CN105160100B - The TMD of spring mass system Optimization Design is installed - Google Patents
The TMD of spring mass system Optimization Design is installed Download PDFInfo
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- CN105160100B CN105160100B CN201510556396.2A CN201510556396A CN105160100B CN 105160100 B CN105160100 B CN 105160100B CN 201510556396 A CN201510556396 A CN 201510556396A CN 105160100 B CN105160100 B CN 105160100B
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Abstract
The invention discloses a kind of Optimization Design for the TMD for installing spring mass system, the present invention includes following four step：Step 1 establishes the Tuned mass damper system model of structure-installation spring mass system；Step 2 establishes the Tuned mass damper system and kinetics equation of structure-installation spring mass system；Step 3 optimizes calculating with simulated annealing to the tuned mass damper for installing spring mass system；Step 4 chooses a kind of tuned mass damper for installing spring mass system of optimum combination parameter designing by comparing.The innovation of the present invention be to design it is a kind of be applied to the structured tuned mass damper for installing spring mass system of institute, will be appreciated that the dynamic respond of Structures under Earthquake can be efficiently controlled, and be better than tuned mass damper.
Description
Technical field
The present invention relates to a kind of design method for installing spring-quality system, more particularly to a kind of installation spring mass system
The TMD (tuned mass damper) of system Optimization Design.
Background technology
Natural calamity of the earthquake as serious threat human life's property safety, huge disaster is caused to the mankind, is
One of numerous multiple states of earthquake, for example, occur in recent years Wenchuan earthquake, Earthquakes in Japan, Yaan earthquake.These violent earthquakes are not
Great economic loss is only caused, people is returned and brings huge grief and serious injury at heart.21 century, with generation
Boundary's rapid development of economy, people propose higher and higher requirement to the security of engineering structure and taking precautions against natural calamities property, it is desirable to engineering
Structure can not be destroyed when natural calamity (such as macroseism and typhoon) happens suddenly, and require that engineering structure can under its effect
Nothing is damaged.Then we propose some revolutionary requirements to preventing and reducing natural disasters for engineering structure, and structural vibration control skill
Art is expected to be to realize this revolutionary desired fundamental way of preventing and reducing natural disasters.Traditional seismic design of structures is generally by enhancing
The intensity of building structure itself resists the effect of external load with rigidity, so as to reach the effect of antidetonation.So we carry out
During Aseismic Design, it is necessary first to it is accurate to estimate external loads, the characteristic of assurance material therefor to be born of structure, and need
The rational design of selection and analysis method.But the height of earthquake load is uncertain, material non-linear and performance when using
Variation and existing structure analysis and design method limitation cause structure exist be unsatisfactory for using function and safety will
The possibility asked.In view of the limitation of traditional structure Seismic Design Method, industry scholars start constantly to seek this new
Method, the design method of structural vibration control are exactly to produce and develop in this case.
Structural vibration control be by take certain control measure with adjust the dynamic characteristics of building structure itself or
Acted on by applying external energy to offset external load, so as to reach quake evaluation performance.According to whether outside resources, knot
Structure control generally can be divided into following four classes：(1) passive control system, a kind of structure control technique for not needing extra power, one
As refer to add a subsystem, or the processing for constructing some components of structure itself at some position of structure to change
The dynamic characteristics (e.g., tuned mass damper (TMD) and multiple tuned mass dampers (MTMD)) of structure changes system；(2) it is main
Autocontrol system, a kind of structure control technique for needing extra power, by applying the controling power opposite with direction of vibration come real
Existing structure control, controling power are determined by the dynamic response of feedforward external excitation and (or) feedback arrangement；(3) semi-active control aystem,
Typically based on passive control, when stature dynamic-load response starts more to prescribe a time limit, using controlling organization come inside active adjustment structure
Parameter, makes structural parameters be in optimum state, and required external energy is smaller；(4) hybrid control system, active control and passive
The use in conjunction of control, makes it coordinate the cooperation that gets up, and this control system takes full advantage of passive control and active control
The advantages of respective, both can largely be dissipated vibrational energy by passive control system, can be protected again using active control system
Demonstrate,prove control effect, such as main passive tuned mass damper (active-passive tuned mass damper, APTMD).
The content of the invention
The defects of existing for prior art, it is an object of the invention to provide a kind of TMD for installing spring-quality system
The Optimization Design of (tuned mass damper).
To reach above-mentioned purpose, the present invention is using such as following technical proposals：
A kind of Optimization Design for the TMD for installing spring-quality system, it is characterised in that comprise the following steps：
Step 1, by quality, damping and the rigidity of building main structure itself, on the basis of single tuned mass damper
On, a small mass is added again between building main structure and single tuned mass damper, in building main structure mass
Between small mass, an additional springs are added between small mass and single tuned mass damper respectively, are then established
Build the mechanical model of the tuned mass damper of main structure-installation spring-quality system；
Step 2, according to building main structure principle of dynamics, to building main structure and single tuned mass damper, small matter
Gauge block carries out force analysis, establishes the kinetic equation of the tuned mass damper of building main structure-installation spring-quality system；
Step 3, single tuned mass damper is contrasted, the tuned mass damper for installing spring-quality system is carried out
The optimization design of vibration control；
Step 4, by comparing building main structure, consider the validity of control and the validity of damping system stroke control,
Optimum combination parameter is selected, with reference to the tuned mass damper of the parameter designing installation spring-quality system of original building main structure.
Preferably, the step 1 establishes the tuned mass damper of building main structure-installation spring-quality system
The process of mechanical model is as follows：Main structure will be built as a single-degree-of-freedom particle, its damping is determined according to its material characteristics
csWith rigidity ks, by single tuned mass damper device in building main structure, hindered in building main structure and single tuning quality
A small mass is added between Buddhist nun's device again, in building main structure mass and small mass, small mass and single tuning matter
It is k to add rigidity respectively between amount dampert1、kt2Additional springs；Building main structure-installation spring mass is formed with this
The tuned mass damper of system.
Preferably, the step 2 establishes the tuning quality damping of building main structure-installation spring-quality system
The kinetic equation of device is expressed as formula：
In formula,For earthquake ground motion acceleration；ysDisplacement for building main structure relative to substrate；yTFor tuning
Mass damper is relative to the displacement for building main structure；ytDisplacement for small mass relative to building main structure；ms、csAnd ks
Respectively build controlled vibration shape quality, damping and the rigidity of main structure；mT、cTAnd kTRespectively tuned mass damper quality, resistance
Buddhist nun and rigidity；mtFor small mass quality；kt1The rigidity for the additional springs added between building main structure and small mass；kt2
The rigidity for the additional springs added between small mass and tuned mass damper.
Preferably, the step 3 carries out vibration control optimization to the tuned mass damper for installing spring-quality system
The content of design is as follows：
Build the displacement (y of the tuned mass damper of main structure-installation spring-quality systems) dynamic magnification factor is
Such as following formula：
The dynamic magnification factor of tuned mass damper stroke is such as following formula：
The dynamic magnification factor of small mass stroke is such as following formula：
In formula：
Im(λ)=N (1- λ2)-2Mξsλ+2E11μTξTfTλ3+E22μtft 2λ2
ReT(λ)=MRe(λ)-NIm(λ)
ImT(λ)=NRe(λ)+MIm(λ)
Ret(λ)=MRe(λ)-NIm(λ)
Imt(λ)=NRe(λ)+MIm(λ)
E11=B21-B11
E21=A21-A11
E22=-A12
M=A11B21-A21B11
N=A12B21
A12=-2 ξTfTλ
B11=-η β ft 2
B21=-λ2+(1+β)ft 2
In formula：λ is the frequency ratio of building main structure；fTFor the frequency ratio of tuned mass damper；ftFor building main structure with
The frequency ratio of additional springs between small mass；ξsTo build the damping ratio of main structure；ξTFor the damping of tuned mass damper
Than；μTFor tuned mass damper and the mass ratio of building main structure；μtFor small mass and the mass ratio of building main structure；η is
The mass ratio of small mass and tuned mass damper；β is additional springs kt2With additional springs kt1Ratio of rigidity；
In optimization process, according to Practical Project, λ, μ are setT、η、ξTValue, to fT、ftCarry out parameter optimization.
Preferably, in the step 4, optimized parameter interpretational criteria is defined：The tuning of installation spring-quality system is set
The minimum of the minimum value of the structure maximum power amplification coefficient of mass damper, i.e., Smaller, then tuned mass damper vibration control has
Effect property is better；Parameter optimization is carried out using Gene hepatitis B vaccine, and compared with tuned mass damper.
Compared with prior art, the present invention have substantive distinguishing features prominent as follows and it is notable the advantages of：The inventive method
Design it is a kind of be applied to the structured tuned mass damper for installing spring-quality system of institute, will be appreciated that can be
The dynamic respond of Structures under Earthquake is efficiently controlled under a small amount of increase control device mass total quality, and better than tuning
Mass damper.
Brief description of the drawings
Fig. 1 is the flow chart of the Optimization Design for the TMD (tuned mass damper) for installing spring-quality system；
Fig. 2 is the model schematic for installing spring-quality system；
Fig. 3 is the f of spring-quality systemTWith ξTVariation relation curve synoptic diagram；
Fig. 4 is the f of spring-quality systemtWith ξTVariation relation curve synoptic diagram；
Fig. 5 is spring-quality systemWith ξTVariation relation curve synoptic diagram；
Fig. 6 is spring-quality systemWith ξTVariation relation curve synoptic diagram；
Fig. 7 is spring-quality systemWith ξTVariation relation curve synoptic diagram.
Embodiment
Below in conjunction with the accompanying drawings, the specific embodiment of the present invention is further described.
As shown in figure 1, the TMD of present invention installation spring-quality system Optimization Design comprises the following steps：
Step 1, by the quality m of building main structure itselfs, damping csWith rigidity ks, in single tuned mass damper
(TMD) on the basis of, add a small mass again between building main structure and single tuned mass damper, led in building
Between the mass of structure and small mass, an additional bullet is added between small mass and single tuned mass damper respectively
Spring, then establish the mechanical model of the tuned mass damper of building main structure-installation spring-quality system；
Step 2, according to building main structure principle of dynamics, to building main structure and single tuned mass damper, small matter
Gauge block carries out force analysis, establishes the kinetic equation of the tuned mass damper of building main structure-installation spring-quality system；
Step 3, single tuned mass damper is contrasted, the tuned mass damper for installing spring-quality system is carried out
The optimization design of vibration control；
Step 4, by comparing building main structure, consider the validity of control and the validity of damping system stroke control,
Optimum combination parameter is selected, with reference to the tuned mass damper of the parameter designing installation spring-quality system of original building main structure
(TMD)。
As shown in Fig. 2 the tuning quality damping of building main structure-installation spring-quality system is established in the step 1
The mechanical model of device spring-quality system：Main structure will be built as a single-degree-of-freedom particle, determined according to its material characteristics
It is damped and rigidity, by single tuned mass damper device in building main structure, in building main structure and single tuning matter
Measure damper between again add a small mass, building main structure mass and small mass, small mass with it is single
It is k to add rigidity between tuned mass damper respectivelyt1、kt2Additional springs；Building main structure-installation bullet is formed with this
The tuned mass damper spring-quality system of spring-quality system.
Tuned mass damper spring-matter of building main structure-installation spring-quality system is established in the step 2
The kinetic equation of amount system：Stress point is carried out to building main structure, tuned mass damper (TMD), small mass (M) respectively
Analysis, according to theory of structural dynamics, it is such as following formula (1) to (3) to list its kinetic equation：
In formula,For earthquake ground motion acceleration；ysDisplacement of the main structure relative to substrate is built for knot；yTTo adjust
Humorous mass damper (TMD) relative to structure displacement；ytDisplacement for small mass (M) relative to structure；ms、csAnd ksPoint
Not Wei structure controlled vibration shape quality, damping and rigidity；mT、cTAnd kTRespectively tuned mass damper (TMD) quality, damping
And rigidity；mtFor small mass (M) quality；kt1The rigidity for the additional springs added between structure and small mass；kt2To be small
The rigidity for the additional springs added between mass and tuned mass damper (TMD).
Carrying out vibration control optimization design to the TMD for installing spring-quality system in the step 3 is：
Build the displacement (y of the tuned mass damper spring-quality system of main structure-installation spring-quality systems)
Dynamic magnification factor is such as following formula (4)：
The dynamic magnification factor of tuned mass damper stroke is such as following formula：
The dynamic magnification factor of small mass stroke is such as following formula：
Meet below equation group (7) to (11) in formula：
Im(λ)=N (1- λ2)-2Mξsλ+2E11μTξTfTλ3+E22μtft 2λ2 (7)
ReT(λ)=MRe(λ)-NIm(λ)
ImT(λ)=NRe(λ)+MIm(λ) (8)
Ret(λ)=MRe(λ)-NIm(λ)
Imt(λ)=NRe(λ)+MIm(λ) (9)
E11=B21-B11
E21=A21-A11
E22=-A12
M=A11B21-A21B11
N=A12B21 (10)
A12=-2 ξTfTλ
B11=-η β ft 2
B21=-λ2+(1+β)ft 2 (11)
In formula：λ is the frequency ratio of building main structure；fTFor the frequency ratio of tuned mass damper (TMD)；ftLed for building
The frequency ratio of additional springs between structure and small mass；ξsTo build the damping ratio of main structure；ξTFor tuned mass damper
(TMD) damping ratio；μTFor tuned mass damper (TMD) and the mass ratio of structure；μtIt is small mass (M) and the main knot of building
The mass ratio of structure；η is the mass ratio of small mass and tuned mass damper (TMD)；β is additional springs kt2With additional springs
kt1Ratio of rigidity.A, B, E, M, N etc. are to derive parameter.
In optimization process, according to Practical Project, λ, μ are setT、η、ξTValue, to fT、ftCarry out parameter optimization.
In the step 4, optimized parameter interpretational criteria is defined：The tuning quality damping of installation spring-quality system is set
The minimum of the minimum value of the structure maximum power amplification coefficient of device, i.e.,WhereinSmaller, then tuned mass damper vibration control validity is better；Parameter optimization is carried out using Gene hepatitis B vaccine, and
Compared with tuned mass damper.
Calculating is optimized with simulated annealing, is drawn in the structure during the TMD of equipment installation spring-quality system
In the structure during the TMD of equipment installation spring-quality system, tuned mass damper (TMD) and original structure frequency compare fT, it is additional
The frequency of spring compares ft, displacement dynamic magnification factorThe dynamic magnification factor of TMD strokesSmall mass
(M) dynamic magnification factor of strokeWith ξTVariation relation curve, as shown in FIG. 3 to 7.
As seen from Figure 5, the single tuning quality of effective sex ratio of the TMD of spring-quality system vibration control is installed
Damper is good, but installs the tuned mass damper spring-quality system of spring-quality system with ξTIncrease, validity
Reduce.
As seen from Figure 6, the tuned mass damper (TMD) of the TMD of spring-quality system damping system is installed
Stroke significantly increases relative to equipped with single tuned mass damper.
By Fig. 6 and 7 it can be seen that working as ξTWith ξ when≤0.004TIncrease tuned mass damper (TMD) strokeThe stroke of small mass (M)It is obviously reduced, works as ξTWith ξ during ＞ 0.004TIncrease tuning quality resistance
The stroke of Buddhist nun's device (TMD)The stroke of small mass (M)Increase, but strokeIt is increased not clear
It is aobvious, and strokeIn 0.004 ＜ ξTIncrease unobvious in the range of ＜ 0.012, work as ξTWhen >=0.012, sharply increase.Work as ξT
When=0.004, the stroke phase of tuned mass damper (TMD) stroke and single tuned mass damper of spring-quality system
Closely, the stroke of small mass (M) is minimum.
Find out that the frequency for installing the TMD of spring-quality system damping system compares f by Fig. 3 to Fig. 7 synthesisTRelative to list
Individual tuned mass damper (TMD) is obviously reduced；The TMD of spring-quality system additional springs frequency compares ftWith damping
Compare ξTIncrease and reduce；And work as ξTWith damping ratio ξ during ＞ 0.01TIncrease, validity substantially reduces, and spring mass system
The big mass TMD of system stroke is big, therefore it is contemplated that 0.004≤ξ in practiceT≤ 0.01 situation.
Compare Fig. 3 to Fig. 7, consider the factor of validity, choose μT=0.01, η=0.05, β=1.0, fT=0.9, ft=
1.576 ξT=0.004, μT=
0.01, η=0.05, β=1.0, fT=0.9, ft=1.461, ξT=0.006,μT=0.01, η=0.05, β=
1.0, fT=0.9, ft=1.275, ξT=0.008, μT=0.01, η=0.05, β=1.0, fT=0.9, ft=1.051, ξT=0.010,This four groups of design data spring mass
System and device, the validity of the spring-quality system device is compared with tuned mass damper (TMD).
Particular embodiments described above, the technical problem, technical scheme and beneficial effect of the solution of invention are carried out
It is further described, should be understood that the specific embodiment that the foregoing is only the present invention, is not limited to this
Invention, within the spirit and principles of the invention, any modification, equivalent substitution and improvements done etc., should be included in this hair
Within bright protection domain.
Claims (5)
1. a kind of Optimization Design for the TMD for installing spring-quality system, it is characterised in that comprise the following steps：
Step 1, by quality, damping and the rigidity of building main structure itself, on the basis of single tuned mass damper,
Build and add a small mass between main structure and single tuned mass damper again, in building main structure mass and small matter
Between gauge block, an additional springs are added between small mass and single tuned mass damper respectively, then establish building master
The mechanical model of the tuned mass damper of structure-installation spring-quality system；
Step 2, according to building main structure principle of dynamics, to building main structure and single tuned mass damper, small mass
Force analysis is carried out, establishes the kinetic equation of the tuned mass damper of building main structure-installation spring-quality system；
Step 3, single tuned mass damper is contrasted, the tuned mass damper for installing spring-quality system is vibrated
The optimization design of control；
Step 4, by comparing building main structure, consider the validity of control and the validity of damping system stroke control, selection
Optimum combination parameter, with reference to the tuned mass damper of the parameter designing installation spring-quality system of original building main structure.
2. the TMD of installation spring-quality system according to claim 1 Optimization Design, it is characterised in that described
The process that step 1 establishes the mechanical model of the tuned mass damper of building main structure-installation spring-quality system is as follows：
Main structure will be built as a single-degree-of-freedom particle, determine that it damps c according to its material characteristicssWith rigidity ks, by single tuning
Mass damper device is in building main structure, and addition is one small again between building main structure and single tuned mass damper
Mass, added respectively between building main structure mass and small mass, small mass and single tuned mass damper
Rigidity is kt1、kt2Additional springs；The tuned mass damper of building main structure-installation spring-quality system is formed with this.
3. the TMD of installation spring-quality system according to claim 1 Optimization Design, it is characterised in that described
The kinetic equation that step 2 establishes the tuned mass damper of building main structure-installation spring-quality system is expressed as
Formula：
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In formula,For earthquake ground motion acceleration；ysDisplacement for building main structure relative to substrate；yTFor tuning quality
Damper is relative to the displacement for building main structure；ytDisplacement for small mass relative to building main structure；ms、csAnd ksRespectively
To build controlled vibration shape quality, damping and the rigidity of main structure；mT、cTAnd kTRespectively tuned mass damper quality, damping and
Rigidity；mtFor small mass quality；kt1The rigidity for the additional springs added between building main structure and small mass；kt2To be small
The rigidity for the additional springs added between mass and tuned mass damper.
4. the TMD of installation spring-quality system according to claim 1 Optimization Design, it is characterised in that described
The content that step 3 carries out vibration control optimization design to the tuned mass damper for installing spring-quality system is as follows：
The displacement dynamic magnification factor for building the tuned mass damper of main structure-installation spring-quality system is such as following formula：
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</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>R</mi>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>I</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
The dynamic magnification factor of tuned mass damper stroke is such as following formula：
<mrow>
<msub>
<mi>DMF</mi>
<msub>
<mi>H</mi>
<mi>T</mi>
</msub>
</msub>
<mo>=</mo>
<mo>|</mo>
<mfrac>
<mrow>
<msubsup>
<mi>&omega;</mi>
<mi>s</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>H</mi>
<mi>T</mi>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mover>
<mi>X</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mi>g</mi>
</msub>
</mfrac>
<mo>|</mo>
<mo>=</mo>
<mfrac>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mover>
<mi>R</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>e</mi>
<mi>T</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mover>
<mi>I</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>m</mi>
<mi>T</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>R</mi>
<mrow>
<mi>e</mi>
<mi>T</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>m</mi>
<mi>T</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
The dynamic magnification factor of small mass stroke is such as following formula：
<mrow>
<msub>
<mi>DMF</mi>
<msub>
<mi>H</mi>
<mi>t</mi>
</msub>
</msub>
<mo>=</mo>
<mo>|</mo>
<mfrac>
<mrow>
<msubsup>
<mi>&omega;</mi>
<mi>s</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>H</mi>
<mi>t</mi>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mover>
<mi>X</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mi>g</mi>
</msub>
</mfrac>
<mo>|</mo>
<mo>=</mo>
<mfrac>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mover>
<mi>R</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>e</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mover>
<mi>I</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>m</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>R</mi>
<mrow>
<mi>e</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>m</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
In formula：
<mrow>
<msub>
<mover>
<mi>R</mi>
<mo>&OverBar;</mo>
</mover>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>M</mi>
<mo>+</mo>
<msub>
<mi>E</mi>
<mn>11</mn>
</msub>
<msub>
<mi>&mu;</mi>
<mi>T</mi>
</msub>
<msubsup>
<mi>f</mi>
<mi>T</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msub>
<mi>E</mi>
<mn>21</mn>
</msub>
<msub>
<mi>&mu;</mi>
<mi>t</mi>
</msub>
<msubsup>
<mi>f</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<msub>
<mover>
<mi>I</mi>
<mo>&OverBar;</mo>
</mover>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>N</mi>
<mo>-</mo>
<mn>2</mn>
<msub>
<mi>E</mi>
<mn>11</mn>
</msub>
<msub>
<mi>&mu;</mi>
<mi>T</mi>
</msub>
<msub>
<mi>&xi;</mi>
<mi>T</mi>
</msub>
<msub>
<mi>f</mi>
<mi>T</mi>
</msub>
<mi>&lambda;</mi>
<mo>-</mo>
<msub>
<mi>E</mi>
<mn>22</mn>
</msub>
<msub>
<mi>&mu;</mi>
<mi>t</mi>
</msub>
<msubsup>
<mi>f</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<msub>
<mi>R</mi>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>M</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>2</mn>
<msub>
<mi>N&xi;</mi>
<mi>s</mi>
</msub>
<mi>&lambda;</mi>
<mo>-</mo>
<msub>
<mi>E</mi>
<mn>11</mn>
</msub>
<msub>
<mi>&mu;</mi>
<mi>T</mi>
</msub>
<msubsup>
<mi>f</mi>
<mi>T</mi>
<mn>2</mn>
</msubsup>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msub>
<mi>E</mi>
<mn>21</mn>
</msub>
<msub>
<mi>&mu;</mi>
<mi>t</mi>
</msub>
<msubsup>
<mi>f</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msub>
<mi>I</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>2</mn>
<msub>
<mi>M&xi;</mi>
<mi>s</mi>
</msub>
<mi>&lambda;</mi>
<mo>+</mo>
<mn>2</mn>
<msub>
<mi>E</mi>
<mn>11</mn>
</msub>
<msub>
<mi>&mu;</mi>
<mi>T</mi>
</msub>
<msub>
<mi>&xi;</mi>
<mi>T</mi>
</msub>
<msub>
<mi>f</mi>
<mi>T</mi>
</msub>
<msup>
<mi>&lambda;</mi>
<mn>3</mn>
</msup>
<mo>+</mo>
<msub>
<mi>E</mi>
<mn>22</mn>
</msub>
<msub>
<mi>&mu;</mi>
<mi>t</mi>
</msub>
<msubsup>
<mi>f</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msub>
<mover>
<mi>R</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>e</mi>
<mi>T</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>E</mi>
<mn>11</mn>
</msub>
<msub>
<mi>R</mi>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>E</mi>
<mn>11</mn>
</msub>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<msub>
<mover>
<mi>R</mi>
<mo>&OverBar;</mo>
</mover>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mover>
<mi>I</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>m</mi>
<mi>T</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>E</mi>
<mn>11</mn>
</msub>
<msub>
<mi>I</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>E</mi>
<mn>11</mn>
</msub>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<msub>
<mover>
<mi>I</mi>
<mo>&OverBar;</mo>
</mover>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
ReT(λ)=MRe(λ)-NIm(λ)
ImT(λ)=NRe(λ)+MIm(λ)
<mrow>
<msub>
<mover>
<mi>R</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>e</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>E</mi>
<mn>21</mn>
</msub>
<msub>
<mi>R</mi>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>E</mi>
<mn>22</mn>
</msub>
<msub>
<mi>I</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>E</mi>
<mn>21</mn>
</msub>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<msub>
<mover>
<mi>R</mi>
<mo>&OverBar;</mo>
</mover>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>E</mi>
<mn>22</mn>
</msub>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<msub>
<mover>
<mi>I</mi>
<mo>&OverBar;</mo>
</mover>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mover>
<mi>I</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>m</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>E</mi>
<mn>21</mn>
</msub>
<msub>
<mi>I</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>E</mi>
<mn>22</mn>
</msub>
<msub>
<mi>R</mi>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>E</mi>
<mn>21</mn>
</msub>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<msub>
<mover>
<mi>I</mi>
<mo>&OverBar;</mo>
</mover>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>E</mi>
<mn>22</mn>
</msub>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<msub>
<mover>
<mi>R</mi>
<mo>&OverBar;</mo>
</mover>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
Ret(λ)=MRe(λ)-NIm(λ)
Imt(λ)=NRe(λ)+MIm(λ)
E11=B21-B11
E21=A21-A11
E22=-A12
M=A11B21-A21B11
N=A12B21
<mrow>
<msub>
<mi>A</mi>
<mn>11</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msubsup>
<mi>f</mi>
<mi>T</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&eta;&beta;f</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
</mrow>
A12=-2 ξTfTλ
<mrow>
<msub>
<mi>B</mi>
<mn>11</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<msubsup>
<mi>&eta;&beta;f</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<msub>
<mi>B</mi>
<mn>21</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>&beta;</mi>
<mo>)</mo>
</mrow>
<msubsup>
<mi>f</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
</mrow>
In formula：λ is the frequency ratio of building main structure；fTFor the frequency ratio of tuned mass damper；ftFor building main structure and small matter
The frequency ratio of additional springs between gauge block；ξsTo build the damping ratio of main structure；ξTFor the damping ratio of tuned mass damper；μT
For tuned mass damper and the mass ratio of building main structure；μtFor small mass and the mass ratio of building main structure；η is small matter
The mass ratio of gauge block and tuned mass damper；β is additional springs kt2With additional springs kt1Ratio of rigidity；
In optimization process, according to Practical Project, λ, μ are setT、η、ξTValue, to fT、ftCarry out parameter optimization.
5. the TMD of installation spring-quality system according to claim 1 Optimization Design, it is characterised in that described
In step 4, optimized parameter interpretational criteria is defined：The main knot of building of the tuned mass damper of installation spring-quality system is set
The minimum of the minimum value of structure maximum power amplification coefficient, i.e.,
WhereinSmaller, then tuned mass damper vibration control validity is just
It is better；Parameter optimization is carried out using Gene hepatitis B vaccine, and compared with tuned mass damper.
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| CN107946030A (en) * | 2017-11-17 | 2018-04-20 | 国网青海省电力公司 | A kind of vibration isolation distribution transformer |
| CN108647383B (en) * | 2018-04-03 | 2022-07-12 | 上海大学 | Optimal design method for structure-enhanced tuned mass damper |
| CN108846240B (en) * | 2018-07-04 | 2022-05-24 | 苏州热工研究院有限公司 | Method for guiding equipment-support system anti-seismic design based on spring-mass model |
| CN109034363A (en) * | 2018-07-26 | 2018-12-18 | 太原科技大学 | Blower fan tower barrel vibration control method based on improved adaptive GA-IAGA |
| CN112867833B (en) * | 2019-07-03 | 2022-02-11 | 广州建筑股份有限公司 | Horizontal vibration control method for high-altitude lifting construction |
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| 《Optimum parameters of tuned mass damper for damped main system》;S.V Bakre and R. S. Jangid;《STRUCTURAL CONTROL AND HEALTH MONITORING》;20060427;第448-470页 * |
| 《TMD系统最优参数的实用设计方法》;李春祥等;《工业建筑》;19990131;第29卷(第1期);第30-34页 * |
| 《阻尼柔性连接TMD的最优动力特性》;李春祥等;《振动与冲击》;20020331;第21卷(第3期);第34-36页 * |
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