Triangular-prism-shaped tuned mass damper suitable for large-span cantilever structure

Abstract

The present invention relates to a triangular-prism-shaped tuned mass damper suitable for a large-span cantilever structure. The triangular-prism-shaped-shaped tuned mass damper comprises a triangular-prism-shaped box (1), and particle damping units (4) and a steel mass block (3), which are arranged in the triangular-prism-shaped box (1), wherein a high damping spring (2) is provided below the triangular-prism-shaped box (1); and each particle damping unit (4) comprises a particle damping chamber (5), three different sizes of particle balls, and a foam rubber pad (9). When the vibration amplitude of the structure is relatively small, the particle balls dissipate energy by means of pressing the foam rubber pads and rolling; and when the vibration amplitude of the structure is relatively large, the particle balls dissipate energy by means of colliding and pressing foam rubber. Compared with the prior art, the present invention realizes a phased energy dissipation mechanism, and also solves the problems of a narrow vibration reduction frequency band, a large motion stroke and noise generated by the particle collision of a traditional mass tuned damper.

Description

A triangular prism tuned mass damper suitable for long-span cantilever structures Technical Field

[0001] The invention belongs to the technical field of civil structure vibration control, and in particular relates to a triangular prism-type tuned mass damper suitable for long-span cantilever structures. Background Art

[0002] With the advancement of civil engineering technology, the size of buildings and the number of people they can accommodate are constantly increasing, and their structural forms are becoming increasingly innovative. To meet the demands of building functionality and aesthetics, records for large spans and long cantilevers are constantly being broken. However, in addition to vibrations caused by earthquakes, large-span and cantilevered structures are prone to vertical resonance due to their low natural frequencies, which are close to the frequencies of human activity. This can increase internal forces and compromise structural reliability. Furthermore, for large-span buildings with dense crowds, such as theaters, airports, and shopping malls, vertical structural vibrations caused by pedestrian movement can produce significant loads. Furthermore, human-induced structural vibrations not only endanger structural safety and reliability, but also affect human comfort. Therefore, improving the vertical vibration damping capacity of large-span cantilevered structures is of great significance.

[0003] Generally, the vibration response of long-span cantilever structures can be reduced by increasing structural stiffness. However, this not only increases material consumption and construction costs, but also increases the structure's inertia, resulting in greater internal forces under dynamic forces. This can also negatively impact the aesthetics of the building. Therefore, to achieve greater economic benefits and structural reliability, long-span cantilever structures can be treated with additional dampers. Among various dampers, tuned mass dampers (TMDs) offer a particularly significant vibration reduction effect.

[0004] A tuned mass damper (TMD) consists of a mass, spring, and damping system. Its vibration frequency is adjusted to near the primary structural frequency, altering the structural resonance characteristics to achieve vibration reduction. TMDs have been used for vertical vibration reduction in large-span structures, such as the Jan Lindzeel Bridge in the Netherlands, the Millennium Bridge in London, and the New Delhi Airport in India. However, TMDs also have significant drawbacks. They are effective only within a narrow frequency range near the resonance zone, resulting in a narrow vibration reduction bandwidth and a large range of motion. Furthermore, if the structure's natural frequency changes, the damper is likely to become detuned. To compensate for this TMD limitation, multiple dampers can be installed to cover multiple frequency bands. However, this inevitably increases construction costs and creates unfavorable economic consequences.

[0005] Summary of the Invention

[0006] The purpose of the present invention is to provide a triangular prism tuned mass damper suitable for large-span cantilever structures in order to solve the problems of narrow vibration damping frequency band, large motion stroke and noise generated by particle collision of traditional tuned mass dampers.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A triangular prism tuned mass damper suitable for long-span cantilever structures comprises a triangular prism box, a high-damping spring installed below the triangular prism box, a steel mass block arranged inside the triangular prism box, and a plurality of particle damping units for vibration reduction.

[0009] Furthermore, the upper end of the high-damping spring is connected to the triangular prism box, and the lower end of the high-damping spring is connected to the large-span cantilever structure that requires vertical vibration control.

[0010] Furthermore, the edges of the steel mass block are connected to the triangular prism box, and the particle damping unit is arranged in the space between the triangular prism box and the steel mass block.

[0011] Furthermore, the particle damping unit includes a particle damping chamber, a foam rubber pad installed on the inner wall of the particle damping chamber, and large particle balls, medium particle balls and small particle balls placed on the foam rubber pad.

[0012] Furthermore, a steel partition is provided between the triangular prism box and the steel mass block, which can separate the space above the steel mass block into two particle damping units.

[0013] Furthermore, two particle damping units are formed on the upper end and both sides of the steel mass block.

[0014] Furthermore, the particle damping unit is in the shape of a triangular prism with a right triangle cross section, so as to increase the collision energy consumption of the particle balls.

[0015] Furthermore, the particle damping units are symmetrically arranged so that the horizontal collision force generated during the collision can be self-balanced within the damper.

[0016] Furthermore, large particle balls, medium particle balls and small particle balls with decreasing diameters are placed in sequence along the direction of decreasing height in the particle damping chamber.

[0017] Furthermore, the distance between the large granular balls is smaller than the diameter of the medium granular balls, and the distance between the medium granular balls is smaller than the diameter of the small granular balls.

[0018] Furthermore, the ratio of the diameter of the large particle ball to the maximum height of the particle damping chamber is 0.56-0.64, preferably 0.6.

[0019] Furthermore, the ratio of the diameter of the medium-sized particle ball to the maximum height of the particle damping chamber is 0.30-0.35, preferably 0.33.

[0020] Furthermore, the ratio of the diameter of the small particle balls to the maximum height of the particle damping chamber is 0.15-0.19, preferably 0.17.

[0021] Furthermore, the large particle ball includes a large particle ball foam rubber outer layer and a large particle ball steel inner core wrapped inside it, the medium particle ball includes a medium particle ball foam rubber outer layer and a medium particle ball steel inner core wrapped inside it, and the small particle ball includes a small particle ball foam rubber outer layer and a small particle ball steel inner core wrapped inside it.

[0022] Furthermore, the surface of the foam rubber pad at the bottom of the particle damping chamber has a plurality of arc concave surfaces, and the large particle balls, medium particle balls and small particle balls are respectively placed tangentially at the bottom of the arc concave surfaces.

[0023] Furthermore, the curvature radius of the arc concave surface is 2.8-3.2 times, preferably 3 times, the radius of the large particle ball, the medium particle ball and the small particle ball respectively.

[0024] Furthermore, when the structural vibration amplitude is small, the granular balls consume energy by squeezing the foam rubber pad and rolling; when the structural vibration amplitude is large, the granular balls consume energy by colliding and squeezing the foam rubber.

[0025] Furthermore, by adjusting the mass of the steel mass block and the stiffness of the high-damping spring, the natural frequency of the damper is made close to the natural frequency of the vertical vibration of the long-span cantilever structure, so as to achieve the purpose of tuning.

[0026] Furthermore, the mass of the steel mass block is such that the ratio of the total mass of the triangular prism box to the mass of the long-span cantilever structure is 0.5%-2%, preferably 1%.

[0027] The present invention also provides an application of a triangular prism-type tuned mass damper suitable for a long-span cantilever structure in the field of vibration control of the long-span cantilever structure.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] (1) The present invention applies particle damping technology to the control of vertical vibration of structures. By setting up particle damping units, the dynamic response of large-span cantilever structures under earthquake or human-induced vibration is reduced, and the energy dissipation mechanism of particle damping under vertical excitation is expanded. Under vibration excitations of different amplitudes, particles and foam rubber pads are used to dissipate energy in different ways, forming a staged energy dissipation mechanism with a relatively simple device structure; using a single damper, the vertical vibration of large-span cantilever structures under human-induced vibration and earthquake is taken into account at the same time. When the structural vibration amplitude is small, the particle balls dissipate energy by squeezing the foam rubber pad and rolling; when the structural vibration amplitude is large, the particle balls dissipate energy by colliding and squeezing the foam rubber. While realizing the staged energy dissipation mechanism, the problems of narrow vibration reduction band, large motion stroke, and noise generated by particle collision of traditional tuned mass dampers are solved.

[0030] (2) Compared with the rectangular particle damping unit, the particle damping unit with a triangular cross-section in the present invention increases the probability of collision between particles and between particles and the inner wall of the chamber under vertical vibration. Since the size change law of the particle balls is consistent with the height change law of the particle damping chamber, when the size of the particle balls and the height of the particle damping chamber meet a certain ratio, the relative positions of the three sizes of particle balls are not easy to change, and the particle balls are not easy to stack. The movement and collision trajectory of each particle is confined to a smaller space, reducing the randomness of the particle movement. In addition, since the top surface of the particle damping chamber is an inclined surface, during the vibration process, the smaller particle balls always move towards and collide with the larger particle balls, and the energy consumption mechanism can always be guaranteed during the vibration process. The inclined surface on the top of the particle damping chamber also has a certain drainage function, which to a certain extent prevents the accumulation of water, snow and dust from affecting the quality of the damper, thereby reducing the possibility of imbalance.

[0031] (3) The present invention utilizes foam rubber pads. On the one hand, it is used as a nonlinear energy-absorbing material to increase energy dissipation, and on the other hand, it reduces the noise generated when particles collide with the inner wall of the chamber. It is particularly suitable for buildings such as theaters that have high acoustic requirements. The foam rubber pads are dispersed on the inner wall of the particle balls and the particle damping chamber. While ensuring the energy dissipation deformation margin, the thickness of the foam rubber pads used can be reduced, and the noise generated by the collision between the particles can be reduced. At the same time, because the surface of the foam rubber pad is relatively rough and the friction coefficient is relatively large, when the particles roll and collide in the chamber, the relative movement between the foam rubber surfaces can increase the energy consumed by friction. Under human-induced vibrations with a small amplitude, the arc concave surface on the foam rubber pad can cause the particles to roll horizontally, increase the rolling friction energy consumption mode, and at the same time, enable the particles to return to their initial position after vibration. Under the action of earthquakes with a large amplitude, when the particles collide obliquely with the bottom of the chamber, the arc concave surface on the foam rubber pad increases the deformation margin of the energy-absorbing material during collision and extrusion, thereby improving the efficiency of energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] FIG1 is a front view of a triangular prism-type tuned mass damper according to the present invention.

[0033] FIG2 is a three-dimensional view of the triangular prism box of the present invention.

[0034] FIG3 is a cross-sectional view of a triangular prism-type tuned mass damper according to the present invention.

[0035] FIG4 is a schematic top view of the particle arrangement of the present invention.

[0036] FIG5 is a cross-sectional view of the granular ball of the present invention.

[0037] FIG6 is a side view schematic diagram of the particle arrangement of the present invention.

[0038] FIG7 is a schematic diagram of the collision mechanism of the particle damping unit of the present invention.

[0039] Numbers in the figure: 1-triangular prism box, 2-high damping spring, 3-steel mass block, 4-particle damping unit, 5-particle damping chamber, 6-large particle ball, 6.1-large particle ball foam rubber outer layer, 6.2-large particle ball steel inner core, 7-medium particle ball, 7.1-medium particle ball foam rubber outer layer, 7.2-medium particle ball steel inner core, 8-small particle ball, 8.1-small particle ball foam rubber outer layer, 8.2-small particle ball steel inner core, 9-foam rubber pad, 9.1-arc concave surface, 10-steel partition. DETAILED DESCRIPTION

[0040] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0041] Example 1:

[0042] This embodiment provides a triangular prism-type tuned mass damper suitable for long-span cantilever structures, which is installed on long-span cantilever structures requiring vertical vibration control. The triangular prism-type tuned mass damper of this embodiment comprises a triangular prism housing 1, a high-damping spring 2 mounted below the housing 1, a steel mass 3 disposed within the housing 1, and multiple particle damping units 4 for vibration reduction. The upper end of the high-damping spring 2 is connected to the housing 1, while the lower end of the high-damping spring 2 is connected to the long-span cantilever structure requiring vertical vibration control. The edges of the steel mass 3 are connected to the housing 1, and the particle damping units 4 are disposed within the remaining space within the housing 1. The particle damping units 4 comprise a particle damping chamber 5, a foam rubber pad 9 mounted on the inner wall of the particle damping chamber 5, and large, medium, and small particle balls 6, 7, and 8 placed on the foam rubber pad 9. When the structural vibration amplitude is small, the granular balls of different sizes consume energy by squeezing the foam rubber pad 9 and rolling; when the structural vibration amplitude is large, the granular balls consume energy by colliding and squeezing the foam rubber pad 9.

[0043] Example 2:

[0044] This embodiment provides a triangular prism-type tuned mass damper suitable for long-span cantilever structures. It is installed mid-span in long-span structures requiring vertical vibration control. As shown in Figure 1, the triangular prism-type tuned mass damper of this embodiment comprises a triangular prism housing 1, a high-damping spring 2 mounted below the housing, and a steel mass 3 and multiple particle damping units 4 disposed within the housing for vibration reduction.

[0045] The upper end of the high-damping spring 2 is connected to the triangular prism housing 1, while the lower end is connected to the long-span cantilever structure that requires vertical vibration control. By adjusting the mass of the steel mass 3 and the stiffness of the high-damping spring 2, the damper's natural frequency is aligned with the vertical natural frequency of the cantilever structure, achieving tuning. The mass of the steel mass 3 is adjusted to ensure a 1% ratio between the total mass of the triangular prism housing 1 and the mass of the long-span cantilever structure.

[0046] As shown in Figure 3, the steel mass 3 in this embodiment is a regular quadrangular prism, with the front and rear ends of the steel mass 3 aligned with the front and rear ends of the triangular prism housing 1. The edges of the steel mass 3 are connected to the triangular prism housing 1, and the particle damping unit 4 is disposed within the remaining space of the triangular prism housing 1. A steel partition 10 is provided between the triangular prism housing 1 and the steel mass 3. Two particle damping units 4 are formed at the top and sides of the steel mass 3. In this embodiment, the particle damping units 4 are in the shape of a triangular prism with a right-angled triangle cross-section. The particle damping units 4 are symmetrically arranged so that horizontal collision forces can be self-balanced within the damper.

[0047] As shown in Figures 3, 4, and 6, the particle damping unit 4 includes a particle damping chamber 5, a foam rubber pad 9 mounted on the inner wall of the particle damping chamber 5, and large particle balls 6, medium particle balls 7, and small particle balls 8 placed on the foam rubber pad 9. The large particle balls 6, medium particle balls 7, and small particle balls 8 are placed in descending order of diameter within the particle damping chamber 5. The distance between the large particle balls 6 is smaller than the diameter of the medium particle balls 7, and the distance between the medium particle balls 7 is smaller than the diameter of the small particle balls 8. The ratio of the diameter of the large particle balls 6 to the maximum height of the particle damping chamber 5 is 0.6, the ratio of the diameter of the medium particle balls 7 to the maximum height of the particle damping chamber 5 is 0.33, and the ratio of the diameter of the small particle balls 8 to the maximum height of the particle damping chamber 5 is 0.17.

[0048] As shown in Figure 5, the large particle ball 6 is composed of a large particle ball foam rubber outer layer 6.1 and a large particle ball steel inner core 6.2 wrapped inside it; the medium particle ball 7 is composed of a medium particle ball foam rubber outer layer 7.1 and a medium particle ball steel inner core 7.2 wrapped inside it; the small particle ball 8 is composed of a small particle ball foam rubber outer layer 8.1 and a small particle ball steel inner core 6.2 wrapped inside it.

[0049] As shown in FIG7 , the surface of the foam rubber pad 9 at the bottom of the particle damping chamber 5 has a plurality of arcuate concave surfaces 9.1. The large particle balls 6, medium particle balls 7, and small particle balls 8 are placed tangentially at the bottom of the arcuate concave surfaces 9.1. In this embodiment, the radius of curvature of the arcuate concave surfaces 9.1 is three times the radius of the large particle balls 6, medium particle balls 7, and small particle balls 8, respectively.

[0050] Example 3:

[0051] This embodiment provides a triangular prism-type tuned mass damper suitable for long-span cantilever structures. The device is installed at the cantilever end of the cantilever structure to be damped. It comprises a triangular prism housing 1 with an isosceles triangle cross-section, a three-dimensional view of which is shown in Figure 2. As shown in Figure 3, triangular prism housing 1 is composed of a steel mass 3 and four particle damping units 4. Below triangular prism housing 1 is a high-damping spring 2, the lower end of which is connected to the long-span cantilever structure requiring vertical vibration control.

[0052] In this embodiment, a steel partition 10 is fixed between the triangular prism box 1 and the steel mass block 3, so that two particle damping units 4 are formed above the steel mass block 3; there are four particle damping units 4 around the steel mass block 3, and the particle damping units 4 are in the shape of a triangular prism and have a right triangle cross-section.

[0053] In this embodiment, each particle damping unit 4 includes a particle damping chamber 5, large particle balls 6, medium particle balls 7, small particle balls 8 and a foam rubber pad 9; the foam rubber pad 9 is fixed to the inner wall of the particle damping unit 4; the large particle balls 6, medium particle balls 7, and small particle balls 8 are placed inside the particle damping chamber 5.

[0054] In this embodiment, as shown in FIG3 , large granular balls 6, medium granular balls 7, and small granular balls 8 are placed in the particle damping unit 4 in descending order of height within the particle damping chamber 5. As shown in FIG4 , the distance between the large granular balls 6 is smaller than the diameter of the medium granular balls 7, and the distance between the medium granular balls 7 is smaller than the diameter of the small granular balls 8.

[0055] In this embodiment, as shown in Figure 5, the large particle ball 6 includes a large particle ball steel inner core 6.2 and a large particle ball foam rubber outer layer 6.1, and the large particle ball foam rubber outer layer 6.1 wraps the large particle ball steel inner core 6.2; the medium particle ball 7 includes a medium particle ball steel inner core 7.2 and a medium particle ball foam rubber outer layer 7.1, and the medium particle ball foam rubber outer layer 7.1 wraps the medium particle ball steel inner core 7.2; the small particle ball 8 includes a small particle ball steel inner core 8.2 and a small particle ball foam rubber outer layer 8.1, and the small particle ball foam rubber outer layer 8.1 wraps the small particle ball steel inner core 8.2.

[0056] Specifically, by adjusting the mass of steel mass 3 and the stiffness of high-damping spring 2, the damper's natural frequency is brought close to the natural frequency of the cantilever structure's vertical vibration, achieving tuning. In this embodiment, the mass of steel mass 3 is such that the ratio of the total mass of the triangular prism box 1 to the mass of the long-span cantilever structure is 1%.

[0057] Specifically, all the particle damping units 4 are arranged symmetrically so that the horizontal collision force generated when the large particle balls 6, the medium particle balls 7, and the small particle balls 8 collide can be self-balanced within the damper; the edges of the steel mass block 3 are connected to the triangular prism box 1, so that the triangular prism box 1 can just accommodate the steel mass block 3.

[0058] Specifically, as shown in Figure 6 , the ratio of the diameter of large particle balls 6 to the maximum height of particle damping chamber 5 is 0.6; the ratio of the diameter of medium particle balls 7 to the maximum height of particle damping chamber 5 is 1 / 3; and the ratio of the diameter of small particle balls 8 to the maximum height of particle damping chamber 5 is 1 / 6. Specifically, the surface of the foam rubber pad 9 at the bottom of particle damping unit 4 has an arc-shaped concave surface 9.1. The radius of arc-shaped concave surface 9.1 is three times the radius of large particle balls 6, medium particle balls 7, and small particle balls 8, respectively. Large particle balls 6, medium particle balls 7, and small particle balls 8 are placed at the bottom of arc-shaped concave surface 9.1.

[0059] The working principle of the present invention is as follows.

[0060] After the damper is frequency-modulated, when the cantilever structure vibrates with relatively small amplitudes under human-induced vibration excitation, the resonance amplitude of the enclosure is relatively small. Due to inertia, the resonance of the triangular prism enclosure 1 causes relative motion between the particle damping chamber 5 and the particle balls, causing the steel core of the particles to squeeze the foam rubber pad 9 and the particle's outer foam rubber coating, dissipating energy through deformation of the foam rubber. During human-induced vibration, walking and leaning on the railings generate horizontal excitations to the structure. Furthermore, the tilt of the damper enclosure during resonance, the uneven contact between the particles and the inner surface of the chamber, and the horizontal restoring force generated by the compression of the foam rubber pad 9 with its arc-shaped concave surface 9.1, can cause the particles to roll even under relatively small amplitudes. While dissipating energy by squeezing the foam rubber pad, the particles also convert kinetic energy into gravitational potential energy by rolling back and forth within the arc-shaped concave surface 9.1, simultaneously dissipating energy through friction. The further the particles deviate from their initial position, the more energy they dissipate through friction, and the greater the restoring force generated by squeezing the foam rubber pad 9. When the vibration ends, the particles return to their initial position.

[0061] When the cantilever structure vibrates with a large amplitude under the action of an earthquake, the resonance amplitude of the box is also large. At this time, the granular balls will bounce in the particle damping chamber 5 and collide inelastically with the inner wall of the particle damping chamber 5, squeezing the foam rubber and dissipating energy.

[0062] The energy dissipation mechanism of particle collision is shown in Figure 7. During the particle bouncing process, due to vertical excitation, the particles undergo horizontal displacement after contacting the inclined surface of the chamber, causing the small particle ball 8 to collide with the medium particle ball 7, the medium particle ball 7 to collide with the large particle ball 6, the large particle ball 6 to collide with the side wall of the chamber, and then the particle ball collides with the bottom of the chamber.

[0063] In this embodiment, by limiting the particle size and the height of the particle damping chamber, we prevent particle stacking while confining the movement and collision paths of each particle to a smaller space. This ensures that the relative positions of the three particle sizes remain constant, reducing the randomness of particle movement. As long as the relative positions of the three particle sizes remain constant, the collision energy dissipation mechanism shown in Figure 7 can be repeatedly achieved.

[0064] At the same time, under vertical vibration, the particles will also produce horizontal movement, increasing the number of collisions and improving energy consumption efficiency. During the collision, the foam rubber pad 9 and the foam rubber outer layer of the particle ball are squeezed, realizing nonlinear energy consumption. What occurs between the particle and the bottom of the chamber is an oblique collision. The foam rubber pad 9 with the arc concave surface 9.1 provides more energy-consuming deformation margin, thereby dissipating more energy. During the vibration process, there may be rolling of particles on the arc concave surface and relative displacement between particles and particles, particles and chambers, so friction can also play a certain role in energy consumption.

[0065] The above description of the embodiments is intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, without departing from the scope of the present invention, should be within the scope of protection of the present invention.

Claims

1. A triangular prism type tuned mass damper suitable for long-span cantilever structures, characterized in that: It comprises a triangular prism box (1), a high damping spring (2) installed below the triangular prism box (1), and a steel mass block (3) and a plurality of particle damping units (4) for vibration reduction arranged inside the triangular prism box (1); The upper end of the high damping spring (2) is connected to the triangular prism box (1), and the lower end of the high damping spring (2) is connected to a large-span cantilever structure that needs to be vertically vibrated; The edges of the steel mass block (3) are connected to the triangular prism box (1), and the particle damping unit (4) is arranged in the space between the triangular prism box (1) and the steel mass block (3); The particle damping unit (4) comprises a particle damping chamber (5), a foam rubber pad (9) mounted on the inner wall of the particle damping chamber (5), and large particle balls (6), medium particle balls (7) and small particle balls (8) placed on the foam rubber pad (9).

2. A triangular prism type tuned mass damper suitable for a long-span cantilever structure according to claim 1, characterized in that: A steel partition plate (10) is arranged between the triangular prism box (1) and the steel mass block (3) and is capable of dividing the space above the steel mass block (3) into two particle damping units (4).

3. The triangular prism type tuned mass damper suitable for a long-span cantilever structure according to claim 1, characterized in that: Two particle damping units (4) are formed at the upper end and both sides of the steel mass block (3); the particle damping units (4) are in the shape of triangular prisms with a right-angled triangle cross section, and the particle damping units (4) are symmetrically arranged.

4. The triangular prism type tuned mass damper suitable for a long-span cantilever structure according to claim 1, characterized in that: Large particle balls (6), medium particle balls (7) and small particle balls (8) with decreasing diameters are placed in sequence along a decreasing height direction in the particle damping chamber (5).

5. The triangular prism type tuned mass damper suitable for a long-span cantilever structure according to claim 4, characterized in that: The distance between the large particle balls (6) is smaller than the diameter of the medium particle balls (7), and the distance between the medium particle balls (7) is smaller than the diameter of the small particle balls (8).

6. The triangular prism type tuned mass damper suitable for a long-span cantilever structure according to claim 4, characterized in that: The ratio of the diameter of the large particle ball (6) to the maximum height of the particle damping chamber (5) is 0.56-0.64, the ratio of the diameter of the medium particle ball (7) to the maximum height of the particle damping chamber (5) is 0.3-0.35, and the ratio of the diameter of the small particle ball (8) to the maximum height of the particle damping chamber (5) is 0.15-0.

18.

7. The triangular prism type tuned mass damper suitable for a long-span cantilever structure according to claim 1, characterized in that: The large particle ball (6) comprises a large particle ball foam rubber outer layer (6.1) and a large particle ball steel inner core (6.2) wrapped therein; the medium particle ball (7) comprises a medium particle ball foam rubber outer layer (7.1) and a medium particle ball steel inner core (7.2) wrapped therein; and the small particle ball (8) comprises a small particle ball foam rubber outer layer (8.1) and a small particle ball steel inner core (8.2) wrapped therein.

8. The triangular prism type tuned mass damper suitable for a long-span cantilever structure according to claim 1, characterized in that: The surface of the foam rubber pad (9) at the bottom of the particle damping chamber (5) has a plurality of arc concave surfaces (9.1), and the large particle balls (6), the medium particle balls (7) and the small particle balls (8) are respectively placed at the bottom of the arc concave surfaces (9.1).

9. The triangular prism type tuned mass damper suitable for a long-span cantilever structure according to claim 8, characterized in that: The curvature radius of the arc concave surface (9.1) is 2.8-3.2 times the radius of the large particle ball (6), the medium particle ball (7) and the small particle ball (8).

10. An application of the triangular prism tuned mass damper suitable for a long-span cantilever structure as claimed in any one of claims 1 to 9 in the field of vibration control of the long-span cantilever structure.

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