An ultra-low frequency tuned mass damper with negative stiffness mechanism

Abstract

The present invention belongs to the technical field of wind-induced vibration control of bridges. In order to address the problems of excessive static spring elongation, excessive spring mass, and high cost in traditional tuned mass dampers when controlling low-frequency vortex vibrations of bridges, an ultra-low frequency tuned mass damper with a negative stiffness mechanism is provided, comprising a mass element, a positive stiffness element, a negative stiffness element, and an energy-absorbing element. The design of the mass element, the positive stiffness element, and the energy-absorbing element is similar to that of a traditional TMD. The negative stiffness is achieved by a slide-roller-spring mechanism, and most of the deadweight of the mass element is borne by the positive stiffness element. While having the same mass and tuning frequency as a traditional TMD, the stiffness of the positive stiffness element of the present invention is much greater than the stiffness of the traditional TMD spring, so the static elongation and mass of the spring are significantly reduced. Based on the characteristics of the clear height inside the box-shaped main beam box of a long-span bridge, the present invention can meet the installation space requirements of an ultra-low frequency tuned mass damper with a natural frequency of 0.1 Hz.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge wind-induced vibration control and relates to an ultra-low frequency tuned mass damper with a negative stiffness mechanism. Background Art

[0002] Significant vortex-induced vibration (VIV) can occur during the operation of long-span bridges. Large-scale VIV can have significant negative social impacts, affect traffic safety, and even cause fatigue damage to bridge structures or components. In recent years, significant VIV has occurred on numerous long-span bridges both domestically and internationally, including the Xihoumen Bridge, Yingwuzhou Bridge, Humen Bridge, the Jindo Bridge in South Korea, the Verrazano-Narrows Bridge in the United States, and the 1915 Çanakkale Bridge in Turkey. These bridges all use box-type main girders, whereas truss bridges generally do not experience VIV.

[0003] In view of the harmfulness of bridge vortex vibration, vortex vibration control has always been a research hotspot in the field of bridge wind engineering. Bridge vortex vibration often occurs in several low-order vertical bending vibration modes of the bridge. Tuned Mass Damper (TMD) is a commonly used mechanical measure for bridge vortex vibration control. Traditional TMD suspends the mass block inside the box girder through coil springs, and sets energy-absorbing elements between the mass block and the main beam. When the TMD frequency is close to the controlled modal frequency of the bridge, the TMD will absorb and dissipate the vibration energy of the controlled mode, thereby improving the damping ratio of the controlled mode and reducing or eliminating the vortex vibration. TMD has been used for vortex vibration control of many bridges, including the Danish Kelp Bridge, the Tokyo Bay Bridge in Japan, the Niterói Bridge in Brazil, the Hong Kong-Zhuhai-Macao Bridge, the Humen Bridge, etc.

[0004] The low-order vertical bending modal frequency of long-span bridges is relatively low. The low-order vertical bending modal frequency of a kilometer-long main span suspension bridge is often lower than 0.2 Hz, or even lower than 0.1 Hz. According to the public literature "Using tuned mass damper inerter to mitigate vortex-induced vibration of long-span bridges: Analytical study" (Xu et al., Engineering Structures, 2019, 182: 101-111), traditional TMD cannot be used for ultra-low frequency bridge vortex vibration control. The reasons are: (1) The static elongation of the TMD spring under the weight of the TMD mass block is g / (2πf) 2(g is the acceleration of gravity, f is the natural frequency of TMD), and is inversely proportional to the square of the natural frequency of TMD (approximately equal to the controlled modal frequency). Therefore, as the controlled modal frequency decreases, the static elongation of TMD spring increases rapidly. When the controlled modal frequency is 0.2 Hz and 0.1 Hz, the static elongation of TMD spring reaches about 6.2 m and 24.8 m respectively. At this time, there is not enough space inside the box girder to install TMD. (2) In order to adapt to the static elongation of TMD spring and ensure that the stress of spring steel wire meets the design requirements, the length and wire diameter of TMD spring also increase with the decrease of controlled modal frequency. Therefore, the mass of TMD spring increases rapidly. Assuming that the design stress of spring steel wire is 370 MPa, when the controlled modal frequency is 0.2 Hz and 0.1 Hz, the ratio of TMD spring mass to TMD mass block mass reaches about 100% and 250% respectively. Therefore, traditional TMD is no longer feasible. Summary of the Invention

[0005] The present invention proposes an ultra-low frequency TMD with a negative stiffness mechanism, which aims to solve the problems of excessive static elongation of the spring and excessive mass of the spring in traditional TMD when controlling ultra-low frequency vortex vibration. By introducing a negative stiffness element, the present invention significantly reduces the static elongation of the spring and the mass of the spring of the TMD, thereby improving the economy and convenience of the TMD in low-frequency (0.2-0.4Hz) vortex vibration control, and at the same time makes the application of TMD in ultra-low frequency (<0.2Hz) vortex vibration control possible. The present invention consists of a mass element, a positive stiffness element, a negative stiffness element and an energy-absorbing element, wherein the design of the mass element, the positive stiffness element and the energy-absorbing element is similar to that of the traditional TMD, and most of the deadweight of the mass element is borne by the positive stiffness element. One end of the negative stiffness element is suspended on the top plate of the box beam or on a bracket fixed inside the box beam, and the other end is connected to the mass element. The stiffness of the positive stiffness element is K postive , the stiffness of the negative stiffness element is K negative , satisfying K postive >-K negative , the total stiffness of the system is K postive -K negative With the same mass and tuning frequency as conventional TMD, the K postive The spring rate is much higher than that of conventional TMD springs, so the static elongation and mass of the spring are significantly reduced. negative =-0.8K postive The spring stiffness of a conventional TMD with the same tuning frequency should be 0.2K postive ; The static elongation of the traditional TMD spring is The static elongation of the spring of the positive stiffness element of the present invention is only This is equivalent to 1 / 5 of the elongation of a traditional TMD spring. In addition, the weight of the spring of the present invention is also significantly reduced compared to a traditional TMD.

[0006] The technical solution of the present invention:

[0007] A super-low frequency tuned mass damper with a negative stiffness mechanism, the super-low frequency tuned mass damper has a symmetrical structure as a whole, including a first spring 1, a mass block 2, a slide 3, a roller 4, a first bearing rod 5, a pillar 6, a bearing 7, a second bearing rod 8, a pull ring 9, a second spring 10, a connecting rod 11, a limit rod 12 and an energy-absorbing element 13; the low-frequency tuned mass damper has a symmetrical structure as a whole, the upper end of the energy-absorbing element 13 is fixed to the top plate of the box beam or to a bracket fixed inside the box beam, and the lower end is fixed to the middle of the mass block 2; the upper end of the first spring 1 is suspended on the top plate of the box beam or on a bracket fixed inside the box beam, and the lower end is connected to the mass block 2; the lower end of the mass block 2 is suspended in the air and maintains a certain distance from the bottom plate of the box beam to ensure that the mass block 2 can vibrate freely inside the box beam; the two slides 3 are fixed respectively on the mass block 2 and the bottom plate of the box beam Block 2 on both sides; the roller 4 rolls freely on the outer wall of the slide 3; four pillars 6 and two first bearing rods 5 are arranged around the slide 3, symmetrically arranged on both sides of the slide 3; a circular hole is opened at the upper and lower ends of the pillar 6; the first bearing rod 5 passes through the roller 4, and at the same time, the first bearing rod 5 passes through the circular hole at the lower end of the pillar 6 and is fixed to it; the first bearing rod 5 is provided with a number of pull rings 9 along the length direction, and the two ends of the second spring 10 are respectively connected to the pull rings 9 on the first bearing rod 5 on both sides; the upper end of the connecting rod 11 is fixed to the top plate of the box beam or fixed on the bracket inside the box beam; the bearing 7 is embedded in the circular hole at the upper end of the pillar 6, and the second bearing rod 8 passes through the bearing 7; the second bearing rod 8 passes through the lower end of the connecting rod 11 and is fixed to the connecting rod 11; a limit rod 12 is provided at the top of the slide 3 to ensure that the roller 4 will not detach from the slide.

[0008] The first spring 1 is a helical tension spring made of spring steel wire, and its cross section is generally circular.

[0009] The mass block 2 is made of steel, and the connection position between the mass block 2 and the first spring 1 is as close to the bottom surface of the mass block 2 as possible, thereby reducing the height occupied by the mass block 2 alone and improving the utilization rate of the internal space of the box beam.

[0010] The slideway 3 is made of stainless steel, and the arc of the outer wall is formed by high-precision laser cutting. After cutting, it should be polished to ensure that the friction coefficient of the outer wall is as small as possible.

[0011] The slideway 3 is made of stainless steel, and its outer wall is the arc track of the roller 4. One or more cross braces are set between the inner walls to ensure that the two side walls have sufficient rigidity and do not undergo obvious deformation under the pressure of the roller 4.

[0012] The roller 4 has a strong load-bearing capacity, a small friction coefficient and strong durability.

[0013] The first bearing rod 5 is made of carbon steel or bearing steel, and has the characteristics of high rigidity and strong load-bearing capacity.

[0014] The support column 6 is made of steel, which has the characteristics of high rigidity and strong bearing capacity.

[0015] The bearing 7 has a strong load-bearing capacity, a small friction coefficient and strong durability.

[0016] The second bearing rod 8 is made of carbon steel or bearing steel, and has the characteristics of high rigidity and strong load-bearing capacity.

[0017] The pull ring 9 is made of steel and should have sufficient load-bearing capacity. The distance between the left and right pull rings can be fine-tuned to adjust the initial length of the second spring 10.

[0018] The second spring 10 is a helical tension spring made of spring steel wire with a generally circular cross section. In the static equilibrium position, the second spring 10 has sufficient initial elongation to ensure that the second spring 10 is always in tension during the vibration of the mass 2.

[0019] The connecting rod 11 is made of steel and has sufficient strength and rigidity.

[0020] The limiting rod 12 is a round steel rod wrapped with rubber, which has sufficient strength, rigidity and a certain buffering capacity.

[0021] The energy dissipation element 13 may be a liquid viscous damper or an eddy current damper to provide linear viscous damping, and the viscous damping coefficient under different amplitudes remains substantially stable.

[0022] The stiffness coefficient K of the negative stiffness mechanism composed of the slide 3, roller 4, first bearing rod 5, support 6, bearing 7, second bearing rod 8, pull ring 9 and second spring 10 negative Set according to actual needs, its absolute value is the stiffness coefficient K of the positive stiffness element postive 0.7-0.9 times of the spring group, the positive stiffness element is the first spring 1.

[0023] According to the open document "Design of Three New Cam-Based Constant-Force Mechanisms" (López-Martínez et al., Journal of Mechanical Design, 2018, 140(8):082302), the output force F of the negative stiffness mechanism and the center motion trajectory of the second spring 10 and the roller 4 satisfy the following relationship:

[0024]

[0025] The definitions of the symbols in the formula refer to Figure 2 , K represents the total stiffness of the spring group formed by the second spring 10, 2Δx represents the elongation of the second spring 10, α represents the angle between the support 6 and the y-axis, β represents the angle between the perpendicular line of the tangent of the motion trajectory of the roller 4 and the x-axis, tanα=x / l t [1-(x / l t ) 2 ] -1 / 2 , l t Represents the straight-line distance between the center of the first bearing rod 5 and the center of the second bearing rod 8.

[0026] Let F = K negative y+F0, then the center motion trajectory of roller 4 is calculated according to formula (3):

[0027]

[0028] The definitions of the symbols in the formula refer to Figure 2 , 2x0 represents the initial length of the second spring 10, l t represents the straight-line distance between the center of the first bearing rod 5 and the center of the second bearing rod 8, x represents the horizontal coordinate, y represents the vertical coordinate, K negative y+F0 represents the output of the negative stiffness mechanism; the x-axis is positive to the right, and the y-axis is positive upward. By numerically integrating the above equation, the xy curve of the center motion trajectory of the rollers 4 on both sides is drawn; the integral starting coordinates of the center motion trajectory of the left roller 4 are (-x0, 0), and the integral starting coordinates of the center motion trajectory of the right roller 4 are (x0, 0); the integral end point is set according to the actual required height of the slide 3.

[0029] The arc line shape of the outer wall of the slide 3 is calculated according to formula (4):

[0030]

[0031] The definitions of the symbols in the formula refer to Figure 2 , R represents the radius of the roller 4.

[0032] The beneficial effects of the present invention are as follows: (1) by introducing a negative stiffness mechanism, the present invention can significantly reduce the static elongation and spring mass of the TMD spring, thereby reducing the cost of the TMD; (2) the present invention can reduce the installation space of the TMD. According to the characteristic that the net height inside the box-shaped main beam box of a large-span bridge is generally in the range of 3-5m, the present invention can meet the installation space requirements of the ultra-low frequency TMD with a natural frequency of 0.1Hz; (3) the mass of the negative stiffness mechanism is mainly concentrated in the slideway 3, and the slideway 3 can be used as a part of the TMD mass element. Therefore, most of the mass of the negative stiffness mechanism can be used as the effective working mass of the TMD. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a structural diagram of an ultra-low frequency TMD with a negative stiffness mechanism;

[0034] Figure 2 It is a plan view of the constant force mechanism components.

[0035] In the figure: 1 first spring, 2 mass block, 3 slideway, 4 roller, 5 first bearing rod, 6 pillar, 7 bearing, 8 second bearing rod, 9 pull ring, 10 second spring, 11 connecting rod, 12 limit rod, 13 energy dissipation element. DETAILED DESCRIPTION

[0036] The specific implementation of the present invention is described in detail below in conjunction with the technical solutions and drawings.

[0037] like Figure 1 As shown, an ultra-low frequency tuned mass damper with a negative stiffness mechanism is shown. The ultra-low frequency tuned mass damper has a symmetrical structure as a whole, including a first spring 1, a mass block 2, a slide 3, a roller 4, a first bearing rod 5, a pillar 6, a bearing 7, a second bearing rod 8, a pull ring 9, a second spring 10, a connecting rod 11, a limit rod 12 and an energy dissipation element 13; the low-frequency tuned mass damper has a symmetrical structure as a whole, the upper end of the energy dissipation element 13 is fixed to the top plate of the box beam or fixed on a bracket inside the box beam, and the lower end is fixed to the middle of the mass block 2; the upper end of the first spring 1 is suspended on the top plate of the box beam or fixed on a bracket inside the box beam, and the lower end is connected to the mass block 2; the lower end of the mass block 2 is suspended in the air and maintains a certain distance from the bottom plate of the box beam to ensure that the mass block 2 can vibrate freely inside the box beam; the two slides 3 are fixed respectively at On both sides of the mass block 2; the roller 4 rolls freely on the outer wall of the slide 3; four pillars 6 and two first bearing rods 5 are arranged around the slide 3, symmetrically arranged on both sides of the slide 3; a circular hole is opened at the upper and lower ends of the pillar 6; the first bearing rod 5 passes through the roller 4, and at the same time, the first bearing rod 5 passes through the circular hole at the lower end of the pillar 6 and is fixed thereto; the first bearing rod 5 is provided with a number of pull rings 9 along the length direction, and the two ends of the second spring 10 are respectively connected to the pull rings 9 on the first bearing rods 5 on both sides; the upper end of the connecting rod 11 is fixed to the top plate of the box beam or fixed on the bracket inside the box beam; the bearing 7 is embedded in the circular hole at the upper end of the pillar 6, and the second bearing rod 8 passes through the bearing 7; the second bearing rod 8 passes through the lower end of the connecting rod 11 and is fixed to the connecting rod 11; a limit rod 12 is provided at the top of the slide 3 to ensure that the roller 4 will not detach from the slide.

[0038] The design of the mass element, positive stiffness element and energy dissipation element of the present invention is similar to that of the traditional TMD, and most of the deadweight of the mass element is borne by the positive stiffness element. The stiffness of the positive stiffness element is K postive , the stiffness of the negative stiffness element is K negative , satisfying K postive >-Knegative , the total stiffness of the system is K total =K postive -K negative The mass of the TMD mass element (including mass block 2 and slide 3) is determined according to the controlled modal mass of the bridge, which is generally about 1% of the controlled modal mass; K is determined according to the controlled modal frequency and TMD mass. total ; Estimate the static elongation of the first spring 1 according to the net height inside the box girder, and thus determine K postive , and further calculate K negative =K postive -K total .

[0039] In practical applications, the outer wall surface of the slideway 3 should be as smooth as possible, and the rolling friction coefficient between the roller 4 and the bearing 7 should be as small as possible.

[0040] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the present invention in any way. Any equivalent changes, modifications, or improvements made to the above embodiment by those skilled in the art when utilizing the technical solution of the present invention should be deemed to fall within the scope of protection of the technical solution of the present invention.

Claims

1. An ultra-low frequency tuned mass damper with a negative stiffness mechanism, characterized in that: The ultra-low frequency tuned mass damper has a symmetrical structure as a whole, comprising a first spring (1), a mass block (2), a slideway (3), a roller (4), a first bearing rod (5), a support (6), a bearing (7), a second bearing rod (8), a pull ring (9), a second spring (10), a connecting rod (11), a limiting rod (12) and an energy dissipation element (13); the low frequency tuned mass damper has a symmetrical structure as a whole, and the upper end of the energy dissipation element (13) is fixed to the top plate of the box beam or fixed inside the box beam. The first spring (1) is mounted on a bracket, and its lower end is fixed to the middle of the mass block (2); the upper end of the first spring (1) is suspended on the top plate of the box beam or fixed on a bracket inside the box beam, and its lower end is connected to the mass block (2); the lower end of the mass block (2) is suspended in the air, and a certain distance is maintained from the bottom plate of the box beam to ensure that the mass block (2) can vibrate freely inside the box beam; two slideways (3) are respectively fixed on both sides of the mass block (2); the roller (4) rolls freely on the outer wall of the slideway (3); four pillars ( 6) and two first bearing rods (5), symmetrically arranged on both sides of the slideway (3); a circular hole is opened at each upper and lower ends of the pillar (6); the first bearing rod (5) passes through the roller (4), and at the same time, the first bearing rod (5) passes through the circular hole at the lower end of the pillar (6) and is fixed thereto; a plurality of pull rings (9) are provided along the length direction of the first bearing rod (5), and the two ends of the second spring (10) are respectively connected to the pull rings (9) on the first bearing rods (5) on both sides; the upper end of the connecting rod (11) is fixed to the box beam The top plate is fixed on a bracket inside the box beam; the bearing (7) is embedded in the circular hole at the upper end of the pillar (6), and the second bearing rod (8) passes through the bearing (7); the second bearing rod (8) passes through the lower end of the connecting rod (11) and is fixed to the connecting rod (11); a limit rod (12) is set at the top of the slideway (3) to ensure that the roller (4) will not be separated from the slideway; the slideway (3) is made of stainless steel, the outer wall of which is the arc track of the roller (4), and one or more cross braces are set between the inner wall surfaces.

2. The ultra-low frequency tuned mass damper with a negative stiffness mechanism according to claim 1, characterized in that: The mass block (2) is made of steel, and the connection position between the mass block (2) and the first spring (1) is as close as possible to the bottom surface of the mass block (2), thereby reducing the height occupied by the mass block (2) alone and improving the utilization rate of the internal space of the box beam.

3. The ultra-low frequency tuned mass damper with a negative stiffness mechanism according to claim 1, characterized in that: The stiffness coefficient K of the negative stiffness mechanism composed of the slideway (3), the roller (4), the first bearing rod (5), the support (6), the bearing (7), the second bearing rod (8), the pull ring (9) and the second spring (10) negative Set according to actual needs, its absolute value is the stiffness coefficient K of the positive stiffness element postive 0.7-0.9 times of the spring group, the positive stiffness element is the first spring (1).

4. The ultra-low frequency tuned mass damper with a negative stiffness mechanism according to claim 1, characterized in that: The center motion trajectory of the roller (4) is calculated as follows: Where K represents the total stiffness of the spring group composed of the second spring (10), 2x0 represents the initial length of the second spring (10), l t represents the straight-line distance between the center of the first bearing rod (5) and the center of the second bearing rod (8), x represents the horizontal coordinate, y represents the vertical coordinate, K negative y+F0 represents the output of the negative stiffness mechanism; the x-axis is positive to the right and the y-axis is positive upward. By numerically integrating the above equation, the xy curves of the center motion trajectories of the rollers (4) on both sides are drawn; the integral starting coordinates of the center motion trajectory of the left roller (4) are (-x0, 0), and the integral starting coordinates of the center motion trajectory of the right roller (4) are (x0, 0); the integral end point is set according to the actual required height of the slideway (3).

5. The ultra-low frequency tuned mass damper with a negative stiffness mechanism according to claim 1, characterized in that: At the static equilibrium position, the second spring (10) has sufficient initial elongation to ensure that the second spring (10) is always in a tensioned state during the vibration of the mass block (2).

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