CN104612279A - Ultralow frequency swinging type tuning mass damper and achieving method thereof - Google Patents

Abstract

The invention belongs to the technical field of structure vibration control and discloses an ultralow frequency swinging type tuning mass damper and an achieving method thereof. The novel tuning mass damper is formed through an added negative stiffness adjusting device with a novel structure, meanwhile, the achieving method of the tuning mass damper is disclosed, accordingly the swinging length of the ultralow frequency swinging type tuning mass damper (TMD) can be effectively shortened, the mounting space of the TMD is decreased, and the engineering application range of the ultralow frequency swinging type TMD is expanded.

Description

Ultralow frequency pendulum-type tuned mass damper and its implementation

Technical field

The invention belongs to structural vibration control technical field, be specifically related to a kind of ultralow frequency pendulum-type tuned mass damper and its implementation.

Background technology

Easily there is low frequency and significantly vibrate in high-rise buildings, in order to suppress this kind of structural vibration, a lot of super highrise building is all provided with huge pendulum-type tuned mass damper (TMD) under wind action.According to the frequency computation part formula of pendulum-type TMD known, for meeting ultralow frequency (the 1st rank beam frequency is generally at the 0.1 ~ 0.2Hz) damping requirements of Super High vibration damping, pendulum-type TMD often needs larger pendulum length.Shake and the TMD of seismic response control as TaiWan, China 101 mansion is used for wind, adopt the high-strength steel cable of 8 group leader 11.5m, diameter 90mm to hang to weigh the mass of 660 tons.

Publication No. is that " the pendulum-type eddy current tuned mass damper device " of CN 103132628A patent discloses a kind of tuned mass damper for high-rise buildings, long hoist cable makes it have lower natural frequency, though can reach the low frequency vibration damping needs of high-rise buildings, its structure is larger.The stiffness elements being used for the TMD of center, Shanghai wind dynamic control according to this Patent design adopts the cable wire of 12, long 25 meters, takes up room huge.

Notification number is the frequency adjusting device that " frequency regulation arrangement of pendulum-type tuned mass damper " of CN 203499048U patent discloses a kind of pendulum-type tuned mass damper, and the vibration damping for high-rise buildings structure etc. controls.Adopt frequency modulation spring, between the mass that frequency modulation spring horizontal is arranged on pendulum-type tuned mass damper and agent structure, frequency modulation spring is arranged symmetrically in the both sides of mass or is evenly distributed on the surrounding of mass, frequency modulation spring one end quality of connection block, the other end connects agent structure, and frequency modulation spring is in pre-tensioned state.But this patent can only realize the increase of mass restoring force in TMD, namely increases system stiffness, natural frequency becomes large, cannot realize the reduction of pendulum-type TMD pendulum length.

Notification number is that " a kind of ultralow frequency tuned mass damper, TMD " of CN 203626078U patent discloses the vertical TMD of a kind of ultralow frequency based on law of buoyancy.The mass (hollow metal sphere) of TMD is suspended in airtight oil-filled container by this patent, thus realizes the reduction that TMD spring element extends only.But this patent is only applicable to vertical TMD vibration absorber, the pendulum-type TMD suppressing tall and slender structure horizontal vibration cannot be applied to, and the adjustment of its damping size is realized by the profile of change ball, is difficult to accomplish quantitative adjustment.

In summary it can be seen: the pendulum-type TMD needed for high-rise buildings vibration damping, all need larger pendulum length, required installing space is huge.

Summary of the invention

The object of the invention is for the long problem and shortage of the low frequency pendulum-type TMD pendulum length of above-mentioned existence, ultralow frequency pendulum-type tuned mass damper and its implementation of a kind of additional installation negative stiffness adjusting device are provided.

For solving the problem and deficiency, the technical scheme taked is:

A kind of ultralow frequency pendulum-type tuned mass damper, comprise the pendulum chamber be arranged in structure, the hoist cable be connected with the structure of pendulum top of chamber, the mass of hanging in hoist cable bottom, be arranged on the viscous damper between mass and structure and negative stiffness adjusting device, the quantity of described viscous damper and negative stiffness adjusting device is two and all arranges in the bilateral symmetry that mass is corresponding, described negative stiffness adjusting device comprises n block and is arranged on the permanent magnet that the polarity of mass wherein on a side is N pole/S pole, with the permanent magnet that the n block polarity be arranged on structure corresponding to this side is S pole/N pole.

Further, described permanent magnet is cylindrical magnet iron.

An implementation method for above-mentioned ultralow frequency pendulum-type tuned mass damper, mainly comprises the steps:

(1) according to the quality m of structural vibration reduction with pendulum-type TMD _tMD, frequency f _tMD, determine the theoretical initial value of pendulum length $l_i=\frac{g}{{\left(2\mathrm{\π}{f}_{\mathrm{TMD}}\right)}^2},$ Rigidity initial theory design load $k_i=4{\mathrm{\π}}^2{m}_{\mathrm{TMD}}{f}_{\mathrm{TMD}}^2;$

(2) basis determine that pendulum length l adjusts interval, wherein f _lrepresent the vibration frequency that pendulum length l is corresponding, and calculate the equivalent stiffness of corresponding pendulum-type system and TMD allow pivot angle wherein A represents the design amplitude of TMD;

(3) the additional stiffness design load k of negative stiffness adjusting device is determined _s=k _l-k _i;

(4) detailed design of negative stiffness adjusting device is carried out:

1. choose cylindrical magnet iron, its concrete dimensional parameters is: the radius r of permanent magnet, permanent magnet magnetize face area A _m=π r ², the thickness δ of permanent magnet, the remanence strength B of permanent magnet _r, definition simultaneously mutually corresponding two block permanent magnets attracted is one group;

2. larger according to the amplitude A primary election one of TMD d ₀, and d ₀> A, wherein d ₀represent the clear spacing between one group of permanent magnet that TMD mass attracts each other when being in equilbrium position;

3. the additional stiffness k that one group of permanent magnet that mass bilateral symmetry is arranged produces _mag(θ (t))=k _n(t)-k _pt (), gets TMD pivot angle θ (t)=0.5 θ _maxtime corresponding instantaneous k _mag(0.5 θ _max) value is as additional stiffness calculated value;

Wherein:

$k_p\left(t\right)=\left|\right[\frac{B_r^2{A}_m^2{(\mathrm{\δ}+r)}^2}{{\mathrm{\π\μ}}_0{\mathrm{\δ}}^2}\left]\right[-\frac{2}{{(d_0+\mathrm{l\θ}\left(t\right))}^3}-\frac{2}{{(d_0+\mathrm{l\θ}\left(t\right)+2\mathrm{\δ})}^3}+\frac{4}{{(d_0+\mathrm{l\θ}\left(t\right)+\mathrm{\δ})}^3}\left]\right|$

$k_n\left(t\right)=\left|\right[\frac{B_r^2{A}_m^2{(\mathrm{\δ}+r)}^2}{{\mathrm{\π\μ}}_0{\mathrm{\δ}}^2}\left]\right[-\frac{2}{{(d_0-\mathrm{l\θ}\left(t\right))}^3}-\frac{2}{{(d_0-\mathrm{l\θ}\left(t\right)+2\mathrm{\δ})}^3}+\frac{4}{{(d_0-\mathrm{l\θ}\left(t\right)+\mathrm{\δ})}^3}\left]\right|$

4. the group number of the permanent magnet of mass both sides is determined

5. mgsin θ is judged _max> n (F _n-F _p) cos θ _maxwhether set up, if set up, d ₀deduct 0.01m to return the and 3. walk, if be false, stop circulation, and get last d ₀the permanent magnet group number n of the mass both sides obtained is as optimum results.

(5), during TMD practical installation and trial, adopt the method for vibration monitoring of engineering structure to the frequency f of TMD _tMDverify, if f _tMDmeasured value is less than normal, by tuning up d ₀reduce additional stiffness, if f _tMDbigger than normal, by turning d down ₀increase additional stiffness.

Adopt technique scheme, acquired beneficial effect is:

1, the present invention effectively can shorten the pendulum length of ultralow frequency pendulum-type TMD by the negative stiffness adjusting device of particular design, reduces the installing space of TMD, expands the engineer applied scope of ultralow frequency pendulum-type TMD.

2, negative stiffness adjusting device adopts the contactless permanent magnet composition attracted each other, and stiffness equivalent is simple, quick, and has very high durability.

3, ultralow frequency pendulum-type tuned mass damper of the present invention is with the size of mass vibration amplitude, and frequency presents small change, and TMD can well realize vibration damping target, automatically can also realize spacing, promote durability simultaneously.When main structure vibration is less, because the vibration frequency at ultralow frequency pendulum-type tuned mass damper (TMD) equilbrium position place of the present invention is a bit larger tham agent structure, make TMD almost motionless, avoid the TMD fatigue damage that small size Long-term Vibration brings, thus improve the durability of TMD system; When main structure vibration is larger, TMD of the present invention just has suitable vibration displacement, now because amplitude increases, the negative stiffness that negative stiffness adjusting device provides is also increasing, namely TMD and the frequency both main structure also more and more close, TMD starts to give full play to tunning effect, thus embodies good effectiveness in vibration suppression; When the amplitude of TMD continues to increase to a certain degree, the negative stiffness provided due to negative stiffness adjusting device is excessive, make the vibration frequency of TMD start become be slightly less than main structure, TMD is under the acting in conjunction of damping and frequency detuning, the amplitude of TMD starts to reduce, thus play the effect of automatic spacing, when being reduced to a certain degree, TMD starts again the tunning effect giving full play to a new round.Through above-mentioned loop cycle, the vibrational energy of main structure is absorbed by TMD gradually, dissipates.

Accompanying drawing explanation

Fig. 1 is the structural representation of ultralow frequency pendulum-type tuned mass damper of the present invention.

Fig. 2 be in Fig. 1 A-A to structural representation.

Fig. 3 is the stressed sketch of TMD mass when being in equilibrium state.

Fig. 4 is the stressed sketch of TMD mass when swinging left from equilbrium position.

Fig. 5 is the stressed sketch of TMD mass when swinging to the right from equilbrium position.

Fig. 6 is the method for designing flow chart of a kind of ultralow frequency pendulum-type of the present invention tuned mass damper.

Fig. 7 is the model testing structural representation made for the present invention.

Fig. 8 is that mass both sides are without TMD mass time of vibration course curve during permanent magnet.

Fig. 9 is that mass both sides are without the TMD mass vibration local time course figure designing peak swing place during permanent magnet.

Figure 10 is mass both sides is the TMD mass vibration local time course figure at design peak swing 50% place without vibration amplitude during permanent magnet.

Figure 11 is mass both sides is the TMD mass vibration local time course figure at design peak swing 20% place without vibration amplitude during permanent magnet.

Figure 12 is the TMD mass time of vibration course curves of mass both sides when respectively placing one group of permanent magnet.

Figure 13 is the TMD mass vibration local time course figure at design peak swing place when respectively placing one group of permanent magnet, mass both sides.

Figure 14 be mass both sides when respectively placing one group of permanent magnet vibration amplitude be the TMD mass vibration local time course figure at design peak swing 50% place.

Figure 15 be mass both sides when respectively placing one group of permanent magnet vibration amplitude be the TMD mass vibration local time course figure at design peak swing 20% place.

Figure 16 is the TMD mass time of vibration course curves of mass both sides when respectively placing two groups of permanent magnets.

Figure 17 is the TMD mass vibration local time course figure at design peak swing place when respectively placing two groups of permanent magnets, mass both sides.

Figure 18 be mass both sides when respectively placing two groups of permanent magnets vibration amplitude be the TMD mass vibration local time course figure at design peak swing 50% place.

Figure 19 be mass both sides when respectively placing two groups of permanent magnets vibration amplitude be the TMD mass vibration local time course figure at design peak swing 20% place.

Sequence number in figure: 1 be hoist cable, 2 for mass, 3 for permanent magnet, 4 for viscous damper, 5 for support, 6 for bearing, 7 for top board, 8 for base plate, 9 for pendulum chamber.

Detailed description of the invention

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is elaborated.

Embodiment one: see Fig. 1, a kind of ultralow frequency pendulum-type tuned mass damper, comprise the pendulum chamber 9 be arranged in structure, the hoist cable 1 be connected with the structure at pendulum top, chamber 9, the mass 2 of hanging in hoist cable 1 bottom, be arranged on the viscous damper 4 between mass 2 and structure and negative stiffness adjusting device, described viscous damper 4 and the quantity of negative stiffness adjusting device are two and all arrange in the bilateral symmetry of mass 2 correspondence, described negative stiffness adjusting device comprises n block and is arranged on the permanent magnet 3 that the polarity of mass 2 wherein on a side is N pole/S pole, with the permanent magnet 3 that the n block polarity be arranged on structure corresponding to this side is S pole/N pole, the permanent magnet 3 of described mass 2 both sides is cylindrical magnet iron.

Embodiment two: the present embodiment is the implementation method of the ultralow frequency pendulum-type tuned mass damper described in a kind of embodiment one.

First operating principle of the present invention is set forth:

(1) by shown in Fig. 1-Fig. 3, when structure is static, the negative stiffness adjusting device of the mass left and right sides of tuned mass damper balances mutually, and mass is in equilibrium state;

(2) when structure vibrates, the pendulum of tuned mass damper also swings thereupon, and as shown in Figure 4, when being flapped toward left pendulum angle θ (θ < 5 °), the attraction now between the permanent magnet of both sides is F ₁>=F ₂, differential equation of motion ml θ " and+p (θ)=0, p (θ) is the restoring force depending on pivot angle θ:

p(θ)＝mgsinθ-(F ₁cosθ-F ₂cosθ)

Because angle θ very little (within 5 degree), approximate gets sin θ ≈ θ, cos θ ≈ 1, can obtain:

p(θ)≈mgθ-(F ₁-F ₂) ①

Wherein

$F_1=\left[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\right][\frac{1}{{(d_0-\mathrm{l\&theta;})}^2}+\frac{1}{{(d_0-\mathrm{l\&theta;}+2\mathrm{\&delta;})}^2}-\frac{2}{{(d_0-\mathrm{l\&theta;}+\mathrm{\&delta;})}^2}]$

$F_2=\left[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\right][\frac{1}{{(d_0+\mathrm{l\&theta;})}^2}+\frac{1}{{(d_0+\mathrm{l\&theta;}+2\mathrm{\&delta;})}^2}-\frac{2}{{(d_0+\mathrm{l\&theta;}+\mathrm{\&delta;})}^2}]$

(3) as shown in Figure 5, when right swinging θ (within 5 degree), restoring force has:

p(θ)≈mgθ-(F ₂-F ₁) ②

Wherein

$F_1=\left[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\right][\frac{1}{{(d_0+\mathrm{l\&theta;})}^2}+\frac{1}{{(d_0+\mathrm{l\&theta;}+2\mathrm{\&delta;})}^2}-\frac{2}{{(d_0+\mathrm{l\&theta;}+\mathrm{\&delta;})}^2}]$

$F_2=\left[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\right][\frac{1}{{(d_0-\mathrm{l\&theta;})}^2}+\frac{1}{{(d_0-\mathrm{l\&theta;}+2\mathrm{\&delta;})}^2}-\frac{2}{{(d_0-\mathrm{l\&theta;}+\mathrm{\&delta;})}^2}]$

Comprehensive 1. 2. formula, obtains the Uniform Formula of restoring force:

p(θ)≈mgθ-(F _n-F _p)

Wherein

$F_n=\left[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\right][\frac{1}{{(d_0-\mathrm{l\&theta;})}^2}+\frac{1}{{(d_0-\mathrm{l\&theta;}+2\mathrm{\&delta;})}^2}-\frac{2}{{(d_0-\mathrm{l\&theta;}+\mathrm{\&delta;})}^2}]$

$F_p=\left[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\right][\frac{1}{{(d_0+\mathrm{l\&theta;})}^2}+\frac{1}{{(d_0+\mathrm{l\&theta;}+2\mathrm{\&delta;})}^2}-\frac{2}{{(d_0+\mathrm{l\&theta;}+\mathrm{\&delta;})}^2}]$

System effective rigidity

k _e＝k _l-k _mag③

Wherein $k_l=\frac{\mathrm{mg}}{l}$ ④

k _mag＝k _n-k _p⑤

$\begin{array}{c}{k}_p=\left|\frac{{\mathrm{\&delta;F}}_p}{\mathrm{\&delta;}(d_0-\mathrm{l\&theta;})}\right|=\left|\frac{{\&PartialD;F}_p}{\&PartialD;(d_0-\mathrm{l\&theta;})}\right|=\left|\frac{{\&PartialD;F}_p}{\&PartialD;\mathrm{\&theta;}}\frac{\mathrm{d\&theta;}}{d(d_0-\mathrm{l\&theta;})}\right|\\ =\left|\right[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{\mathrm{\&pi;}{\mathrm{\&mu;}}_0{\mathrm{\&delta;}}^2}\left]\right[-\frac{2}{{(d_0+\mathrm{l\&theta;})}^3}-\frac{2}{{(d_0+\mathrm{l\&theta;}+2\mathrm{\&delta;})}^3}+\frac{4}{{(d_0+\mathrm{l\&theta;}+\mathrm{\&delta;})}^3}\left]\right|\end{array}$

$k_n=\left|\frac{{\mathrm{\&delta;F}}_n}{\mathrm{\&delta;}(d_0-\mathrm{l\&theta;})}\right|=\left|\frac{{\&PartialD;F}_n}{\&PartialD;(d_0-\mathrm{l\&theta;})}\right|=\left|\frac{{\&PartialD;F}_n}{\&PartialD;\mathrm{\&theta;}}\frac{\mathrm{d\&theta;}}{d(d_0-\mathrm{l\&theta;})}\right|$

$=\left|\right[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\left]\right[-\frac{2}{{(d_0-\mathrm{l\&theta;})}^3}-\frac{2}{{(d_0-\mathrm{l\&theta;}+2\mathrm{\&delta;})}^3}+\frac{4}{{(d_0-\mathrm{l\&theta;}+\mathrm{\&delta;})}^3}\left]\right|$

All there is k obvious corresponding TMD mass optional position _mag> 0, therefore k _e< k _l, namely original system rigidity reduces, now TMD natural frequency decline, thus realize lower vibration frequency with shorter pendulum length.

Secondly, when TMD amplitude is constant, its vibration frequency remains unchanged, and is the important guarantee of TMD for structure high-efficiency vibration damping.According to the symmetry of the pendulum-type TMD structure of this patent design, only need verify that the time-preserving that pendulum-type TMD mass moves to right side maximum pendulum angle from left side maximum pendulum angle can be proven.Method of proof is as follows:

The oscillatory differential equation of single pendulum system: ml θ "+p (θ)=0

$\frac{d^2\mathrm{\&theta;}}{{\mathrm{dt}}^2}=\frac{d}{\mathrm{dt}}\left(\frac{\mathrm{d\&theta;}}{\mathrm{dt}}\right)=\frac{d\left(\frac{\mathrm{d\&theta;}}{\mathrm{dt}}\right)}{\mathrm{d\&theta;}}\frac{\mathrm{d\&theta;}}{\mathrm{dt}}=\frac{\mathrm{d\&theta;}}{\mathrm{dt}}\frac{d\left(\frac{\mathrm{d\&theta;}}{\mathrm{dt}}\right)}{\mathrm{d\&theta;}}={\mathrm{\&theta;}}^{\&prime;}\frac{d{\mathrm{\&theta;}}^{\&prime;}}{\mathrm{d\&theta;}}$

Namely

$\mathrm{ml}{\mathrm{\&theta;}}^{\&prime;}\frac{{\mathrm{d\&theta;}}^{\&prime;}}{\mathrm{d\&theta;}}+p\left(\mathrm{\&theta;}\right)=0$

Integration is carried out to θ in both sides simultaneously, has

$\frac{1}{2}\mathrm{ml}{\left({\mathrm{\&theta;}}^{\&prime;}\right)}^2+\&Integral;p\left(\mathrm{\&theta;}\right)\mathrm{d\&theta;}=C$

Then

$\frac{\mathrm{d\&theta;}}{\mathrm{dt}}=\sqrt{\frac{2(C-\&Integral;p\left(\mathrm{\&theta;}\right)\mathrm{d\&theta;})}{\mathrm{ml}}}$

$\mathrm{dt}=\frac{\mathrm{d\&theta;}}{\sqrt{\frac{2(C-\&Integral;p\left(\mathrm{\&theta;}\right)\mathrm{d\&theta;})}{\mathrm{ml}}}}$

If pendulum when being positioned on the right of equilbrium position pivot angle for just, then put the time t moving to right side maximum pendulum angle from left side maximum pendulum angle and calculated by following formula:

$t={\&Integral;}_{-{\mathrm{\&theta;}}_{\max }}^{{\mathrm{\&theta;}}_{\max }}\frac{1}{\sqrt{\frac{2(C-\&Integral;p\left(\mathrm{\&theta;}\right)\mathrm{d\&theta;})}{\mathrm{ml}}}}\mathrm{d\&theta;}$

According to the character of definite integral, the value of t only with integrand and θ _maxrelevant, because integrand is constant, so t is constant when amplitude is constant.From structural symmetry, put and move to the time of left side maximum pendulum angle also for t from right side maximum pendulum angle.

To sum up, the cycle T=2t of pendulum-type TMD of the present invention, cycle when therefore TMD amplitude of the present invention is constant remains unchanged.

The implementation method of ultralow frequency pendulum-type tuned mass damper of the present invention is:

(1) according to the quality m of structural vibration reduction with pendulum-type TMD _tMD, frequency f _tMD, determine the theoretical initial value of pendulum length $l_i=\frac{g}{{\left(2\mathrm{\&pi;}{f}_{\mathrm{TMD}}\right)}^2},$ Rigidity theory initial design values $k_i=4{\mathrm{\&pi;}}^2{m}_{\mathrm{TMD}}{f}_{\mathrm{TMD}}^2;$

(2) basis determine that pendulum length l adjusts interval (f _lrepresent pendulum length l _icorresponding vibration frequency), and calculate the equivalent stiffness of corresponding pendulum-type system and TMD allow pivot angle (A represents the design amplitude of TMD, θ _maxgenerally should be less than 5 °);

(3) the additional stiffness design load k of negative stiffness adjusting device is determined _s=k _l-k _i;

(4) detailed design of negative stiffness adjusting device is carried out:

1. determine model and the size of Circular permanent magnet iron, major parameter has: r (permanent magnet radius) and A _m=π r ²(permanent magnet magnetize face area), δ (permanent magnet thickness, namely magnetize length), B _r(permanent magnet remanence strength), defining a pair permanent magnet attracted each other is one group;

2. larger according to the amplitude A primary election one of TMD d ₀(d ₀represent the spacing of a pair permanent magnet that TMD mass attracts each other when being in equilbrium position), and d ₀> A;

3. the additional stiffness k that one group of permanent magnet that mass bilateral symmetry is arranged produces _mag(θ (t))=k _n(t)-k _pt (), gets TMD pivot angle θ (t)=0.5 θ _maxtime corresponding instantaneous k _mag(0.5 θ _max) value is as additional stiffness calculated value;

Wherein

$k_p\left(t\right)=\left|\right[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\left]\right[-\frac{2}{{(d_0+\mathrm{l\&theta;}\left(t\right))}^3}-\frac{2}{{(d_0+\mathrm{l\&theta;}\left(t\right)+2\mathrm{\&delta;})}^3}+\frac{4}{{(d_0+\mathrm{l\&theta;}\left(t\right)+\mathrm{\&delta;})}^3}\left]\right|$

$k_n\left(t\right)=\left|\right[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\left]\right[-\frac{2}{{(d_0-\mathrm{l\&theta;}\left(t\right))}^3}-\frac{2}{{(d_0-\mathrm{l\&theta;}\left(t\right)+2\mathrm{\&delta;})}^3}+\frac{4}{{(d_0-\mathrm{l\&theta;}\left(t\right)+\mathrm{\&delta;})}^3}\left]\right|$

4. the group number of the permanent magnet of mass both sides is determined

5. mgsin θ is judged _max> n (F _n-F _p) cos θ _maxwhether set up, if set up, d ₀deduct 0.01m to return and 3. walk; If be false, stop circulation, and get last d ₀the permanent magnet group number of the mass both sides obtained is as optimum results.

(5), during TMD practical installation and trial, adopt the method for vibration monitoring of engineering structure to the frequency f of TMD _tMDverify, if f _tMDmeasured value is less than normal, by tuning up d ₀(fine setting) reduces additional negative stiffness, if f _tMDbigger than normal, by turning d down ₀(fine setting) increases additional negative stiffness.

Embodiment three: for the wind-induced vibration Vibration Absorption Designing of TaiWan, China 101 mansion, adopts structure of the present invention and method for designing: the pendulum-type tuned mass damper design parameter of TaiWan, China 101 mansion wind-induced vibration Vibration Absorption Designing: quality m _tMDbe 660 tons, frequency f _tMDfor 0.147Hz, pendulum length l _i=11.5m, TMD design amplitude A=0.80m.

Get determine pendulum length target adjustment value l=8.7m, the frequency adjustment method final optimization pass result using this patent to provide is: distance d during permanent magnet equilbrium position ₀=0.79m, needs model N38, is of a size of the Circular permanent magnet iron 128 groups (totally 256 groups, mass both sides, add up to 512 block permanent magnets, gross mass is about 678kg, and required expense is approximately 200,000) of D150 × 10mm.Now calculate correspondence meet the design object of 0.147Hz.

In summary it can be seen, adopt the negative stiffness adjusting device of particular design of the present invention, 8.7m is down to from 11.5m with the pendulum-type TMD pendulum length that namely cost of 200,000 yuan can realize TaiWan, China 101 Building design adopts, be equivalent to the space saving first floor, no matter the space of this first floor under saving is for office or view, its economic worth brought all is far longer than 200,000 yuan, reduces the installation difficulty of TMD simultaneously.Further, when the damper that TMD selects damping adjustable, frequency ratio can increase further, when β gets 1.2, pendulum length can be reduced to 8.0m further.

Embodiment four: " the pendulum-type eddy current tuned mass damper device " that apply the present invention to center, Shanghai, can reduce to 18.9m by intrinsic 25m pendulum length when getting β=1.15, reduces setting height(from bottom) 6.1m, by the space of saving two floor, and remarkable in economical benefits.

In addition, adopt the effective rigidity of the ultralow frequency pendulum-type tuned mass damper of the present invention's design to change with the change of mass vibration amplitude, TMD frequency also will present small change.This feature makes TMD can well realize vibration damping target, automatically can also realize spacing, promote durability simultaneously.

Embodiment five: the method provided according to the present invention has made test model as shown in Figure 7, form the chamber that shakes between support 5, top board 7, base plate 8, bearing 6 is arranged on both sides corresponding to mass, and for fixing permanent magnet.Wherein, pendulum length l=1.9m, mass quality m=10kg, the design maximum pendulum angle θ of pendulum _max=3 °.Distance d during this experiment permanent magnet equilbrium position ₀=18cm, Circular permanent magnet swage N38, dimension D 150 × 10mm.Experimental result sees attached list 1.

Experimental result as can be seen from subordinate list 1, adopt the inventive method to reducing the frequency effects of pendulum-type TMD clearly, when pendulum reaches its design amplitude, 1 group of permanent magnet is placed in mass both sides can make TMD frequency reduce by 5.7%, and 2 groups of permanent magnets are placed in mass both sides can make TMD frequency reduce by 11.9%.

Subordinate list 1

Claims (3)

1. a ultralow frequency pendulum-type tuned mass damper, it is characterized in that, comprise the pendulum chamber be arranged in structure, the hoist cable be connected with the structure of pendulum top of chamber, the mass of hanging in hoist cable bottom, be arranged on the viscous damper between mass and structure and negative stiffness adjusting device, the quantity of described viscous damper and negative stiffness adjusting device is two and all arranges in the bilateral symmetry that mass is corresponding, described negative stiffness adjusting device comprises n block and is arranged on the permanent magnet that the polarity of mass wherein on a side is N pole/S pole, with the permanent magnet that the n block polarity be arranged on structure corresponding to this side is S pole/N pole.

2. ultralow frequency pendulum-type tuned mass damper according to claim 1, is characterized in that, described permanent magnet is cylindrical magnet iron.

3. an implementation method for ultralow frequency pendulum-type tuned mass damper according to claim 1, comprises the steps:

(1) according to the quality m of structural vibration reduction with pendulum-type TMD _tMD, frequency f _tMD, determine the theoretical initial value of pendulum length $l_i=\frac{g}{{\left({2\mathrm{\&pi;f}}_{\mathrm{TMD}}\right)}^2},$ Rigidity initial theory design load $k_i={4\mathrm{\&pi;}}^2{m}_{\mathrm{TMD}}{f}_{\mathrm{TMD}}^2;$

(2) basis determine that pendulum length l adjusts interval, wherein f _lrepresent the vibration frequency that pendulum length l is corresponding, and calculate the equivalent stiffness of corresponding pendulum-type system and TMD allow pivot angle wherein A represents the design amplitude of TMD;

(3) the additional stiffness design load k of negative stiffness adjusting device is determined _s=k _l-k _i;

(4) detailed design of negative stiffness adjusting device is carried out:

1. choose cylindrical magnet iron, its concrete dimensional parameters is: the radius r of permanent magnet, permanent magnet magnetize face area A _m=π r ², the thickness δ of permanent magnet, the remanence strength B of permanent magnet _r, definition simultaneously mutually corresponding two block permanent magnets attracted is one group;

2. larger according to the amplitude A primary election one of TMD d ₀, and d ₀> A, wherein d ₀represent the clear spacing between one group of permanent magnet that TMD mass attracts each other when being in equilbrium position;

3. the additional stiffness k that one group of permanent magnet that mass bilateral symmetry is arranged produces _mag(θ (t))=k _n(t)-k _pt (), gets TMD pivot angle θ (t)=0.5 θ _maxtime corresponding instantaneous k _mag(0.5 θ _max) value is as additional stiffness calculated value;

Wherein:

$k_p\left(t\right)=\left|\right[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\left]\right[-\frac{2}{{(d_0+\mathrm{l\&theta;}\left(t\right))}^3}-\frac{2}{{(d_0+\mathrm{l\&theta;}\left(t\right)+2\mathrm{\&delta;})}^3}+\frac{4}{{(d_0+\mathrm{l\&theta;}\left(t\right)+\mathrm{\&delta;})}^3}\left]\right|$

$k_n\left(t\right)=\left|\right[\frac{B_r^2{A}_m^2{(\mathrm{\&delta;}+r)}^2}{{\mathrm{\&pi;\&mu;}}_0{\mathrm{\&delta;}}^2}\left]\right[-\frac{2}{{(d_0+\mathrm{l\&theta;}\left(t\right))}^3}-\frac{2}{{(d_0+\mathrm{l\&theta;}\left(t\right)+2\mathrm{\&delta;})}^3}+\frac{4}{{(d_0+\mathrm{l\&theta;}\left(t\right)+\mathrm{\&delta;})}^3}\left]\right|$

4. the group number of the permanent magnet of mass both sides is determined

5. mgsin θ is judged _max> n (F _n-F _p) cos θ _maxwhether set up, if set up, d ₀deduct 0.01m to return the and 3. walk, if be false, stop circulation, and get last d ₀the permanent magnet group number n of the mass both sides obtained is as optimum results.

(5), during TMD practical installation and trial, adopt the method for vibration monitoring of engineering structure to the frequency f of TMD _tMDverify, if f _tMDmeasured value is less than normal, by tuning up d ₀reduce additional negative stiffness, if f _tMDbigger than normal, by turning d down ₀increase additional negative stiffness.