 合肥工业大学 | Dynamic design method for tuned mass damper array in leaf disk vibration reduction structure |
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