CN105332440A - Optimal design method of double-series-parallel tuned mass damper (DSPTMD) - Google Patents

Abstract

The invention provides an optimal design method of a double-series-parallel tuned mass damper (DSPTMD). The method includes: building a structure-DSPTMD system model; building a building main structure-DSPTMD system dynamic equation according to the principle of structural dynamics, comparing with a TMD and a DPTMD, and using a genetic algorithm to perform optimal design controlled by vibration on the DSPTMD; considering control effectiveness and damping system stroke control effectiveness by referencing the optimization result, and selecting optimal combination parameters to guide actual engineering design. Compared with the TMD, the DSPTMD has the advantages that the effectiveness can be increased greatly by adjusting the specific value between two mass blocks, and meanwhile, the stroke of the DSPTMD can be lowered greatly in a certain mass ratio range, and structure displacement response under a seismic action can be controlled effectively. Compared with the DPTMD, the DSPTMD has the advantages that the effectiveness of the DSPTMD is increased slightly while damping of the DSPTMD can be lowered greatly, the stroke of the DSPTMD can be lowered continuously when the ratio between the two mass blocks is in a certain range, and optimal control is achieved.

Description

Connection in series-parallel tuned mass damper Optimal Design Method

Technical field

The present invention relates to a kind of connection in series-parallel tuned mass damper (Double-Series-ParallelTunedMassDampers, DSPTMD) Optimal Design Method.

Background technology

Earthquake is a kind of common and natural calamity happened suddenly again, and foresight is still very low so far, and widely distributed, destroy serious, once occur to cause very serious loss by the mankind.Earthquake except cause house to destroy and collapse, casualties etc. is directly except impact, also can the secondary disaster such as initiation fire and disease, cause huge potential safety hazard and economic loss.China is one of the most serious country that suffers disaster from an earthquake in the world.

The investigation and application of vibration control of civil engineering structure is considered to the important breakthrough in structures under wind earthquake research field.It breaches traditional construction design method, even if only rely on change structure self performance such as to increase, method that the rigidity of structure, damping and change Mass Distribution etc. resist environmental load (such as high wind and macroseism) develops into by the dynamic response of structure-wind resistance antidetonation vibration control system control structure on one's own initiative.1972, Chinese descendant in America scholar Yao Zhiping first systematically proposed Structure Active Control concept.He advises application classics or modern control theory, structurally installs some control systems.Structure is under Wind and earthquake effect, and these control systems be mounted thereon produce control, significantly can reduce the dynamic response of structure.Structural vibration control according to the need of outside resources, is generally divided into Passive Control, ACTIVE CONTROL, semi-active control and Hybrid mode four class.

Structure intelligent is the important component part of building intelligent.And structure intelligentization most importantly its to the defence capability of natural calamity (such as high wind and macroseism).The disaster response of real-time measurement and monitoring structure, the damage of detecting structure and surrender, the servo-drive system that machine processes online as calculated implements control from trend structure.Structural vibration control technology is that the reparation of the not enough building of existing wind resistance shock resistance and durability and transformation provide feasible and solution thoroughly, also for future architecture structure provides feasible method based on the seismic design of performance-based.In each branch of structural vibration control, mass tuning damping technology is a kind of technology of relative maturity, because it has control element requirement low, directly can be installed on building structure, just can be applicable to a series of features such as existed building without the need to revising structure design, obtaining a wide range of applications in highrise building, tall and slender structure, Longspan Bridge.In recent years, the application of tuned mass damper at home and abroad on some important buildings is more extensive.Such as: the pendulum-type eddy current tuned mass damper of Shanghai Center Building; The wind damper that Shanghai World Financial Center is two 150 tons; Swing TMD (TunedMassDampers, the tuned mass damper) system etc. of Taipei 101 mansion.

TMD has obtained very deep research thoroughly as the high-performance vibration reduction equipment of generally acknowledging in a kind of world wide.But the two large subject matters that TMD exists are: first, only have self natural frequency of natural frequency and structure as TMD consistent or close to time, the vibration isolation effect of TMD just can reach optimum state, and because the reason of construction or the impact of external environment can cause the natural frequency of TMD not reach expecting state in Practical Project, cause off resonance.TMD can only carry out damping, for Near-source earthquake poor effect within the scope of limited bandwidth simultaneously; The stroke of the second, TMD mass is excessive, is easy to collide with superstructure when mass carries out tuning vibration damping, have impact on the application of Practical Project.At present, one of main Research Thinking of Chinese scholars is exactly a kind of new vibration control apparatus of invention design, takes into account validity and stroke problem simultaneously, realizes the vibration damping damping of building structure.

Summary of the invention

For the defect that prior art exists, technical problem to be solved by this invention is to provide a kind of connection in series-parallel tuned mass damper Optimal Design Method, for TMD, the significantly lifting of validity can be realized by the ratio adjusted between two masses; Simultaneously in certain quality than in scope, the stroke of DSPTMD can significantly reduce, simultaneously the dynamic respond of structure under Earthquake occurrence control effect effectively.For DPTMD, DSPTMD significantly can reduce damping on the basis that validity slightly promotes, and can continue to reduce stroke simultaneously, realize optimum control when the ratio of two masses is in a certain scope.

For solving the problems of the technologies described above, the present invention adopts as following technical proposals: a kind of connection in series-parallel tuned mass damper Optimization Design, it is characterized in that, it comprises the steps:

Step one, set up the model of connection in series-parallel tuned mass damper, detailed process is as follows: on the basis of traditional TMD first mass, increase by second mass, and installation in parallel, spring and damper is adopted the first mass and the second mass to be connected in building main structure respectively, form the parallel resonant mass damper be made up of the first mass and the second mass, on the basis of parallel resonant mass damper, between the first mass and the second mass, connect a damper again, its damping is designated as c _t, form connection in series-parallel tuned mass damper;

Step 2, according to structural dynamics principle, carries out force analysis to building main structure and connection in series-parallel tuned mass damper, sets up the kinetic equation of building main structure-DSPTMD system;

Step 3, contrast TMD, parallel resonant mass damper DPTMD, carry out the optimal design of vibration isolation to connection in series-parallel tuned mass damper;

Step 4, by reference to optimum results, considers the validity of validity and the damping system stroke control controlled, selects optimum combination parameter, 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 system is set up: main structure will be built as a single-degree-of-freedom particle in described step one, its damping and rigidity is determined according to its material characteristics, on the basis of traditional TMD first mass, increase by second mass, and installation in parallel, adopt spring and damper the first mass and the second mass to be connected in building main structure respectively, form the parallel resonant mass damper be made up of the first mass and the second mass; On the basis of parallel resonant mass damper, between the first mass and the second mass, connect a damper again, its damping is designated as c _t, form connection in series-parallel tuned mass damper, namely build main structure-DSPTMD system.

Preferably, described step 2 is set up the kinetic equation building main structure-DSPTMD system and is expressed as following formula:

In formula, for earthquake ground motion acceleration; y _sfor building main structure is relative to the displacement of substrate; for building main structure is relative to the speed of substrate; for building main structure is relative to the acceleration of substrate; y ₁, y ₂for TMD1, TMD2 mass is relative to the displacement of building main structure; for TMD1, TMD2 mass is relative to the speed of building main structure; for ATMD mass is relative to the acceleration of building main structure; m _s, c _sand k _sbe respectively the controlled vibration shape quality of building main structure, damping and rigidity; m ₁, c ₁and k ₁be respectively the quality of TMD1, damping and rigidity; m ₂, c ₂and k ₂be respectively the quality of TMD2, damping and rigidity; c _tfor connecting the damping of the first mass and the second mass.

Preferably, the optimal design of carrying out vibration isolation to connection in series-parallel tuned mass damper in described step 3 is following content:

Building main structure-DSPTMD system displacement dynamic magnification factor as shown in the formula:

The dynamic magnification factor of TMD1 stroke be as shown in the formula:

The dynamic magnification factor of TMD2 stroke be as shown in the formula:

In formula: λ is the frequency ratio of building main structure; External excitation load, by supposing that building main structure suffers to try to achieve during simple harmonic quantity external excitation, is expressed as by dynamic magnification factor y _s=[H _s(-iw)] e ^-iwt, y ₁=[H ₁(-iw)] e ^-iwt, y ₂=[H ₂(-iw)] e ^-iwt.

Preferably, define optimized parameter interpretational criteria in described step 4: minimizing of the minimum value of the building main structure maximum power amplification coefficient of connection in series-parallel tuned mass damper is set; Utilize genetic algorithm to carry out parameter optimization, and compare with TMD, DPTMD.

Compared with prior art, the present invention has following outstanding substantive distinguishing features and significant advantage: for TMD, can be realized the significantly lifting of validity by the ratio adjusted between two masses; Simultaneously in certain quality than in scope, the stroke of DSPTMD can significantly reduce, and effectively builds the dynamic respond of main structure under Earthquake occurrence control effect simultaneously.For DPTMD, DSPTMD significantly can reduce damping on the basis that validity slightly promotes, and can continue to reduce stroke simultaneously, realize optimum control when the ratio of two masses is in a certain scope.

Accompanying drawing explanation

Fig. 1 is connection in series-parallel tuned mass damper (DSPTMD) design analysis procedure chart;

Fig. 2 is the schematic diagram of connection in series-parallel tuned mass damper (DSPTMD) system model;

Fig. 3 is the flow chart adopting genetic algorithm optimization;

When Fig. 4 is μ=0.01, during the corresponding different η of TMD, DPTMD, DSPTMD the schematic diagram of variation relation curve;

When Fig. 5 is μ=0.01, f during DPTMD, DSPTMD corresponding different η ₁the schematic diagram of variation relation curve;

When Fig. 6 is μ=0.01, f during DPTMD, DSPTMD corresponding different η ₂the schematic diagram of variation relation curve;

When Fig. 7 is μ=0.01, ξ during DPTMD, DSPTMD corresponding different η ₁the schematic diagram of variation relation curve;

When Fig. 8 is μ=0.01, ξ during DPTMD, DSPTMD corresponding different η ₂the schematic diagram of variation relation curve;

When Fig. 9 is μ=0.01, ξ during DSPTMD corresponding different η _tthe schematic diagram of variation relation curve;

When Figure 10 is μ=0.01, during the corresponding different η of TMD, DPTMD, DSPTMD the schematic diagram of variation relation curve;

When Figure 11 is μ=0.01, during the corresponding different η of TMD, DPTMD, DSPTMD the schematic diagram of variation relation curve.

Detailed description of the invention

Below in conjunction with accompanying drawing, specific embodiments of the invention are further described.

As shown in Figure 1, connection in series-parallel tuned mass damper Optimization Design of the present invention comprises the steps:

Step one, set up the model (namely building main structure-DSPTMD system model) of connection in series-parallel tuned mass damper, detailed process is as follows: on the basis of traditional TMD first mass m1, increase by a second mass m2, and installation in parallel, adopt spring and damper to be connected to by the first mass m1 and the second mass m2 in building main structure respectively, form the parallel resonant mass damper be made up of two masses (the first mass m1 and the second mass m2).On the basis of parallel resonant mass damper, between two masses (the first mass m1 and the second mass m2), connect a damper again, its damping is designated as c _t, form connection in series-parallel tuned mass damper.

Step 2, according to structural dynamics principle, carries out force analysis to building main structure and connection in series-parallel tuned mass damper, sets up the kinetic equation of building main structure-DSPTMD system;

Step 3, contrast TMD, parallel resonant mass damper DPTMD, carry out the optimal design of vibration isolation to connection in series-parallel tuned mass damper;

Step 4, by reference to optimum results, considers the validity of validity and the damping system stroke control controlled, selects optimum combination parameter, with reference to the parameter designing connection in series-parallel tuned mass damper of original structure.

As shown in Figure 2, the mechanical model of structure-DSPTMD system is set up: main structure will be built as a single-degree-of-freedom particle in described step one, its damping and rigidity is determined according to its material characteristics, on the basis of traditional TMD first mass m1, increase by a second mass m2, and installation in parallel, adopt spring and damper to be connected to by m1 and m2 in building main structure respectively, form the parallel resonant mass damper be made up of two masses (the first mass m1 and the second mass m2).On the basis of parallel resonant mass damper, between two masses (the first mass m1 and the second mass m2), connect a damper again, its damping is designated as c _t, form connection in series-parallel tuned mass damper, namely build main structure-DSPTMD system.

The kinetic equation of building main structure-DSPTMD system is set up: respectively force analysis is carried out to building main structure, TMD mass in described step 2, according to theory of structural dynamics, listing its system equation is following formula (1), (2), (3):

In formula, for earthquake ground motion acceleration; y _sfor building main structure is relative to the displacement of substrate; for building main structure is relative to the speed of substrate; for building main structure is relative to the acceleration of substrate; y ₁, y ₂for TMD1, TMD2 mass is relative to the displacement of building main structure; for TMD1, TMD2 mass is relative to the speed of building main structure; for ATMD mass is relative to the acceleration of building main structure; m _s, c _sand k _sbe respectively the controlled vibration shape quality of building main structure, damping and rigidity; m ₁, c ₁and k ₁be respectively the quality of TMD1, damping and rigidity; m ₂, c ₂and k ₂be respectively the quality of TMD2, damping and rigidity; c _tfor connecting the damping of the first mass m1 and the second mass m2.

The optimal design of carrying out vibration isolation to connection in series-parallel tuned mass damper in described step 3 is following content:

Displacement (the y of building main structure-DSPTMD system _s) dynamic magnification factor is as shown in the formula (4):

The dynamic magnification factor of TMD1 stroke is as shown in the formula (5):

The dynamic magnification factor of TMD2 stroke is as shown in the formula (6):

In order to formulae discovery is succinct, order:

D1a＝2ξ ₁f ₁λ+βξ _Tλ(f ₁+f ₂)(1+η)

D1b＝2ξ ₁f ₁λ+βξ _Tλ(f ₁+f ₂)

D2a＝2ξ ₂f ₂λ+βξ _Tλ(f ₁+f ₂)(1+η)

D1＝2ξ ₁f ₁λD2＝2ξ ₂f ₂λDs＝2ξ _sλDT＝βξ _Tλ(f ₁+f ₂)

Following equation is met, as shown in the formula (7) to formula (18) in above-mentioned formula:

Re ₂(λ)＝Re(λ)……………(17)

Im ₂(λ)＝Im(λ)……………(18)

In formula: λ is the frequency ratio of building main structure; f ₁for the frequency ratio of TMD1; f ₂for the frequency ratio of TMD2; ξ _sfor building the damping ratio of main structure; ξ ₁for the damping ratio of TMD1; ξ ₂for the damping ratio of TMD2; ξ _tfor connecting the damping ratio of damping; μ is two TMD sums and the mass ratio building main structure; η is the ratio of the first mass m1 and the second mass m2.

In optimizing process, according to Practical Project, setting ξ _s, μ, η value, to f ₁, f ₂, ξ ₁, ξ ₂, ξ _tcarry out parameter optimization.

Optimized parameter interpretational criteria is defined: minimizing of the minimum value of the building main structure maximum power amplification coefficient of connection in series-parallel tuned mass damper is set, namely in described step 4 less, then device vibration isolation validity is just about good; Utilize genetic algorithm to carry out parameter optimization, and compare with TMD, DPTMD.

Genetic algorithm is used to be optimized calculating, ratio η for the first mass m1 and the second mass m2 gets η=0.125, η=0.25, η=0.5, η=0.75, η=1.0 5 kind of situation discussion, for mass ratio, incorporation engineering reality only considers the situation of μ=0.01.

As seen from Figure 4, when total mass ratio is constant, by adjusting the mass ratio of the first mass m1 and the second mass m2, can make the vibration isolation of DSPTMD validity be improved significantly, and decline gradually along with the continuous increase validity of η, η is less, and validity is better.And the validity of DSPTMD is obviously better than TMD, slightly promotes relative to DPTMD.

By the variation tendency that Fig. 5 is DPTMD, DSPTMD mass 1 optimal frequency ratios, along with the increase of η, the f of DPTMD _{1, opt}in rising trend, tend towards stability afterwards; And the f of DSPTMD _{1, opt}on a declining curve.Fig. 6 is the variation tendency of DPTMD, DSPTMD mass 2 optimal frequency ratios, along with the increase of η, and the equal f of DPTMD, DSPTMD _{2, opt}in rising trend.Comparison diagram 5, Fig. 6 we can obviously find out, the vibration isolation effective bandwidth of DSPTMD is obviously greater than the bandwidth of DPTMD.Further illustrate the vibration isolation effect of DSPTMD excellence.

Fig. 7 is the variation tendency of DPTMD, DSPTMD mass 1 Optimal damping ratio, along with the increase of η, and the ξ of DPTMD _{1, opt}on a declining curve, and the ξ of DSPTMD _{1, opt}be always 0.Fig. 8 is the variation tendency of DPTMD, DSPTMD mass 2 Optimal damping ratio, along with the increase of η, and the ξ of DPTMD, DSPTMD _{2, opt}all on a declining curve.Fig. 9 is the connection Optimal damping ratio ξ of DSPTMD _{t, opt}variation tendency, along with the increase ξ of η _{t, opt}reduce gradually.Complex chart 7, Fig. 8, Fig. 9 can find, although have employed three dampers in DSPTMD system, the result of actual optimization shows ξ _{1, opt}value be always zero, therefore can to remove in Practical Project.When all adopting two dampers, two optimization dampings of DSPTMD are all starkly lower than the optimization damping of DPTMD, but validity can promote to some extent, not only economy but also efficient.

Figure 10, Figure 11 are respectively the first mass m1 of DPTMD, DSPTMD and the situation of change of stroke with η of the second mass m2 and the stroke of TMD, in general, the stroke of two masses (the first mass m1 and the second mass m2) of DPTMD, DSPTMD nearly all increases along with the increase of the ratio η of mass.But for TMD, the stroke of DPTMD, DSPTMD two masses is all significantly less than the stroke of the single mass of TMD.When η is when 0.25 ~ 0.5 within the scope of this, the stroke of DSPTMD two masses is all less than the stroke of DPTMD two masses.

Complex chart 4 to Figure 11 can find: when oeverall quality is than time constant, the validity of DPTMD and DSPTMD all has relative to TMD and significantly promotes, when the ratio η of two masses is in certain limit, the stroke of both two masses is also all less than the stroke of the single mass of TMD.The validity of DSPTMD vibration isolation slightly promotes relative to DPTMD, but the damping of two masses but has and significantly reduces.When the ratio η of two masses is in certain limit, the stroke of two masses of DSPTMD also has obvious reduction relative to DPTMD.

Describe more than comprehensive, consider the possibility of economic factor and realization, provide optimal design parameters combination for connection in series-parallel tuned mass damper as follows: μ _s=0.02, μ=0.01, η=0.25, f ₁=1.44, ξ ₁=0, f ₂=0.67, ξ ₂=0.092, ξ _t=0.108, above parameter, can carry out the design of DSPTMD device all in the reasonable scope with reference to these group data in Practical Project.

Claims (5)

1. a connection in series-parallel tuned mass damper Optimization Design, is characterized in that, it comprises the steps:

Step one, set up the model of connection in series-parallel tuned mass damper, detailed process is as follows: on the basis of traditional TMD first mass, increase by second mass, and installation in parallel, spring and damper is adopted the first mass and the second mass to be connected in building main structure respectively, form the parallel resonant mass damper be made up of the first mass and the second mass, on the basis of parallel resonant mass damper, between the first mass and the second mass, connect a damper again, its damping is designated as c _t, form connection in series-parallel tuned mass damper;

Step 2, according to structural dynamics principle, carries out force analysis to building main structure and connection in series-parallel tuned mass damper, sets up the kinetic equation of building main structure-DSPTMD system;

Step 3, contrast TMD, parallel resonant mass damper DPTMD, carry out the optimal design of vibration isolation to connection in series-parallel tuned mass damper;

Step 4, by reference to optimum results, considers the validity of validity and the damping system stroke control controlled, selects optimum combination parameter, with reference to the parameter designing connection in series-parallel tuned mass damper of original structure.

2. connection in series-parallel tuned mass damper Optimization Design according to claim 1, it is characterized in that, the mechanical model of building main structure-DSPTMD system is set up: main structure will be built as a single-degree-of-freedom particle in described step one, its damping and rigidity is determined according to its material characteristics, on the basis of traditional TMD first mass, increase by second mass, and installation in parallel, spring and damper is adopted the first mass and the second mass to be connected in building main structure respectively, form the parallel resonant mass damper be made up of the first mass and the second mass, on the basis of parallel resonant mass damper, between the first mass and the second mass, connect a damper again, its damping is designated as c _t, form connection in series-parallel tuned mass damper, namely build main structure-DSPTMD system.

3. connection in series-parallel tuned mass damper Optimization Design according to claim 1, is characterized in that, the kinetic equation that described step 2 sets up building main structure-DSPTMD system is expressed as following formula:

$m_S\[{\stackrel{\·\·}{x}}_g\left(t\right)+{\stackrel{\·\·}{y}}_S\]+c_S{\stackrel{\·}{y}}_S+k_S{y}_S=c_1{\stackrel{\·}{y}}_1+k_1{y}_1+c_2{\stackrel{\·}{y}}_2+k_2{y}_2$

$m_1\[{\stackrel{\·\·}{x}}_g\left(t\right)+{\stackrel{\·\·}{y}}_S+{\stackrel{\·\·}{y}}_1\]+c_1{\stackrel{\·}{y}}_1+k_1{y}_1+c_T({\stackrel{\·}{y}}_1-{\stackrel{\·}{y}}_2)=0$

$m_2\[{\stackrel{\·\·}{x}}_g\left(t\right)+{\stackrel{\·\·}{y}}_S+{\stackrel{\·\·}{y}}_2\]+c_2{\stackrel{\·}{y}}_2+k_2{y}_2=c_T({\stackrel{\·}{y}}_1-{\stackrel{\·}{y}}_2)$

In formula, for earthquake ground motion acceleration; y _sfor building main structure is relative to the displacement of substrate; for building main structure is relative to the speed of substrate; for building main structure is relative to the acceleration of substrate; y ₁, y ₂for TMD1, TMD2 mass is relative to the displacement of building main structure; for TMD1, TMD2 mass is relative to the speed of building main structure; for ATMD mass is relative to the acceleration of building main structure; m _s, c _sand k _sbe respectively the controlled vibration shape quality of building main structure, damping and rigidity; m ₁, c ₁and k ₁be respectively the quality of TMD1, damping and rigidity; m ₂, c ₂and k ₂be respectively the quality of TMD2, damping and rigidity; c _tfor connecting the damping of the first mass and the second mass.

4. connection in series-parallel tuned mass damper Optimization Design according to claim 1, is characterized in that, the optimal design of carrying out vibration isolation to connection in series-parallel tuned mass damper in described step 3 is following content:

Building main structure-DSPTMD system displacement dynamic magnification factor as shown in the formula:

$\begin{array}{c}{\mathrm{DMF}}_{H_S}=\left|{\mathrm{TRF}}_{H_S}(-iw)\right|=\left|\frac{w_S^2{H}_S(-i\mathrm{\λ})}{{\stackrel{\·\·}{X}}_g(-i\mathrm{\λ})}\right|\\ =\left|\frac{\stackrel{\‾}{\mathrm{Re}}\left(\mathrm{\λ}\right)+i\stackrel{\‾}{\mathrm{Im}}\left(\mathrm{\λ}\right)}{\mathrm{Re}\left(\mathrm{\λ}\right)+i\mathrm{Im}\left(\mathrm{\λ}\right)}\right|=\frac{\sqrt{{\[\stackrel{\‾}{\mathrm{Re}}\left(\mathrm{\λ}\right)\]}^2+{\[\stackrel{\‾}{\mathrm{Im}}\left(\mathrm{\λ}\right)\]}^2}}{\sqrt{{\[\mathrm{Re}\left(\mathrm{\λ}\right)\]}^2+{\[\mathrm{Im}\left(\mathrm{\λ}\right)\]}^2}}\end{array}$

The dynamic magnification factor of TMD1 stroke be as shown in the formula:

$\begin{array}{c}{\mathrm{DMF}}_{H_1}=\left|{\mathrm{TRF}}_{H_1}(-iw)\right|=\left|\frac{w_S^2{H}_1(-i\mathrm{\λ})}{{\stackrel{\·\·}{X}}_g(-i\mathrm{\λ})}\right|\\ =\left|\frac{{\stackrel{\‾}{\mathrm{Re}}}_1\left(\mathrm{\λ}\right)+i{\stackrel{\‾}{\mathrm{Im}}}_1\left(\mathrm{\λ}\right)}{{\mathrm{Re}}_1\left(\mathrm{\λ}\right)+{\mathrm{iIm}}_1\left(\mathrm{\λ}\right)}\right|=\frac{\sqrt{{\[{\stackrel{\‾}{\mathrm{Re}}}_1\left(\mathrm{\λ}\right)\]}^2+{\[{\stackrel{\‾}{\mathrm{Im}}}_1\left(\mathrm{\λ}\right)\]}^2}}{\sqrt{{\[{\mathrm{Re}}_1\left(\mathrm{\λ}\right)\]}^2+{\[{\mathrm{Im}}_1\left(\mathrm{\λ}\right)\]}^2}}\end{array}$

The dynamic magnification factor of TMD2 stroke be as shown in the formula:

$\begin{array}{c}{\mathrm{DMF}}_{H_2}=\left|{\mathrm{TRF}}_{H_2}(-iw)\right|=\left|\frac{w_S^2{H}_2(-i\mathrm{\λ})}{{\stackrel{\·\·}{X}}_g(-i\mathrm{\λ})}\right|\\ =\left|\frac{{\stackrel{\‾}{\mathrm{Re}}}_2\left(\mathrm{\λ}\right)+i{\stackrel{\‾}{\mathrm{Im}}}_2\left(\mathrm{\λ}\right)}{{\mathrm{Re}}_2\left(\mathrm{\λ}\right)+{\mathrm{iIm}}_2\left(\mathrm{\λ}\right)}\right|=\frac{\sqrt{{\[{\stackrel{\‾}{\mathrm{Re}}}_2\left(\mathrm{\λ}\right)\]}^2+{\[{\stackrel{\‾}{\mathrm{Im}}}_2\left(\mathrm{\λ}\right)\]}^2}}{\sqrt{{\[{\mathrm{Re}}_2\left(\mathrm{\λ}\right)\]}^2+{\[{\mathrm{Im}}_2\left(\mathrm{\λ}\right)\]}^2}}\end{array}$

In formula: λ is the frequency ratio of building main structure; External excitation load table, by supposing that building main structure suffers to try to achieve during simple harmonic quantity external excitation, is by dynamic magnification factor y _s=[H _s(-iw)] e ^-iwt, y ₁=[H ₁(-iw)] e ^-iwt, y ₂=[H ₂(-iw)] e ^-iwt.

5. connection in series-parallel tuned mass damper Optimization Design according to claim 1, it is characterized in that, in described step 4, define optimized parameter interpretational criteria: minimizing of the minimum value of the building main structure maximum power amplification coefficient of connection in series-parallel tuned mass damper is set; Utilize genetic algorithm to carry out parameter optimization, and compare with TMD, DPTMD.