CN105332440B - Connection in series-parallel tuned mass damper Optimal Design Method - Google Patents
Connection in series-parallel tuned mass damper Optimal Design Method Download PDFInfo
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Abstract
The present invention provides a kind of connection in series-parallel tuned mass damper optimum design method, it comprises the following steps：Establish the system model of structure-DSPTMD；According to Structural Dynamics principle, building main structure-DSPTMD system dynamics equations are established；TMD, DPTMD are contrasted, carries out the optimization design of vibration control using genetic algorithm to connection in series-parallel tuned mass damper；By reference to optimum results, consider the validity of control and the validity of damping system stroke control, optimum combination parameter is selected, for instructing actual engineering design.The present invention can realize the significantly lifting of validity by adjusting the ratio between two mass blocks for TMD；At the same time in the range of certain mass ratio, the stroke of DSPTMD can be greatly lowered, simultaneously effective the dynamic respond of Earthquake occurrence control effect lower structure.For DPTMD, damping can be greatly lowered on the basis of validity is slightly lifted in DSPTMD, while can continue reduction stroke when the ratio between two mass blocks are in a certain scope, realize optimum control.
Description
Technical field
The present invention relates to a kind of connection in series-parallel tuned mass damper (Double-Series-Parallel Tuned Mass
Dampers, DSPTMD) Optimal Design Method.
Background technology
Earthquake is natural calamity that is a kind of common and happening suddenly again, and foresight is still very low so far, and widely distributed, destruction is sternly
Weight, once occur that very serious loss will be caused to the mankind.Earthquake except cause house destroy and collapse, casualties etc. it is straight
It is outer to connect influence, can also trigger the secondary disasters such as fire and disease, cause huge security risk and economic loss.China is the world
On suffer disaster from an earthquake one of the country of most serious.
The research and application of vibration control of civil engineering structure are considered as the great prominent of structures under wind earthquake research field
It is broken.It breaches traditional construction design method, for example increases the rigidity of structure, resistance even if only relying on and changing structure self performance
Buddhist nun and change Mass Distribution etc. are developed into by structure-wind resistance antidetonation to resist the method for environmental load (such as high wind and macroseism)
Vibration control system actively controls the dynamic response of structure.1972, Chinese descendant in America scholar Yao Zhiping was systematically proposed first
Structure Active Control concept.He suggests, using classical or modern control theory, some control systems being installed in structure.Structure
Under wind and geological process, these control systems being mounted thereon produce controling power, can significantly reduce the dynamic response of structure.
Structural vibration control is generally divided into passive control, active control, semi- active control and mixing control according to whether outside resources
Make four classes.
Structure intelligent is the important component of building intellectualization.And structure intelligent is most importantly it to natural calamity
The defence capability of evil (such as high wind and macroseism).In real time measurement and monitoring structure disaster respond, the damage of detecting structure and bend
Clothes, implement controling power through the servo-drive system that computer is handled online from trend structure.Structural vibration control technology is existing wind resistance
The reparation and transformation of shock resistance and durability deficiency building provide feasible and thoroughly solve method, are also built for future
Aseismic Design of the building structure based on performance-based provides feasible method.In each branch of structural vibration control, mass tuning
Damping technology is a kind of technology of relative maturity, because it is low with requiring control element, can be directly mounted at building structure, nothing
Structure design need to be changed and just can be suitably used for a series of feature such as existed building, in skyscraper, tall and slender structure, Longspan Bridge
In have been widely used.In recent years, application of the tuned mass damper at home and abroad on some important buildings is more wide
It is general.Such as：The pendulum-type eddy current tuned mass damper of Shanghai Center Building；The wind that 150 tons of Shanghai World Financial Center two
Damper；Swing TMD (Tuned Mass Dampers, tuned mass damper) system of Taipei 101 mansion etc..
TMD has been obtained for very deep thorough grind as the high-performance vibration reduction equipment generally acknowledged in a kind of world wide
Study carefully.But two big main problems are existing for TMD：First, only when the natural frequency of vibration and structure of TMD, itself natural frequency of vibration is consistent
Or when close, the vibration control effect of TMD can just reach optimum state, and in Practical Project due to construction or the external world
The influence of environment can cause the natural frequency of vibration of TMD not reach expecting state, cause off resonance.TMD can only be in limited frequency band at the same time
Damping is carried out in wide scope, it is ineffective for Near-source earthquake；The stroke of second, TMD mass block is excessive, when mass block is adjusted
It is easy to collide with superstructure during humorous vibration damping, have impact on the application of Practical Project.At present, the main of domestic and foreign scholars is ground
It is exactly that invention designs a kind of new vibration control apparatus to study carefully one of thinking, while takes into account validity and stroke problem, realizes building
The vibration damping damping of structure.
The content of the invention
In view of the defects existing in the prior art, the technical problems to be solved by the invention are to provide a kind of connection in series-parallel tuning matter
Damper Optimal Design Method is measured, for TMD, can be realized effectively by adjusting the ratio between two mass blocks
The significantly lifting of property；At the same time in the range of certain mass ratio, the stroke of DSPTMD can be greatly lowered, simultaneously effective
Earthquake occurrence control acts on the dynamic respond of lower structure.For DPTMD, DSPTMD can on the basis of validity is slightly lifted
Damping is greatly lowered, while reduction stroke can be continued when the ratio between two mass blocks are in a certain scope, realized most
Excellent control.
In order to solve the above technical problems, the present invention is using such as following technical proposals：A kind of connection in series-parallel tuned mass damper
Optimum design method, it is characterised in that it includes the following steps：
Step 1, establishes the model of connection in series-parallel tuned mass damper, and detailed process is as follows：In traditional TMD mono- first
On the basis of mass block, increase by second mass block, and installation in parallel, spring and damper is respectively adopted by the first matter
Gauge block and the second mass block are connected in building main structure, form the parallel resonant being made of the first mass block and the second mass block
Mass damper, on the basis of parallel resonant mass damper, one is reconnected between the first mass block and the second mass block
A damper, its damping are denoted as cT, form connection in series-parallel tuned mass damper；
Step 2, according to Structural Dynamics principle, stress is carried out to building main structure and connection in series-parallel tuned mass damper
Analysis, establishes the kinetic equation of building main structure-DSPTMD systems；
Step 3, contrast TMD, parallel resonant mass damper DPTMD, vibrates connection in series-parallel tuned mass damper
The optimization design of control；
Step 4, by reference to optimum results, considers the validity of control and the validity of damping system stroke control, choosing
Optimum combination parameter is selected, with reference to the parameter designing connection in series-parallel tuned mass damper of original structure.
Preferably, the mechanical model of building main structure-DSPTMD systems is established in the step 1：Main structure will be built
As a single-degree-of-freedom particle, its damping and rigidity are determined according to its material characteristics, in traditional mono- the first mass block of TMD
On the basis of, increase by second mass block, and installation in parallel, is respectively adopted spring and damper by the first mass block and the
Two mass blocks are connected in building main structure, form the parallel resonant Tuned mass damper being made of the first mass block and the second mass block
Device；On the basis of parallel resonant mass damper, a damper is reconnected between the first mass block and the second mass block,
Its damping is denoted as cT, connection in series-parallel tuned mass damper is formed, that is, builds main structure-DSPTMD systems.
Preferably, the kinetic equation of the step 2 foundation building main structure-DSPTMD systems is expressed as following formula：
In formula,For earthquake ground motion acceleration；ySDisplacement for building main structure relative to substrate；To build
Build speed of the main structure relative to substrate；Acceleration for building main structure relative to substrate；y1、y2For TMD1, TMD2 matter
Gauge block is relative to the displacement for building main structure；Speed for TMD1, TMD2 mass block relative to building main structure；Acceleration for ATMD mass blocks relative to building main structure；mS、cSAnd kSRespectively build the controlled vibration shape of main structure
Quality, damping and rigidity；m1、c1And k1The respectively quality of TMD1, damping and rigidity；m2、c2And k2Respectively the quality of TMD2,
Damping and rigidity；cTFor the damping of the first mass block of connection and the second mass block.
Preferably, the optimization design for carrying out vibration control in the step 3 to connection in series-parallel tuned mass damper is as follows
Content：
Build the displacement dynamic magnification factor such as following formula of main structure-DSPTMD systems：
The dynamic magnification factor of TMD1 strokes is such as following formula：
The dynamic magnification factor of TMD2 strokes is such as following formula：
In formula：λ is the frequency ratio of building main structure；Dynamic magnification factor is by assuming building main structure by simple harmonic quantity external excitation
When try to achieve, external excitation load is expressed asyS=[HS(-iw)]e-iwt, y1=[H1(-iw)]e-iwt, y2=[H2(-iw)]e-iwt。
Preferably, optimized parameter interpretational criteria defined in the step 4：Building for connection in series-parallel tuned mass damper is set
Build the minimum of the minimum value of main structure maximum power amplification coefficient；Using genetic algorithm carry out parameter optimization, and with TMD,
DPTMD is compared.
Compared with prior art, the present invention has the advantages that the substantive distinguishing features and notable protruded as follows：Relative to TMD
Speech, the significantly lifting of validity can be realized by adjusting the ratio between two mass blocks；At the same time in certain mass ratio
In the range of, the stroke of DSPTMD can be greatly lowered, and the simultaneously effective displacement of the lower building main structure of Earthquake occurrence control effect is rung
Should.For DPTMD, damping can be greatly lowered on the basis of validity is slightly lifted in DSPTMD, while two
The ratio between a mass block can continue to reduce stroke when being in a certain scope, realize optimum control.
Brief description of the drawings
Fig. 1 is connection in series-parallel tuned mass damper (DSPTMD) design analytic process figure；
Fig. 2 is the schematic diagram of connection in series-parallel tuned mass damper (DSPTMD) system model；
Fig. 3 is the flow chart using genetic algorithm optimization；
When Fig. 4 is μ=0.01, when TMD, DPTMD, DSPTMD correspond to different ηThe signal of variation relation curve
Figure；
When Fig. 5 is μ=0.01, f when DPTMD, DSPTMD correspond to different η1Variation relation curve schematic diagram；
When Fig. 6 is μ=0.01, f when DPTMD, DSPTMD correspond to different η2Variation relation curve schematic diagram；
When Fig. 7 is μ=0.01, ξ when DPTMD, DSPTMD correspond to different η1Variation relation curve schematic diagram；
When Fig. 8 is μ=0.01, ξ when DPTMD, DSPTMD correspond to different η2Variation relation curve schematic diagram；
When Fig. 9 is μ=0.01, ξ when DSPTMD corresponds to different ηTVariation relation curve schematic diagram；
When Figure 10 is μ=0.01, when TMD, DPTMD, DSPTMD correspond to different ηThe signal of variation relation curve
Figure；
When Figure 11 is μ=0.01, when TMD, DPTMD, DSPTMD correspond to different ηThe signal of variation relation curve
Figure.
Embodiment
Below in conjunction with the accompanying drawings, the specific embodiment of the present invention is further described.
As shown in Figure 1, connection in series-parallel tuned mass damper optimum design method of the present invention includes the following steps：
Step 1, establishes the model (building main structure-DSPTMD system models) of connection in series-parallel tuned mass damper,
Detailed process is as follows：On the basis of traditional mono- the first mass block m1 of TMD, increase by a second mass block m2, and it is flat with it
Row installation, is respectively adopted spring and damper and the first mass block m1 and the second mass block m2 is connected in building main structure, structure
Into the parallel resonant mass damper being made of two mass blocks (the first mass block m1 and the second mass block m2).In parallel resonant
On the basis of mass damper, a damping is reconnected between two mass blocks (the first mass block m1 and the second mass block m2)
Device, its damping are denoted as cT, form connection in series-parallel tuned mass damper.
Step 2, according to Structural Dynamics principle, stress is carried out to building main structure and connection in series-parallel tuned mass damper
Analysis, establishes the kinetic equation of building main structure-DSPTMD systems；
Step 3, contrast TMD, parallel resonant mass damper DPTMD, vibrates connection in series-parallel tuned mass damper
The optimization design of control；
Step 4, by reference to optimum results, considers the validity of control and the validity of damping system stroke control, choosing
Optimum combination parameter is selected, with reference to the parameter designing connection in series-parallel tuned mass damper of original structure.
As shown in Fig. 2, the mechanical model of structure-DSPTMD systems is established in the step 1：Main structure conduct will be built
One single-degree-of-freedom particle, determines its damping and rigidity, in the base of traditional mono- the first mass block m1 of TMD according to its material characteristics
On plinth, increase by a second mass block m2, and installation in parallel, is respectively adopted spring and damper and is connected to m1 and m2 and build
Build in main structure, form the parallel resonant Tuned mass damper being made of two mass blocks (the first mass block m1 and the second mass block m2)
Device.On the basis of parallel resonant mass damper, between two mass blocks (the first mass block m1 and the second mass block m2)
A damper is reconnected, its damping is denoted as cT, connection in series-parallel tuned mass damper is formed, that is, builds main structure-DSPTMD systems
System.
The kinetic equation of building main structure-DSPTMD systems is established in the step 2：Respectively to building main structure, TMD
Mass block carries out force analysis, according to theory of structural dynamics, lists its system equation as following formula (1), (2), (3)：
In formula,For earthquake ground motion acceleration；ySDisplacement for building main structure relative to substrate；To build
Build speed of the main structure relative to substrate；Acceleration for building main structure relative to substrate；y1、y2For TMD1, TMD2 matter
Gauge block is relative to the displacement for building main structure；Speed for TMD1, TMD2 mass block relative to building main structure；Acceleration for ATMD mass blocks relative to building main structure；mS、cSAnd kSRespectively build the controlled vibration shape of main structure
Quality, damping and rigidity；m1、c1And k1The respectively quality of TMD1, damping and rigidity；m2、c2And k2Respectively the quality of TMD2,
Damping and rigidity；cTTo connect the damping of the first mass block m1 and the second mass block m2.
The optimization design for carrying out vibration control in the step 3 to connection in series-parallel tuned mass damper is following content：
Build the displacement (y of main structure-DSPTMD systemss) dynamic magnification factor such as following formula (4)：
The dynamic magnification factor of TMD1 strokes is such as following formula (5)：
The dynamic magnification factor of TMD2 strokes is such as following formula (6)：
In order to which formula calculates succinct, order：
D1a=2 ξ1f1λ+βξTλ(f1+f2)(1+η)
D1b=2 ξ1f1λ+βξTλ(f1+f2)
D2a=2 ξ2f2λ+βξTλ(f1+f2)(1+η)
D1=2 ξ1f1λ D2=2 ξ2f2λ Ds=2 ξsλ DT=β ξTλ(f1+f2)
Meet below equation in above-mentioned formula, such as following formula (7) to formula (18)：
Re2(λ)=Re (λ) ... ... ... (17)
Im2(λ)=Im (λ) ... ... ... (18)
In formula：λ is the frequency ratio of building main structure；f1For the frequency ratio of TMD1；f2For the frequency ratio of TMD2；ξSFor building
The damping ratio of main structure；ξ1For the damping ratio of TMD1；ξ2For the damping ratio of TMD2；ξTFor the damping ratio of connection damping；μ is two
The sum of TMD and the mass ratio for building main structure；η is the ratio between the first mass block m1 and the second mass block m2.
In optimization process, according to Practical Project, ξ is setS, μ, η value, to f1、f2、ξ1、ξ2、ξTCarry out parameter optimization.
Optimized parameter interpretational criteria defined in the step 4：The building main structure of connection in series-parallel tuned mass damper is set
The minimum of the minimum value of maximum power amplification coefficient, i.e., More
Small, then device vibration control validity is just about good；Parameter optimization is carried out using genetic algorithm, and compared with TMD, DPTMD.
Optimize calculating with genetic algorithm, for the ratio between the first mass block m1 and the second mass block m2 η take η=
0.125th, η=0.25, η=0.5, η=0.75, η=1.0 5 kind situation discussion, for mass ratio, incorporation engineering actually only considers
The situation of μ=0.01.
As seen from Figure 4, in the case where total mass ratio is constant, by adjusting the first mass block m1 and the second mass
The mass ratio of block m2, can make DSPTMD vibration control validity be improved significantly, and being continuously increased with η
Effect property is gradually reduced, and η is smaller, and validity is better.And the validity of DSPTMD is substantially better than TMD, slightly carried relative to DPTMD
Rise.
By the variation tendency that Fig. 5 is 1 optimal frequency ratios of DPTMD, DSPTMD mass block, with the increase of η, DPTMD's
f1,optIt is in rising trend, tend towards stability afterwards；And the f of DSPTMD1,optIt is on a declining curve.Fig. 6 is DPTMD, DSPTMD mass block
The variation tendency of 2 optimal frequency ratios, with the increase of η, the equal f of DPTMD, DSPTMD2,optIt is in rising trend.Comparison diagram 5, Fig. 6
We are, it is apparent that the vibration control effective bandwidth of DSPTMD is significantly greater than the bandwidth of DPTMD.Further illustrate
Vibration control effect excellent DSPTMD.
Fig. 7 is the variation tendency of 1 Optimal damping ratio of DPTMD, DSPTMD mass block, with the increase of η, the ξ of DPTMD1,opt
It is on a declining curve, and the ξ of DSPTMD1,optIt is always 0.Fig. 8 is that the change of 2 Optimal damping ratio of DPTMD, DSPTMD mass block becomes
Gesture, with the increase of η, the ξ of DPTMD, DSPTMD2,optIt is on a declining curve.Fig. 9 is the connection Optimal damping ratio of DSPTMD
ξT,optVariation tendency, with the increase ξ of ηT,optGradually reduce.Complex chart 7, although, Fig. 8, Fig. 9 be it can be found that DSPTMD systems
Employ three dampers in system, but actual optimization the result shows that ξ1,optValue be always zero, therefore can in Practical Project
To remove.In the case where using two dampers, two optimization dampings of DSPTMD are all optimal significantly lower than DPTMD
Change damping, but validity can have been lifted, it is not only economical but also efficient.
Figure 10, Figure 11 are respectively the stroke of the first mass block m1 and the second mass block m2 of DPTMD, DSPTMD with the change of η
The stroke of change situation and TMD, in general, two mass blocks (the first mass block m1 and the second matter of DPTMD, DSPTMD
Gauge block m2) stroke nearly all increase with the increase of the ratio between mass block η.But for TMD, DPTMD, DSPTMD
The stroke of two mass blocks is all significantly less than the stroke of TMD single mass.When η 0.25~0.5 in the range of this when,
The stroke of two mass blocks of DSPTMD is respectively less than the stroke of two mass blocks of DPTMD.
Complex chart 4 is can be found that to Figure 11：When overall quality than it is constant when, the validity of DPTMD and DSPTMD relative to
TMD, which has, significantly to be lifted, when the ratio between two mass blocks η is in a certain range, the stroke of both two mass blocks
The respectively less than stroke of TMD single mass.The validity of DSPTMD vibration controls is slightly lifted relative to DPTMD, but two
The damping of mass block is but greatly lowered.When the ratio between two mass blocks η is in a certain range, two quality of DSPTMD
The stroke of block also has obvious reduction relative to DPTMD's.
In summary describe, consider economic factor and the possibility realized, provided for connection in series-parallel tuned mass damper
Optimal design parameters combination is as follows：μS=0.02, μ=0.01, η=0.25, f1=1.44, ξ1=0, f2=0.67, ξ2=
0.092, ξT=0.108,Above parameter is in zone of reasonableness
It is interior, the design that this group of data carry out DSPTMD devices is may be referred in Practical Project.
Claims (5)
1. a kind of connection in series-parallel tuned mass damper optimum design method, it is characterised in that it includes the following steps：
Step 1, establishes the model of connection in series-parallel tuned mass damper DSPTMD, and detailed process is as follows：At traditional TMD mono-
On the basis of one mass block TMD1, increase by a second mass block TMD2, and installation in parallel, spring and damping is respectively adopted
First mass block TMD1 and the second mass block TMD2 are connected in building main structure by device, are formed by the first mass block TMD1 and the
The parallel resonant mass damper DPTMD of two mass block TMD2 compositions, on the basis of parallel resonant mass damper DPTMD,
A damper is reconnected between the first mass block TMD1 and the second mass block TMD2, its damping is denoted as cT, form connection in series-parallel
Tuned mass damper DSPTMD；
Step 2, according to Structural Dynamics principle, building main structure and connection in series-parallel tuned mass damper DSPTMD are carried out by
Power is analyzed, and establishes the kinetic equation of building main structure-connection in series-parallel tuned mass damper DSPTMD systems；
Step 3, contrast TMD, parallel resonant mass damper DPTMD, shakes connection in series-parallel tuned mass damper DSPTMD
The optimization design of dynamic control；
Step 4, by reference to optimum results, considers the validity of vibration control and the validity of damping system stroke control, choosing
Optimum combination parameter is selected, with reference to the parameter designing connection in series-parallel tuned mass damper DSPTMD of original structure.
2. connection in series-parallel tuned mass damper optimum design method according to claim 1, it is characterised in that the step
The mechanical model of building main structure-connection in series-parallel tuned mass damper DSPTMD systems is established in one：Main structure conduct will be built
One single-degree-of-freedom particle, determines its damping and rigidity, traditional mono- the first mass block TMD1's of TMD according to its material characteristics
On the basis of, increase by a second mass block TMD2, and installation in parallel, spring and damper is respectively adopted by the first mass block
TMD1 and the second mass block TMD2 is connected in building main structure, is formed by the first mass block TMD1 and the second mass block TMD2 groups
Into parallel resonant mass damper DPTMD；On the basis of parallel resonant mass damper DPTMD, in the first mass block
A damper is reconnected between TMD1 and the second mass block TMD2, its damping is denoted as cT, form the damping of connection in series-parallel tuning quality
Device DSPTMD, that is, build main structure-connection in series-parallel tuned mass damper DSPTMD systems.
3. connection in series-parallel tuned mass damper optimum design method according to claim 1, it is characterised in that the step
Two kinetic equations for establishing building main structure-connection in series-parallel tuned mass damper DSPTMD systems are expressed as following formula：
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</msub>
<mo>+</mo>
<msub>
<mi>k</mi>
<mn>2</mn>
</msub>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>c</mi>
<mi>T</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>y</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>y</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
In formula,For earthquake ground motion acceleration；ySDisplacement for building main structure relative to substrate；For building
Main structure relative to substrate speed；Acceleration for building main structure relative to substrate；y1、y2For the first mass block
TMD1, the second mass block TMD2 are relative to the displacement for building main structure；For the first mass block TMD1, the second mass block
TMD2 is relative to the speed for building main structure；It is the first mass block TMD1, the second mass block TMD2 relative to building
The acceleration of main structure；mS、cSAnd kSRespectively build controlled vibration shape quality, damping and the rigidity of main structure；m1、c1And k1Respectively
For quality, damping and the rigidity of the first mass block TMD1；m2、c2And k2Respectively the quality of the second mass block TMD2, damping and just
Degree；cTTo connect the damping of the damper of the first mass block TMD1 and the second mass block TMD2.
4. connection in series-parallel tuned mass damper optimum design method according to claim 1, it is characterised in that the step
The optimization design for carrying out vibration control in three to connection in series-parallel tuned mass damper DSPTMD is following content：
Build the displacement dynamic magnification factor such as following formula of main structure-connection in series-parallel tuned mass damper DSPTMD systems：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>DMF</mi>
<msub>
<mi>H</mi>
<mi>S</mi>
</msub>
</msub>
<mo>=</mo>
<mo>|</mo>
<msub>
<mi>TRF</mi>
<msub>
<mi>H</mi>
<mi>S</mi>
</msub>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>w</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<mo>=</mo>
<mo>|</mo>
<mfrac>
<mrow>
<msubsup>
<mi>w</mi>
<mi>S</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>H</mi>
<mi>S</mi>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mi>g</mi>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>|</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mo>|</mo>
<mfrac>
<mrow>
<mover>
<mi>Re</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>i</mi>
<mover>
<mi>Im</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>Re</mi>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>i</mi>
<mi>Im</mi>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>|</mo>
<mo>=</mo>
<mfrac>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>&lsqb;</mo>
<mover>
<mi>Re</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<mover>
<mi>Im</mi>
<mo>&OverBar;</mo>
</mover>
<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>
<mi>Re</mi>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<mi>Im</mi>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula,For the transmission function expression formula of main structure；wsFor main structure circular frequency；W is external excitation circle frequency
Rate；Re is the real part after formula arranges；Im is the imaginary part after formula arranges；H function represents transmission function；λ is to build
Build the frequency ratio of main structure；
The dynamic magnification factor of first mass block TMD1 strokes is such as following formula：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>DMF</mi>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
</msub>
<mo>=</mo>
<mo>|</mo>
<msub>
<mi>TRF</mi>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>w</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<mo>=</mo>
<mo>|</mo>
<mfrac>
<mrow>
<msubsup>
<mi>w</mi>
<mi>S</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mi>g</mi>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>|</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mo>|</mo>
<mfrac>
<mrow>
<msub>
<mover>
<mi>Re</mi>
<mo>&OverBar;</mo>
</mover>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>i</mi>
<msub>
<mover>
<mi>Im</mi>
<mo>&OverBar;</mo>
</mover>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>Re</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>iIm</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>|</mo>
<mo>=</mo>
<mfrac>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mover>
<mi>Re</mi>
<mo>&OverBar;</mo>
</mover>
<mn>1</mn>
</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>Im</mi>
<mo>&OverBar;</mo>
</mover>
<mn>1</mn>
</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>Re</mi>
<mn>1</mn>
</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>Im</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula,For the transmission function expression formula of the first mass block TMD1；
The dynamic magnification factor of second mass block TMD2 strokes is such as following formula：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>DMF</mi>
<msub>
<mi>H</mi>
<mn>2</mn>
</msub>
</msub>
<mo>=</mo>
<mo>|</mo>
<msub>
<mi>TRF</mi>
<msub>
<mi>H</mi>
<mn>2</mn>
</msub>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>w</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<mo>=</mo>
<mo>|</mo>
<mfrac>
<mrow>
<msubsup>
<mi>w</mi>
<mi>S</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>H</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mi>g</mi>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>i</mi>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>|</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mo>|</mo>
<mfrac>
<mrow>
<msub>
<mover>
<mi>Re</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>i</mi>
<msub>
<mover>
<mi>Im</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>Re</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>iIm</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>|</mo>
<mo>=</mo>
<mfrac>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mover>
<mi>Re</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</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>Im</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</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>Re</mi>
<mn>2</mn>
</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>Im</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula：TRFH2(- iw) is the transmission function expression formula of the second mass block TMD2；Dynamic magnification factor builds main knot by assuming
Tried to achieve when structure is by simple harmonic quantity external excitation, be by external excitation load tableyS=[HS(-
iw)]e-iwt, y1=[H1(-iw)]e-iwt, y2=[H2(-iw)]e-iwt。
5. connection in series-parallel tuned mass damper optimum design method according to claim 1, it is characterised in that the step
Optimized parameter interpretational criteria defined in four：The building main structure maximum power of connection in series-parallel tuned mass damper DSPTMD is set to put
The minimum of the minimum value of big coefficient；Using genetic algorithm carry out parameter optimization, and with TMD, parallel resonant mass damper
DPTMD is compared.
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| CN101832359A (en) * | 2010-05-21 | 2010-09-15 | 北京工业大学 | Optimization method of tuned mass damper of elastic support dry friction |
| TW201113449A (en) * | 2009-10-13 | 2011-04-16 | Nat Applied Res Laboratories | Planar unsymmetrical structure vibration suppression method, coupled-tuned mass damper design method, computer program product and coupled-tuned mass damper |
| CN104131629A (en) * | 2014-04-09 | 2014-11-05 | 上海大学 | Wind-induced vibration control and optimum design method for structure hybrid active tuned mass damper |
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| CN101413295A (en) * | 2008-11-24 | 2009-04-22 | 中国海洋大学 | Self-adapting frequency conversion tuning quality damping vibration attenuation apparatus and self-adapting frequency conversion method thereof |
| TW201113449A (en) * | 2009-10-13 | 2011-04-16 | Nat Applied Res Laboratories | Planar unsymmetrical structure vibration suppression method, coupled-tuned mass damper design method, computer program product and coupled-tuned mass damper |
| CN101832359A (en) * | 2010-05-21 | 2010-09-15 | 北京工业大学 | Optimization method of tuned mass damper of elastic support dry friction |
| CN104131629A (en) * | 2014-04-09 | 2014-11-05 | 上海大学 | Wind-induced vibration control and optimum design method for structure hybrid active tuned mass damper |
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