CN204456498U - Ultralow frequency pendulum-type tuned mass damper - Google Patents

Abstract

The utility model belongs to the technical field of structural vibration control. An ultra-low frequency pendulum tuned mass damper, comprising a pendulum cavity arranged in a structure, a sling connected to the structure at the top of the pendulum cavity, a mass block suspended at the lower end of the sling, a mass block and the structure body Between the viscous damper and the negative stiffness adjustment device, the number of the viscous damper and the negative stiffness adjustment device are two and are arranged symmetrically on both sides corresponding to the mass block, and the negative stiffness adjustment device It includes n pieces of permanent magnets arranged on one side of the mass block with the polarity of N pole/S pole, and n pieces of permanent magnets arranged on the corresponding structure of the side surface with the polarity of S pole/N pole. The utility model can effectively shorten the pendulum length of the ultra-low frequency pendulum TMD through the specially designed negative stiffness adjusting device, reduce the installation space of the TMD, and expand the engineering application range of the ultra-low frequency pendulum TMD.

Description

Ultra-low frequency pendulum tuned mass damper

technical field

The utility model belongs to the technical field of structural vibration control, in particular to an ultra-low frequency pendulum type tuned mass damper.

Background technique

Tall buildings are prone to low-frequency and large-scale vibrations under wind loads. In order to suppress such structural vibrations, many super high-rise buildings are equipped with giant pendulum-type tuned mass dampers (TMD). According to the frequency calculation formula of pendulum TMD It can be seen that in order to meet the ultra-low frequency (the first-order bending vibration frequency is generally 0.1-0.2 Hz) vibration reduction requirements for super high-rise vibration reduction, the pendulum TMD often needs a larger pendulum length. For example, the TMD used in the Taiwan 101 Building for wind vibration and seismic response control uses 8 sets of high-strength steel cables with a length of 11.5m and a diameter of 90mm to suspend a mass block weighing 660 tons.

The publication number is CN 103132628 A "pendulum type eddy current tuned mass damper device" patent discloses a tuned mass damper for high-rise buildings, the long sling makes it have a lower natural frequency, although it can reach the The low frequency vibration damping of the building is required, but its structure is larger. According to this patent, the stiffness element of the TMD designed for the wind vibration control of Shanghai Center uses 12 steel cables with a length of 25 meters, which takes up a huge space.

The patent "Frequency Adjustment Device for Pendulum Tuned Mass Damper" with the notification number CN 203499048 U discloses a frequency adjustment device for pendulum tuned mass damper, which is used for vibration reduction control of high-rise building structures. The frequency modulation spring is adopted, and the frequency modulation spring is horizontally arranged between the mass block and the main structure of the pendulum tuning mass damper. The frequency modulation spring is symmetrically arranged on both sides of the mass block or evenly distributed around the mass block. One end of the frequency modulation spring is connected to the mass block The other end is connected to the main structure, and the FM spring is in a pre-tensioned state. However, this patent can only increase the restoring force of the mass block in the TMD, that is, increase the stiffness of the system, increase the natural frequency, and cannot reduce the pendulum length of the pendulum TMD.

The patent "A Ultra-low Frequency FM Mass Damper" with the notification number CN 203626078 U discloses an ultra-low frequency vertical TMD based on the principle of buoyancy. This patent suspends the TMD mass (hollow metal ball) in a closed oil-filled container, thereby reducing the net elongation of the TMD spring element. However, this patent is only applicable to the vertical TMD vibration damping device, and cannot be applied to the pendulum TMD that suppresses the horizontal vibration of towering structures, and the adjustment of the damping size is realized by changing the shape of the ball, which is difficult to achieve quantitative adjustment.

In summary, it can be seen that the pendulum TMD required for vibration reduction of tall buildings requires a relatively large pendulum length and requires a huge installation space.

Utility model content

The object of the present invention is to provide an ultra-low frequency pendulum tuned mass damper additionally equipped with a negative stiffness adjustment device for the above-mentioned problems and shortcomings of the low frequency pendulum TMD pendulum length being too long.

In order to solve the above problems and deficiencies, the technical solutions adopted are:

An ultra-low frequency pendulum tuned mass damper, comprising a pendulum cavity arranged in a structure, a sling connected to the structure at the top of the pendulum cavity, a mass block suspended at the lower end of the sling, a mass block and the structure body Between the viscous damper and the negative stiffness adjustment device, the number of the viscous damper and the negative stiffness adjustment device are two and are arranged symmetrically on both sides corresponding to the mass block, and the negative stiffness adjustment device It includes n pieces of permanent magnets arranged on one side of the mass block with the polarity of N pole/S pole, and n pieces of permanent magnets arranged on the corresponding structure of the side surface with the polarity of S pole/N pole.

The permanent magnet is a cylindrical permanent magnet.

Adopt above-mentioned technical scheme, the beneficial effect that obtains is:

1. The invention can effectively shorten the pendulum length of the ultra-low frequency pendulum TMD through the specially designed negative stiffness adjustment device, reduce the installation space of the TMD, and expand the engineering application scope of the ultra-low frequency pendulum TMD.

2. The negative stiffness adjustment device is composed of non-contact permanent magnets that attract each other. The stiffness adjustment is simple, fast, and has high durability.

3. The frequency of the ultra-low frequency pendulum tuned mass damper of the present invention varies slightly with the vibration amplitude of the mass block. The TMD can not only achieve the vibration reduction target well, but also automatically realize the limit position, and at the same time improve the durability . When the vibration of the main structure is small, since the vibration frequency at the balance position of the ultra-low frequency pendulum type tuned mass damper (TMD) of the present invention is slightly higher than that of the main structure, the TMD hardly moves, avoiding the TMD fatigue damage caused by the small long-term vibration, Thereby the durability of the TMD system is improved; when the vibration of the main structure is relatively large, the TMD of the present invention will have a considerable vibration displacement. At this time, due to the increase of the amplitude, the negative stiffness provided by the negative stiffness adjusting device is also increasing, namely The frequencies of the TMD and the main structure are getting closer and closer, and the TMD begins to play a full role in tuning, thus showing a better damping effect; when the amplitude of the TMD continues to increase to a certain extent, due to the negative stiffness adjustment device provided The negative stiffness is too large, so that the vibration frequency of TMD becomes slightly smaller than that of the main structure. Under the joint action of damping and frequency detuning of TMD, the amplitude of TMD begins to decrease, thus playing the role of automatic limit. After a certain level, TMD began to give full play to a new round of tuning. After the above cycle, the vibration energy of the main structure is gradually absorbed and dissipated by the TMD.

Description of drawings

Fig. 1 is a schematic structural diagram of the ultra-low frequency pendulum tuned mass damper of the present invention.

Fig. 2 is a schematic diagram of the structure along the direction A-A in Fig. 1 .

Figure 3 is a schematic diagram of the force of the TMD mass when it is in a balanced state.

Figure 4 is a schematic diagram of the force on the TMD mass when it swings to the left from the equilibrium position.

Figure 5 is a schematic diagram of the force on the TMD mass when it swings from the equilibrium position to the right.

Fig. 6 is a schematic structural diagram of a model test made for the present invention.

Fig. 7 is the vibration time history curve of the TMD mass block when there are no permanent magnets on both sides of the mass block.

Fig. 8 is a local time history diagram of the vibration of the TMD mass block at the design maximum amplitude when there are no permanent magnets on both sides of the mass block.

Fig. 9 is a local time history diagram of the vibration of the TMD mass block at the place where the vibration amplitude is 50% of the design maximum amplitude when there are no permanent magnets on both sides of the mass block.

Fig. 10 is a local time history diagram of the vibration of the TMD mass block at the place where the vibration amplitude is 20% of the design maximum amplitude when there are no permanent magnets on both sides of the mass block.

Fig. 11 is the vibration time history curve of the TMD mass block when a set of permanent magnets are placed on both sides of the mass block.

Fig. 12 is a local time history diagram of the vibration of the TMD mass at the design maximum amplitude when a set of permanent magnets are placed on both sides of the mass.

Fig. 13 is a partial time history diagram of the vibration of the TMD mass block at the place where a set of permanent magnets are placed on both sides of the mass block and the vibration amplitude is 50% of the design maximum amplitude.

Fig. 14 is a partial time history diagram of the vibration of the TMD mass block at the place where a set of permanent magnets are placed on both sides of the mass block and the vibration amplitude is 20% of the design maximum amplitude.

Fig. 15 is the vibration time history curve of the TMD mass block when two sets of permanent magnets are placed on both sides of the mass block.

Fig. 16 is a local time history diagram of the vibration of the TMD mass at the design maximum amplitude when two sets of permanent magnets are placed on both sides of the mass.

Fig. 17 is a partial time history diagram of the vibration of the TMD mass block at the point where the vibration amplitude is 50% of the design maximum amplitude when two sets of permanent magnets are placed on both sides of the mass block.

Fig. 18 is a local time history diagram of the vibration of the TMD mass block at the position where the vibration amplitude is 20% of the design maximum amplitude when two sets of permanent magnets are placed on both sides of the mass block.

Serial numbers in the figure: 1 is a sling, 2 is a mass block, 3 is a permanent magnet, 4 is a viscous damper, 5 is a bracket, 6 is a support, 7 is a top plate, 8 is a bottom plate, and 9 is a swing chamber.

Detailed ways

Embodiment 1: Referring to Fig. 1, an ultra-low frequency pendulum-type tuned mass damper includes a pendulum chamber 9 disposed in the structure, a sling 1 connected to the structure at the top of the pendulum chamber 9, and hung on the lower end of the sling 1 The mass block 2 of the part, the viscous damper 4 and the negative stiffness adjustment device arranged between the mass block 2 and the structure, the number of the viscous damper 4 and the negative stiffness adjustment device are two and are in The two sides corresponding to the mass block 2 are symmetrically arranged, and the negative stiffness adjustment device includes n pieces of permanent magnets 3 with N pole/S pole polarity arranged on one side of the mass block 2, and n pieces are arranged on the side surface The polarity of the corresponding structure is the permanent magnet 3 of S pole/N pole, and the permanent magnets 3 on both sides of the mass block 2 are cylindrical permanent magnets.

The working principle of the present utility model is:

(1) As shown in Figures 1-3, when the structure is stationary, the negative stiffness adjustment devices on the left and right sides of the mass block of the tuned mass damper balance each other, and the mass block is in a balanced state;

(2) When the structure vibrates, the pendulum of the tuned mass damper also swings accordingly, as shown in Figure 4, when the pendulum swings to the left at an angle θ (θ<5°), the permanent magnets on both sides at this time The attractive force is F ₁ ≥ _{F 2} , the motion differential equation mlθ″+p(θ)=0, p(θ) is the restoring force dependent on the swing angle θ:

p(θ)＝mgsinθ-(F ₁ cosθ-F ₂ cosθ)

Because the angle θ is very small (within 5 degrees), approximately taking sinθ≈θ and cosθ≈1, we can get:

p(θ)≈mgθ-(F ₁ -F ₂ ) ①

in

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;\&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;\&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>$

(3) As shown in Figure 5, when the right swing angle θ (within 5 degrees), the restoring force is:

p(θ)≈mgθ-(F ₂ -F ₁ ) ②

in

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;\&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;\&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>$

Combining formulas ① and ②, the unified formula of restoring force is obtained:

p(θ)≈mgθ-(F _n -F _p )

in

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;\&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;\&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>$

System Effective Stiffness

k _e ＝k _l -k _mag ③

in $k_l=\frac{\mathrm{mg}}{l}$ ④

k _mag =k _n -k _p ⑤

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{\mathrm{<span\; class="notranslate">\; \&delta;F</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{<span\; class="notranslate">\; \&PartialD;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span>\\ <span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;\&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; |</span>\end{array}$

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{\mathrm{<span\; class="notranslate">\; \&delta;F</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{<span\; class="notranslate">\; \&PartialD;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span>\\ <span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;\&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l\&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; |</span>\end{array}$

Obviously, k _mag >0 corresponds to any position of the TMD mass block, so k _e <k _l , that is, the stiffness of the original system decreases. At this time, the TMD natural frequency down, resulting in a lower vibration frequency with a shorter pendulum length.

Embodiment two: referring to Fig. 6-Fig. 18, Fig. 6 is the test model of making, wherein forms vibration chamber between support 5, top plate 7, base plate 8, and support 6 is arranged on the both sides corresponding to mass block, and is used for fixing permanent magnet. Wherein, the length of the pendulum is l=1.9m, the mass of the mass block is m=10kg, and the design maximum swing angle of the pendulum is θ _max =3°. In this experiment, the distance d ₀ at the equilibrium position of the permanent magnet is 18cm, the circular permanent magnet is model N38, and the size is D150×10mm. The experimental results are shown in Table 1.

As can be seen from the experimental results in attached table 1, the method of the present invention has a very obvious effect on reducing the frequency of the pendulum TMD. When the pendulum reaches its design amplitude, placing a group of permanent magnets on both sides of the mass can reduce the TMD frequency by 5.7 %, placing 2 sets of permanent magnets on both sides of the mass can reduce the TMD frequency by 11.9%.

Schedule 1:

Claims (2)

1. A kind of ultra-low frequency pendulum type tuned mass damper, it is characterized in that, comprise the swing cavity that is arranged on the structure body, the sling that is connected with the structure body of swing cavity top, hang on the mass block at the lower end of sling, set The viscous damper and the negative stiffness adjustment device between the mass block and the structure body, the number of the viscous damper and the negative stiffness adjustment device are two and are symmetrically arranged on the two sides corresponding to the mass block, so The negative stiffness adjusting device described above comprises n pieces of permanent magnets arranged on one side of the mass block with the polarity of N pole/S pole, and n pieces of permanent magnets arranged on the corresponding structure on the side surface with the polarity of S pole/N pole. pole permanent magnet. 2. The ultra-low frequency pendulum tuned mass damper according to claim 1, wherein the permanent magnet is a cylindrical permanent magnet.