CN105155714B - Parallel resonant mass damper Optimal Design Method - Google Patents
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Abstract
The present invention provides a kind of parallel resonant mass damper Optimization Design, and it comprises the following steps：Establish building main structure-DPTMD system model；According to Structural Dynamics principle, building main structure-DPTMD system dynamics equations are established；Tuned mass damper is contrasted, carries out the optimization design of vibration control using genetic algorithm to parallel resonant 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 increase substantially the validity of vibration control within the specific limits by adjusting the ratio between mass, significantly decrease stroke, simultaneously effective the dynamic respond of the lower structure of Earthquake occurrence control effect relative to TMD.
Description
Technical field
The present invention relates to a kind of parallel resonant mass damper (Double-Parallel Tuned Mass Dampers,
DPTMD) Optimization Design.
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 potential safety hazard 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 from trend structure through the servo-drive system that computer is handled online.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, requires low to control element because it has, 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 obtain a wide range of applications.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.In the last few years, it is to seek new vibration control to set in one of structural vibration control research field, research direction of scholars
It is standby, the validity of vibration control is further enhanced, reduces stroke.Simultaneously in order to consider the possibility realized, economic factor is also
One significant problem.On the premise of economical rationality, easily realizing, it is vibration to seek a kind of efficiently succinct vibration control equipment
One new research direction of control field.
The content of the invention
The defects of existing for prior art, the technical problems to be solved by the invention are to provide a kind of parallel resonant quality
Damper Optimal Design Method, compared to traditional TMD, by adjusting the ratio between two masses, it is possible to achieve have
The significantly lifting of effect property；Simultaneously relative to traditional TMD, in the range of certain mass ratio, DPTMD stroke can be significantly
Degree reduces, simultaneously effective the dynamic respond of the lower structure of Earthquake occurrence control effect.
In order to solve the above technical problems, the present invention is using such as following technical proposals：A kind of parallel resonant mass damper is excellent
Change design method, it is characterised in that it comprises the following steps：
Step 1, establishes the model of parallel resonant mass damper, and detailed process is as follows：In traditional mono- the first matter of TMD
On the basis of measuring m1, increase by second mass, and installation in parallel, spring and damper is respectively adopted by the first mass
Block and the second mass are connected in building main structure, form the parallel resonant mass damper being made up of two masses；
Step 2, according to Structural Dynamics principle, stress point is carried out to building main structure and parallel resonant mass damper
Analysis, establish the kinetic equation of building main structure-DPTMD systems；
Step 3, TMD is contrasted, the optimization design of vibration control is carried out to parallel resonant mass damper；
Step 4, by reference to optimum results, consider the validity of control and the validity of damping system stroke control, choosing
Optimum combination parameter is selected, with reference to the parameter designing parallel resonant mass damper of original building main structure.
Preferably, the mechanical model of building main structure-DPTMD systems is established in the step 1：Building main structure is made
For a single-degree-of-freedom particle, its damping and rigidity are determined according to its material characteristics, on the basis of traditional masses of TMD first
One the second mass of parallel increase, the first mass and the second mass using two sleeve springs and damping be connected to and built respectively
Build in main structure, constitute the parallel resonant mass damper being made up of two masses, that is, build main structure-DPTMD systems
System.
Preferably, the kinetic equation of the step 2 foundation building main structure-SPTMD 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 relative to building main structure；Acceleration for ATMD masses relative to building main structure；mS、cSAnd kSRespectively building the controlled of main structure is shaken
Type quality, damping and rigidity；m1、c1And k1Respectively TMD1 quality, damping and rigidity；m2、c2And k2Respectively TMD2 matter
Amount, damping and rigidity.
Preferably, the optimization design for carrying out vibration control in the step 3 to parallel resonant mass damper is following interior
Hold：
Build the displacement dynamic magnification factor such as following formula of main structure-DPTMD 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, be by external excitation load tableyS=[HS(-iw)]e-iwt, y1=[H1(-iw)]e-iwt,
y2=[H2(-iw)]e-iwt。
Preferably, optimized parameter interpretational criteria defined in the step 4：The building of parallel resonant mass damper is set
The minimum of the minimum value of main structure maximum power amplification coefficient；Parameter optimization is carried out using genetic algorithm, and is entered with traditional TMD
Row compares.
Compared with prior art, the present invention have substantive distinguishing features prominent as follows and it is notable the advantages of：For existing skill
The defects of art is present, the technical problems to be solved by the invention are to provide a kind of parallel resonant mass damper optimized design side
Method, compared to traditional TMD, by adjusting the ratio between two masses, it is possible to achieve the significantly lifting of validity；Together
When relative to traditional TMD, in the range of certain mass ratio, DPTMD stroke can be greatly lowered, and simultaneously effective control
The dynamic respond of Structures under Earthquake processed.
Brief description of the drawings
Fig. 1 is parallel resonant mass damper (DPTMD) design analysis procedure chart；
Fig. 2 is the schematic diagram of parallel resonant mass damper (DPTMD) system model；
Fig. 3 is the flow chart using genetic algorithm optimization；
When Fig. 4 is μ=0.01, f when DPTMD corresponds to different η1Variation relation curve schematic diagram；
When Fig. 5 is μ=0.01, f when DPTMD corresponds to different η2Variation relation curve schematic diagram；
When Fig. 6 is μ=0.01, ξ when DPTMD corresponds to different η1Variation relation curve schematic diagram；
When Fig. 7 is μ=0.01, ξ when DPTMD corresponds to different η2Variation relation curve schematic diagram；
When Fig. 8 is μ=0.01, TMD'sAnd DPTMD is when corresponding to different ηVariation relation curve shows
It is intended to；
When Fig. 9 is μ=0.01, TMD'sAnd DPTMD is when corresponding to different ηVariation relation curve shows
It is intended to；
When Figure 10 is μ=0.01, TMD'sAnd DPTMD is when corresponding to different ηVariation relation curve shows
It is intended to.
Embodiment
Below in conjunction with the accompanying drawings, the specific embodiment of the present invention is further described.
As shown in figure 1, parallel resonant mass damper Optimization Design of the present invention comprises the following steps：
Step 1, establish the model (building main structure-DPTMD system models) of parallel resonant mass damper.It has
Body composition is as follows：On the basis of traditional mono- the first mass m1 of TMD, increase by a second mass m2, and it is in parallel
Installation, spring and damper is respectively adopted the first mass m1 and the second mass m2 are connected in building main structure, form
The parallel resonant mass damper being made up of two masses.
Step 2, according to Structural Dynamics principle, stress point is carried out to building main structure and parallel resonant mass damper
Analysis, establish the kinetic equation of building main structure-DPTMD systems；
Step 3, TMD is contrasted, the optimization design of vibration control is carried out to parallel resonant mass damper；
Step 4, by reference to optimum results, consider the validity of control and the validity of damping system stroke control, choosing
Optimum combination parameter is selected, with reference to the parameter designing parallel resonant mass damper of original structure.
As shown in Fig. 2 the mechanical model of building main structure-DPTMD systems is established in the step 1：Main knot will be built
Structure determines its damping and rigidity, traditional the first masses of TMD m1's as a single-degree-of-freedom particle according to its material characteristics
On the basis of one the second mass m2 of parallel increase, using two sleeve springs and damping respectively by the first mass m1 and the second mass
Block m2 be connected to building main structure on, constitute it is being made up of two masses (the first mass m1 and the second mass m2) and
Join tuned mass damper, that is, build main structure-DPTMD systems.
The kinetic equation of building main structure-DPTMD systems is established in the step 2：Structure, TMD are carried out respectively by
Power is analyzed, and 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 relative to building main structure；Acceleration for ATMD masses relative to building main structure；mS、cSAnd kSRespectively building the controlled of main structure is shaken
Type quality, damping and rigidity；m1、c1And k1Respectively TMD1 quality, damping and rigidity；m2、c2And k2Respectively TMD2 matter
Amount, damping and rigidity.
The optimization for carrying out vibration control in the step 3 to the connection in series-parallel tuned mass damper based on controllable stroke is set
It is calculated as following content：
Build the displacement (y of main structure-DPTMD 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：
D1=2 ξ1f1λ D2=2 ξ2f2λ Ds=2 ξsλ
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 TMD1 frequency ratio；f2For TMD2 frequency ratio；ξSFor building
The damping ratio of main structure；ξ1For TMD1 damping ratio；ξ2For TMD2 damping ratio；μ is two TMD sums and building main structure
Mass ratio；η is the ratio between the first mass m1 and the second mass m2.
In optimization process, according to Practical Project, ξ is setS, μ, η value, to f1、f2、ξ1、ξ2Carry out parameter optimization.
Optimized parameter interpretational criteria defined in the step 4：Enhanced active tuning quality based on damping connection is set
The minimum of the minimum value of the structure maximum power amplification coefficient of damper, i.e., Smaller, then device vibration control validity is just about good；Parameter optimization is carried out using genetic algorithm, and compared with TMD.
Optimize calculating with genetic algorithm, for the ratio between the first mass m1 and the second mass m2 η take η=
0.125th, η=0.25, η=0.5, η=0.75, η=1.0 5 kind situation discussion, for total mass ratio, incorporation engineering is actually only examined
Consider 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 m1 and the second mass
Block m2 mass ratio, can make DPTMD 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.As η=1.0, DPTMD validity and TMD validity approach, still
For other points, DPTMD validity is far superior to TMD.
By the variation tendency that Fig. 5, Fig. 6 are two mass optimal frequency ratios of DPTMD, with η increase, f1、f2In rising
Trend, tend towards stability afterwards.Fig. 7, Fig. 8 are the variation tendency of two mass Optimal damping ratios of DPTMD, with η increase,
ξ1、ξ2It is on a declining curve.
Fig. 9, Figure 10 are the stroke of two masses of DPTMD (the first mass m1 and the second mass m2) with η change
Situation, in general, stroke increase with the ratio between mass η increase, but for TMD, two matter of DPTMD
The stroke of gauge block is all significantly less than the stroke of TMD single mass.
Comparison diagram 4 is can be found that to Figure 10：The validity of DPTMD integral vibration dampings is substantially better than TMD, and stroke is significantly less than
TMD.η is smaller, and the validity of vibration damping is better, and stroke is smaller, but damps bigger.
In summary describe, consider economic factor and the possibility realized, provided most for parallel resonant mass damper
Excellent design parameter combination is as follows：μS=0.02, μ=0.01, η=0.25, f1=0.98, ξ1=0.134, f2=0.76, ξ2=
0.207, Above parameter in the reasonable scope, Practical Project
In may be referred to the design that this group of data carry out DPTMD devices.
Claims (3)
1. a kind of parallel resonant mass damper Optimization Design, it is characterised in that it comprises the following steps：
Step 1, establishes the model of parallel resonant mass damper, and detailed process is as follows：In traditional mono- the first mass m1 of TMD
On the basis of, increase by second mass, and installation in parallel, be respectively adopted spring and damper by the first mass and
Second mass is connected in building main structure, forms the parallel resonant mass damper being made up of two masses；
Step 2, according to Structural Dynamics principle, force analysis is carried out to building main structure and parallel resonant mass damper, built
The kinetic equation of vertical building main structure-DPTMD systems, is concretely comprised the following steps：The step 2 establishes building main structure-DPTMD
The kinetic equation of system is expressed as following formula：
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In formula,For earthquake ground motion acceleration；ySDisplacement for building main structure relative to substrate；To build main knot
Structure relative to substrate speed；Acceleration for building main structure relative to substrate；y1、y2It is relative for TMD1, TMD2 mass
In the displacement of building main structure；Speed for TMD1, TMD2 mass relative to building main structure；For ATMD
Mass is relative to the acceleration for building main structure；mS、cSAnd kSRespectively build main structure controlled vibration shape quality, damping and
Rigidity；m1、c1And k1Respectively TMD1 quality, damping and rigidity；m2、c2And k2Respectively TMD2 quality, damping and rigidity；
Step 3, TMD is contrasted, the optimization design of vibration control is carried out to parallel resonant mass damper；
Step 4, by reference to optimum results, consider the validity of control and the validity of damping system stroke control, selection is most
Excellent combination parameter, with reference to the parameter designing parallel resonant mass damper of original building main structure.
2. parallel resonant mass damper Optimization Design according to claim 1, it is characterised in that the step 1
The middle mechanical model for establishing building main structure-DPTMD systems：Main structure will be built as a single-degree-of-freedom particle, according to it
Material characteristicses determine its damping and rigidity, and one the second mass of parallel increase, is adopted on the basis of traditional masses of TMD first
The first mass and the second mass are connected in building main structure respectively with two sleeve springs and damping, constituted by two matter
The parallel resonant mass damper of gauge block composition, that is, build main structure-DPTMD systems.
3. parallel resonant mass damper Optimization Design according to claim 1, it is characterised in that the step 4
Defined in optimized parameter interpretational criteria：The building main structure maximum power amplification coefficient of parallel resonant mass damper is set most
The minimum of small value；Parameter optimization is carried out using genetic algorithm, and compared with traditional TMD.
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