Parameter design method of ultra-low frequency tuning lever mass inertia damper

Abstract

The present application relates to bridge damping technical field, specifically to a kind of super low frequency tuning lever mass inertial mass damper parameter design method, the damper includes: lever, mass, spring and inertial mass mechanism.Lever middle part is rotatably arranged on the structure to be damped, and lever is divided into power arm and resistance arm;Mass is arranged on power arm;Spring one end is connected with resistance arm, and the other end is connected with the structure to be damped;Inertial mass mechanism includes: arc rack, rotating shaft, flywheel and gear;Rotating shaft is rotatably connected with power arm;Flywheel is arranged on rotating shaft;Gear is arranged on rotating shaft, arc rack is fixedly arranged, and cooperates with gear, power arm swings, gear rotates relative to arc rack, and drives flywheel to rotate.This scheme can solve the problem that the elongation and the amount of TMD spring are increased in the prior art by using super low frequency TMD scheme, the installation space of TMD is limited, and the use cost of TMD is greatly increased, and the influence of TMD self weight on bridge structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge vibration reduction, and in particular to a parameter design method of an ultra-low frequency tuning lever mass inertia damper. BACKGROUND

[0002] In recent years, with the use of high-strength lightweight materials, the emergence of new technologies and the improvement of construction technology, the main span of cable-stayed bridges has broken through 1000m, and the main span of suspension bridges is breaking through 2000m, but the characteristics of such super-long span bridge systems, such as light and thin, small damping and low natural frequency, are becoming more and more obvious. Under the action of wind, people, vehicles and earthquakes, etc., various forms of vibration are easy to occur, especially the phenomenon of buffeting and vortex-induced vibration during the construction and operation period, which seriously affects the service life and driving safety of the bridge. Vibration control has become an important problem.

[0003] TMD can effectively control the buffeting and vortex vibration of such long-span bridge structures. Tuned mass damper (TMD) mainly includes three components: spring, mass and damping. However, the installation of TMD in the box girder of long-span bridge requires sufficient net height to meet the static elongation of TMD spring and the displacement during vibration.

[0004] Therefore, the net elongation of the large spring under the self-weight of the traditional suspension TMD (for example, the first-order vertical bending frequency of Yangpu Bridge is 0.286 Hz, and the net elongation of the TMD spring is more than 3 m) will not meet the installation space, and the nonlinearity of the spring of TMD will cause frequency detuning. The relationship between frequency and spring elongation is shown in . Figure 7

[0005] In addition, the lower the frequency, the greater the elongation of the TMD spring, which will also lead to a sharp increase in the amount of TMD, such as the elongation of the TMD spring for controlling the frequency of 0.3 Hz is 2.76 m, and the amount of spring is 30% of the mass block ratio; the elongation of the TMD spring for controlling the frequency of 0.2 Hz is 6.21 m, and the amount of spring is 50% of the mass block ratio; the elongation of the TMD spring for controlling the frequency of 0.1 Hz is 24.82 m, and the amount of spring is 200% of the mass block ratio. The relationship between frequency and spring amount under different strokes is shown in Figure 8 .

[0006] Therefore, the use of ultra-low frequency TMD scheme will increase the elongation and amount of TMD spring, limit the installation space of TMD, and greatly increase the use cost of TMD and the impact of TMD self-weight on the bridge structure. SUMMARY

[0007] ​In view of the defects in the prior art, the purpose of the present application is to provide a kind of ultra-low frequency tuning lever mass inertia damper parameter design method, the scheme can solve the problem that the elongation and the amount of TMD spring are increased in the prior art using ultra-low frequency TMD scheme, the installation space of TMD is limited, and the use cost of TMD is greatly increased and the influence of TMD self weight on bridge structure.

[0008] To achieve the above purpose, the technical scheme adopted by the present application is:

[0009] In one aspect, the present application provides an ultra-low frequency tuning lever mass inertia damper, comprising:

[0010] A lever, the middle part of which is rotatably arranged on the structure to be damped, dividing the lever into a power arm and a resistance arm;

[0011] A mass block arranged on the power arm;

[0012] A spring, one end of which is connected with the resistance arm, and the other end is used to connect with the structure to be damped, so as to keep the power arm horizontal when there is no vibration;

[0013] An inertia mechanism, comprising:

[0014] A rotating shaft rotatably connected with the power arm;

[0015] A flywheel arranged on the rotating shaft;

[0016] A gear arranged on the rotating shaft,

[0017] An arc-shaped rack fixedly arranged and matched with the gear, when the power arm swings, the gear rotates relative to the arc-shaped rack and drives the flywheel to rotate.

[0018] In some optional schemes, the ultra-low frequency tuning lever mass inertia damper further comprises a support frame for connecting with the structure to be damped, and the middle part of the lever is rotatably connected with the support frame.

[0019] In some optional schemes, the lever is in L-shaped structure, the bending part of the L-shaped structure is rotatably connected with the support frame, dividing the L-shaped structure into a power arm and a resistance arm, and when there is no vibration, the resistance arm is in vertical state.

[0020] In some optional schemes, the ultra-low frequency tuning lever mass inertia damper further comprises a mounting plate for being arranged on the structure to be damped, and the support frame is connected with the mounting plate.

[0021] In some alternatives, the support frame is a portal frame, the L-shaped structure comprises two L-shaped rods, the two L-shaped rods are respectively arranged on two sides of the portal frame, and the bending portions of the L-shaped rods are rotatably connected with the portal frame, thereby dividing the L-shaped rods into power rods and resistance rods.

[0022] In some alternatives, the two ends of the rotating shaft are rotatably connected with the power rods of the two L-shaped rods respectively.

[0023] In some alternatives, the gear is located at the middle of the rotating shaft.

[0024] In some alternatives, the rotating shaft is provided with a flywheel at equal intervals on both sides of the gear.

[0025] In another aspect, the application also provides a parameter design method of an ultra-low frequency tuning lever mass inertial mass damper, characterized by being used for designing the ultra-low frequency tuning lever mass inertial mass damper in any of the above aspects, and comprising the following steps:

[0026] Based on the controlled frequency, a theoretical static elongation of the spring is determined;

[0027] According to the installation space, a maximum actual static elongation of the spring, a maximum length of the power arm and a maximum length of the resistance arm are determined;

[0028] According to the maximum actual static elongation of the spring and the theoretical static elongation of the spring, a minimum elongation amplification coefficient is determined;

[0029] According to an inertial moment power balance equation, a spring stiffness amplification coefficient is determined;

[0030] According to the minimum elongation amplification coefficient and the spring stiffness amplification coefficient, in combination with the maximum length of the power arm, the maximum length of the resistance arm and a static force balance equation, the setting positions of the mass block and the inertial mass mechanism and the design parameters of the inertial mass mechanism are determined.

[0031] In some alternatives, the determination of the spring stiffness amplification coefficient according to the inertial moment power balance equation comprises:

[0032] According to the inertial moment power balance equation: , the following is obtained: ;

[0033] According to the formulas and , the circular frequency is calculated.

[0034] According to , the following is obtained: ;

[0035] According to The spring stiffness amplification factor is obtained as follows: ;

[0036] Where M represents the mass of the block during its motion, and y2 represents the dynamic displacement of the block. Let the acceleration of the mass be... L2 is the inertial force; L2 is the distance from the mass block to the rotation center of the lever; m is the mass of the gear assembly itself, and the inertial force is... , Let M be the acceleration of the gear assembly, β = (m + b) / M be the inertia coefficient, and b be the inertial mass of the gear rack inertia container. r1 is the radius of the gear, r2 is the radius of the flywheel; L1 is the distance from the rotating shaft to the rotation center of the lever; K For spring stiffness; For the spring elongation; l Let be the distance from the connection point of the lever to the center of rotation of the lever; take . , , This represents the dynamic displacement of the gear assembly.

[0037] Compared with the prior art, the advantages of the present invention are: the present invention uses the lever principle to control the frequency of the structure to be vibration-damped. f With the mass m of the mass block remaining constant, the spring stiffness should be increased by n. 2 This multiplier can reduce the theoretical static elongation of the spring to 1 / n of its original value, and the spring's stroke can also be reduced to 1 / n of the mass block's stroke, where n is the lever amplification factor. This facilitates spring design and selection, ensures spring stability, and reduces the overall height of the damper, meeting the installation height requirements of long-span bridges. By setting an inertial capacitance mechanism on the lever's power arm, the rotating shaft of the inertial capacitance mechanism is rotatably connected to the power arm; the flywheel and gear are both mounted on the rotating shaft and fixed relative to it; and the gear engages with a fixed arc-shaped rack. When the mass block displaces, the swinging of the power arm drives the gear to displace, causing the gear to rotate relative to the power arm, and the flywheel also begins to rotate, generating inertial mass. This further increases the amplification factor, reduces the amount of spring used in the TMD, lowers the TMD's operating cost, and reduces the impact of the TMD's self-weight on the bridge structure. Combined with the lever principle, the spring stiffness should be amplified. This multiple can shorten the theoretical rest length of a spring to its original value. The stroke of the spring can be reduced to twice that of the stroke of the mass block, and the stroke of the spring can also be shortened to twice that of the stroke of the mass block. This design facilitates spring selection and ensures spring stability, while also reducing the overall height of the damper to meet the installation height requirements of long-span bridges. Attached Figure Description

[0038] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative effort based on these drawings.

[0039] Figure 1 It is a three-dimensional structural schematic diagram of the first kind of ultra-low frequency tuning lever mass inertia damper in the embodiments of the present application.

[0040] Figure 2 It is a front view structural schematic diagram of the first kind of ultra-low frequency tuning lever mass inertia damper in the embodiments of the present application.

[0041] Figure 3 It is a three-dimensional structural schematic diagram of the second kind of ultra-low frequency tuning lever mass inertia damper in the embodiments of the present application.

[0042] Figure 4 It is a front view structural schematic diagram of the second kind of ultra-low frequency tuning lever mass inertia damper in the embodiments of the present application.

[0043] Figure 5 It is a static force balance principle diagram of the ultra-low frequency tuning lever mass inertia damper in the embodiments of the present application.

[0044] Figure 6 It is a dynamic force balance principle diagram of the ultra-low frequency tuning lever mass inertia damper in the embodiments of the present application.

[0045] Figure 7 It is a relationship diagram of frequency-spring elongation in the prior art.

[0046] Figure 8 It is a relationship diagram of frequency-spring elongation in the prior art.

[0047] In the figure: 1, lever; 11, dynamic arm; 12, resistance arm; 2, mass block; 3, spring; 4, inertia mechanism; 41, rotating shaft; 42, gear; 43, arc-shaped rack; 44, flywheel; 5, support frame; 6, mounting plate. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, and not all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative effort belong to the scope of protection of the present application.

[0049] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0050] like Figure 1 and Figure 2 As shown, on one hand, the present invention provides an ultra-low frequency tuned lever mass inertia damper, comprising: lever 1, mass block 2, spring 3 and inertia capacitive mechanism 4.

[0051] The lever 1 is rotatably mounted on the structure to be damped, dividing it into a power arm 11 and a resistance arm 12. A mass block 2 is mounted on the power arm 11. One end of a spring 3 is connected to the resistance arm 12, and the other end is used to connect to the structure to be damped, keeping the power arm 11 horizontal when there is no vibration. The inertial-capacitance mechanism 4 includes an arc-shaped rack 43, a rotating shaft 41, a flywheel 44, and a gear 42. The rotating shaft 41 is rotatably connected to the power arm 11. The flywheel 44 is mounted on the rotating shaft 41. The gear 42 is mounted on the rotating shaft 41. The arc-shaped rack 43 is fixedly mounted and cooperates with the gear 42. When the power arm 11 swings, the gear 42 rotates relative to the arc-shaped rack 43, driving the flywheel 44 to rotate.

[0052] This invention utilizes the lever principle to control the frequency of the structure to be vibration-damped. f With the mass m of block 2 remaining constant, the spring stiffness should be increased by n. 2 The theoretical static elongation of the spring can be shortened to 1 / n times its original value, and the stroke of spring 3 can also be shortened to 1 / n times the stroke of mass block 2. Here, n is the lever amplification factor, which is the ratio of the distance from the mass block to the lever's rotation axis to the distance from the connection point of spring 3 and resistance arm 12 to the lever's rotation axis. This facilitates the design and selection of spring 3, ensures its stability, and reduces the overall height of the damper, allowing it to meet the installation height requirements of long-span bridges. By setting an inertial capacitance mechanism 4 on the power arm 11 of lever 1, the rotation shaft 41 of the inertial capacitance mechanism 4 is rotatably connected to the power arm 11. The flywheel 44 and gear 42 are both located on the rotation shaft 41 and fixed relative to it. Furthermore, the gear 42 engages with the fixed arc-shaped rack 43. When mass block 2 is displaced, the swinging of the power arm 11 causes the gear 42 to rotate relative to the power arm 11, and the flywheel 44 also begins to rotate, generating inertial mass. This can further increase the amplification factor, reduce the amount of springs used in the TMD, and lower the cost of using the TMD and the impact of the TMD's self-weight on the bridge structure. Combining the lever principle, the spring stiffness can be amplified. This multiple can shorten the theoretical rest length of a spring to its original value. The stroke of the spring can be reduced to twice that of the stroke of the mass block, and the stroke of the spring can also be shortened to twice that of the stroke of the mass block. This design facilitates spring selection and ensures spring stability, while also reducing the overall height of the damper to meet the installation height requirements of long-span bridges.

[0053] In this example, the opening of the arc-shaped rack 43 is directed towards the rotation axis of the lever 1, and the lever 1 moves relative to the arc-shaped rack 43, which can drive the gear 42 to rotate relative to the arc-shaped rack 43, thereby driving the flywheel 44 arranged on the same rotation shaft 41 to rotate. The tension spring of the spring 3.

[0054] In this example, the inertia mechanism 4 can be arranged between the mass block 2 and the rotation axis of the lever 1; as shown in Figure 1 and Figure 2 , the mass block 2 can also be arranged between the inertia mechanism 4 and the rotation axis of the lever 1, which can be determined according to the design parameters and the installation space, as shown in Figure 3 and Figure 4 .

[0055] The static balance principle is shown in Figure 5 , assuming that the mass of the lever 1 and the spring 3 is ignored, the mass of the mass block 2 is M, the distance from the mass block 2 to the rotation axis of the lever 1 is L2, and the lever amplification factor of the mass block 2 is ; the total weight of the gear and the flywheel is m, the distance from the gear to the rotation axis of the lever 1 is L1, and the gear rack lever amplification factor is ; the spring stiffness K, the distance from the spring to the rotation axis of the lever 1 is l , and the spring elongation is x , according to the lever principle , then , which can ensure that the spring is always in a horizontal state.

[0056] The dynamic balance principle is shown in Figure 6 , assuming that the mass of the lever 1 and the spring 3 is ignored during the movement, the mass block 2 bears its own gravity Mg during the movement, the dynamic displacement is y2, and the acceleration is , then the inertia force is ; the gear assembly itself gravity mg (m is the effective mass excluding the fixed rack, including: rotation shaft 41, gear 42 and flywheel 44), inertia force , is the acceleration of the gear assembly, is the dynamic displacement of the gear assembly, and the inertia coefficient β = (m + b) / M is taken, wherein b is the inertia mass of the gear rack inertia container, , r1 is the radius of the gear 42, and r2 is the radius of the flywheel 44; take , , , is the elongation of the spring 3, and the dynamic spring force of the spring 3 is , so the inertia moment dynamic balance equation of the mass block 2 is: At this time, , that is , that is , according to , the calculated circular frequency , so the TMD control frequency is , the spring stiffness , K0 is the spring design stiffness of the mass without any amplification and inertial mass. The static elongation of the spring 3 can be shortened to times of the static elongation of the spring without the lever amplification and the inertial mass, and the stroke of the spring 3 can be shortened to times of the stroke of the mass.

[0057] In some alternative embodiments, the ultra-low frequency tuned lever mass inertial damper further comprises a support frame 5 for connecting with the structure to be damped, and the middle part of the lever 1 is rotatably connected with the support frame 5.

[0058] In this embodiment, when there is a position on the structure to be damped where the lever 1 can be installed, the rotation axis of the lever 1 can be directly connected with the structure to be damped, as long as the installation space of the spring 3 can be left. When there is no suitable position to install the lever 1, the support frame 5 can be directly arranged on the structure to be damped, and the lever 1 is rotatably connected with the support frame 5 to meet the installation requirement of the spring 3.

[0059] In some alternative embodiments, the lever 1 is in an L-shaped structure, the bending part of the L-shaped structure is rotatably connected with the support frame 5, and the L-shaped structure is divided into a power arm 11 and a resistance arm 12, and the resistance arm 12 is in a vertical state when there is no vibration.

[0060] In this embodiment, the lever 1 is designed in an L-shaped structure, so that the power arm 11 is in a horizontal position and the resistance arm 12 is in a vertical position when there is no vibration, and at this time the spring 3 can be installed horizontally, thereby reducing the installation space requirement of the spring 3.

[0061] In some alternative embodiments, the ultra-low frequency tuned lever mass inertial damper further comprises a mounting plate 6 arranged on the structure to be damped, and the support frame 5 is connected with the mounting plate 6.

[0062] In this embodiment, the mounting plate 6 is arranged on the structure to be damped, which can facilitate the installation of the spring 3.

[0063] In some alternative embodiments, the support frame 5 is a portal frame, the L-shaped structure includes two L-shaped rods, the two L-shaped rods are arranged on the two sides of the portal frame respectively, and the bending parts of the L-shaped rods are rotatably connected with the portal frame, and the L-shaped rods are divided into power rods and resistance rods.

[0064] In this embodiment, two L-shaped rods and two springs 3 are adopted, the two springs 3 are respectively connected with the resistance rods of the two L-shaped rods, and are arranged in a horizontal direction, which can improve the stability of the whole structure.

[0065] In some optional embodiments, the two ends of the rotating shaft 41 are rotatably connected with the power rods of the two L-shaped rods respectively.

[0066] In the embodiment, the rotating shaft 41 is located between the two L-shaped rods and rotatably connected with the power rods of the two L-shaped rods at the two ends, so that the stability between the two L-shaped rods is improved and the setting of the inertial mass damper 4 is facilitated. In the embodiment, the gear 42 of the inertial mass damper 4 is arranged on the rotating shaft 41 between the two L-shaped rods.

[0067] In some optional embodiments, the rotating shaft 41 is rotatably connected with the L-shaped rod through a first ball bearing.

[0068] In the embodiment, the rotating shaft 41 is rotatably connected with the L-shaped rod through a first ball bearing, so that the friction is reduced and the service life of the device is improved.

[0069] In some optional embodiments, the gear 42 is located at the middle of the rotating shaft 41.

[0070] In the embodiment, the gear 42 is located at the middle of the rotating shaft 41, so that the force transmitted to the two L-shaped rods through the rotating shaft 41 is more balanced when the device vibrates, and the entire device is more stable during use.

[0071] In some optional embodiments, the rotating shaft 41 is provided with a flywheel 44 at equal intervals on both sides of the gear 42.

[0072] In the embodiment, the two flywheels 44 are symmetrically arranged on both sides of the gear 42, so that the inertial masses generated by the two flywheels 44 are equal when the gear rotates, and the reaction forces on the gear 42 and the two L-shaped rods are also equal, so that the entire device is more stable during use.

[0073] In some optional embodiments, the support frame 5 is provided with support shafts on both sides, the L-shaped rod is provided with mounting holes at the bending portions, the mounting holes are provided with second ball bearings, and the support shafts are connected with the inner rings of the second ball bearings.

[0074] In the embodiment, the L-shaped rod is sleeved on the support shafts protruding from the two sides of the support frame 5 through the mounting holes arranged at the bending portions, and the second ball bearings are arranged in the mounting holes and sleeved on the support shafts, so that the L-shaped rod can be conveniently installed and the friction is reduced to improve the service life of the entire device.

[0075] On the other hand, the application also provides a parameter design method of the ultra-low frequency tuning lever mass inertial damper, which is used for designing the parameters of the ultra-low frequency tuning lever mass inertial damper and includes the following steps.

[0076] S1: determining the theoretical static elongation of the spring based on the controlled frequency.

[0077] In the embodiment, the damping target requirement of the damping structure to be damped determines the controlled frequency f .

[0078] According to the controlled frequency f , the spring theoretical static elongation of the TMD without taking the lever amplification measure and the additional inertia mass can be determined: , the controlled frequency f of the structure is 0.2 Hz, the spring theoretical static elongation is 6.25 m. Wherein, m is the mass of the mass block, f is the controlled frequency, k is the spring stiffness.

[0079] S2: According to the installation space, the maximum spring actual static elongation, the maximum length of the power arm and the maximum length of the resistance arm are determined.

[0080] When the length direction installation space is large enough, the lever 1 with the power arm 11 and the resistance arm 12 located in the same horizontal plane can be adopted. When the length direction installation space is insufficient, the L-shaped lever and the support frame can be adopted. As shown in Figure 1 and 5 , the mass block 2 is M, the distance from the mass block 2 to the rotation center of the lever 1, that is, the length of the power arm is L2, the distance from the connection of the spring 3 to the rotation center of the lever 1, that is, the length of the resistance arm is l ; the total weight of the gear and the flywheel is m, and the distance from the rotation shaft 41 to the rotation center of the lever 1 is L1.

[0081] In some optional embodiments, in order to meet the installation space, the maximum spring actual static elongation, the maximum length of the power arm and the maximum length of the resistance arm can be determined according to the installation space, so as to ensure that the damper which can be designed can be installed.

[0082] S3: According to the maximum spring actual static elongation and the spring theoretical static elongation, the minimum elongation amplification coefficient is determined.

[0083] The minimum elongation amplification coefficient is determined according to the formula , wherein δ is the maximum spring actual static elongation, and δ0 is the spring theoretical static elongation.

[0084] S4: According to the inertia moment power balance equation, the spring stiffness amplification coefficient is determined.

[0085] Step S4 specifically includes:

[0086] S41: According to the inertia moment power balance equation: , the formula is obtained.

[0087] S42: According to the formula and , the circular frequency .

[0088] In this example, the and are solved simultaneously, that is, .

[0089] S43: According to , the spring stiffness amplification factor is .

[0090] S44: According to , the spring stiffness amplification factor is .

[0091] where M is the mass of the mass block 2 in the motion process, y2 is the dynamic displacement of the mass block 2, is the acceleration of the mass block 2, is the inertia force; L2 is the distance from the mass block 2 to the rotation center of the lever 1; m is the mass of the gear assembly (including the rotating shaft 41, the gear 42 and the flywheel 44, that is, the effective mass excluding the circular arc rack 43), the inertia force , is the acceleration of the gear assembly, β=(m+b) / M is the inertia coefficient, b is the inertia mass of the gear rack, , r1 is the radius of the gear 42, r2 is the radius of the flywheel 44; L1 is the distance from the rotating shaft 41 to the rotation center of the lever 1; K is the spring stiffness; is the spring elongation of l is the distance from the connection of the lever 1 to the rotation center of the lever 1; take , , is the dynamic displacement of the gear assembly.

[0092] Spring dynamic force , , the lever amplification factor of the mass block 2 is ; the lever amplification factor of the gear assembly is , the spring stiffness k ; is the ratio of the amplification factors of the mass block 2 and the gear assembly.

[0093] The dynamic balance principle is shown in Figure 6 , assuming that the mass of the lever 1 and the spring 3 in the motion process is ignored, the mass block 2 bears its own gravity Mg in the motion process, the dynamic displacement of the mass block 2 is y2, the acceleration of the mass block 2 is , and the inertia force is ; the gear assembly bears its own gravity mg (m is the effective mass excluding the fixed rack), the inertia force is , and the acceleration of the gear assembly is , For the dynamic displacement of the gear assembly, take the inertial mass coefficient β = (m + b) / M, where b is the inertial mass of the gear rack inertance, , r1 is the radius of the gear 42, r2 is the radius of the flywheel 44; take , , , the spring dynamic force , is the spring elongation, so the inertia moment dynamic balance equation of the mass block 2 is: At this time, , that is , according to , the calculation can get the circular frequency , the TMD control frequency is .

[0094] S5: According to the minimum elongation amplification coefficient and the spring stiffness amplification coefficient, combined with the maximum length of the dynamic arm, the maximum length of the resistance arm and the static force balance equation, the setting position of the mass block and the inertance mechanism and the design parameters of the inertance mechanism are determined.

[0095] The static force balance principle is shown in Figure 5 , assuming that the mass of lever 1 and spring 3 is ignored, the mass block 2 weighs M, the distance from the mass block 2 to the rotating shaft of lever 1 is L2, and the lever amplification coefficient of the mass block 2 is ; the total weight of the gear and flywheel is m, the distance from the gear and flywheel to the rotating shaft of lever 1 is L1, and the gear rack lever amplification coefficient is ; the spring stiffness K, the distance from the spring to the rotating lever 1 is l , the spring elongation is x , according to the lever principle , then , which can ensure that the spring is always in a horizontal state.

[0096] In this example, the spring stiffness , K0 is the spring design stiffness of the mass block without any amplification and inertial mass. The static elongation of spring 3 can be shortened to times of the mass block without using lever amplification and inertial mass, and the stroke of spring 3 can be shortened to times of the mass block, that is, the elongation amplification coefficient of the spring of the above damper is . Let , be the minimum elongation amplification coefficient.

[0097] In addition, according to the effect of vibration reduction, the mass ratio mu (M / M0) required by the TMD vibration reduction is determined, M0 is the control modal mass of the structure to be reduced, the mass M of the TMD mass 2 is determined; according to the effect of vibration reduction, the stroke of the mass 2, that is, the dynamic displacement y2 of the mass 2 is determined.

[0098] M, y2 is brought into , and L1 and L2 are both less than the maximum length of the power arm, and l less than the maximum length of the resistance arm, combined with the installation space and the appearance, the setting position of the inerter and the mass is determined, that is, the distance from the rotating shaft 41 to the rotating center of the lever 1 is L1, the distance from the mass 2 to the rotating center of the lever 1 is L2, and the parameters of the inerter, including the radius r1 of the gear 42, the radius r2 of the flywheel 44, and the mass m of the gear assembly itself.

[0099] In summary, the application improves the spring stiffness, reduces the spring elongation and stroke, the length and stroke of the damper, ensures the stability of the spring, and reduces the height of the entire damper, so that it meets the installation height requirement of the long-span bridge; by adding the inertia mass, the spring elongation and the amount are further reduced, and the low-frequency vibration control during the construction and operation of the long-span bridge is met. f and the mass m of the mass is unchanged, the spring stiffness should be amplified n 2 times, the spring theoretical extension length can be shortened to 1 / n times of the original, and the stroke of the spring can also be shortened to 1 / n times of the stroke of the mass, n is the lever amplification coefficient, which is convenient for the design and selection of the spring, ensures the stability of the spring, and reduces the height of the entire damper, so that it meets the installation height requirement of the long-span bridge. times, the spring theoretical extension length can be shortened to 1 / n times of the original, and the stroke of the spring can also be shortened to 1 / n times of the stroke of the mass, n is the lever amplification coefficient, which is convenient for the design and selection of the spring, ensures the stability of the spring, and reduces the height of the entire damper, so that it meets the installation height requirement of the long-span bridge.

[0100] In summary, the application improves the spring stiffness, reduces the spring elongation and stroke, the length and stroke of the damper, ensures the stability of the spring, and reduces the height of the entire damper, so that it meets the installation height requirement of the long-span bridge; by adding the inertia mass, the spring elongation and the amount are further reduced, and the low-frequency vibration control during the construction and operation of the long-span bridge is met.

[0101] ​​In the description of the present application, it should be noted that the terms "upper", "lower", and the like are used for indicating the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. Unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connecting" should be interpreted broadly, for example, can be fixed connection, can also be detachable connection, or integrally connected; can be mechanical connection, can also be electrical connection; can be directly connected, can also be indirectly connected through an intermediate medium, can be the internal communication of two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0102] It should be noted that in the present application, relational terms such as "first" and "second", and the like are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus including a series of elements includes not only those elements, but also other elements not explicitly listed, or other elements inherent in such a process, method, article or apparatus. Without more limitations, the element defined by the statement "comprising a" does not exclude the presence of other identical elements in the process, method, article or apparatus including the element.

[0103] The above is only a specific embodiment of the present application, which enables those skilled in the art to understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features applied herein.

Claims

1. A method for designing parameters of an ultra-low frequency tuned mass damper, characterized in that, The super-low frequency tuning lever mass inertia damper comprises: a lever (1) having a middle part rotatably arranged on a structure to be damped, and dividing the lever (1) into a power arm (11) and a resistance arm (12); a mass block (2) arranged on the power arm (11); a spring (3) having one end connected with the resistance arm (12) and the other end used for being connected with the structure to be damped to keep the power arm (11) horizontal when there is no vibration; an inertia mechanism (4) comprising: a rotating shaft (41) rotatably connected with the power arm (11); a flywheel (44) arranged on the rotating shaft (41); a gear (42) arranged on the rotating shaft (41), an arc-shaped rack (43) fixedly arranged and matched with the gear (42), and when the power arm (11) swings, the gear (42) rotates relative to the arc-shaped rack (43) and drives the flywheel (44) to rotate; the arrangement positions of the mass block and the inertia mechanism and the design parameters of the inertia mechanism are designed according to the following steps: determining a spring theoretical static elongation based on a controlled frequency; determining a maximum spring actual static elongation, a maximum power arm length and a maximum resistance arm length according to an installation space; determining a minimum elongation amplification coefficient according to the maximum spring actual static elongation and the spring theoretical static elongation; determining a spring stiffness amplification coefficient according to an inertia moment power balance equation, comprising: According to the moment of inertia dynamic balance equation: , we get ; According to the formula and , the circular frequency is calculated; According to , the controlled frequency is obtained; According to , the spring stiffness amplification coefficient is ; wherein M is the mass of the mass block (2) in the process of motion, y2 is the dynamic displacement of the mass block (2), is the acceleration of the mass block (2), is the inertia force thereof; L2 is the distance from the mass block (2) to the rotation center of the lever (1); m is the mass of the gear assembly, and the inertia force , is the acceleration of the gear assembly, β=(m+b) / M is the inertia coefficient, b is the inertia mass of the gear rack inertia container, , r1 is the radius of the gear (42), r2 is the radius of the flywheel (44); L1 is the distance from the rotation shaft (41) to the rotation center of the lever (1); K is the spring stiffness; is the spring elongation of the spring; l is the distance from the connection of the lever (1) to the rotation center of the lever (1); take is the lever amplification coefficient of the mass block (2), is the ratio of the amplification coefficient of the mass block (2) and the gear assembly, is the dynamic displacement of the gear assembly; determining the arrangement positions of the mass block and the inertia mechanism and the design parameters of the inertia mechanism according to the minimum elongation amplification coefficient and the spring stiffness amplification coefficient, in combination with the maximum power arm length, the maximum resistance arm length and the static force balance equation.

2. The method of claim 1, wherein: a support frame (5) used for being connected with the structure to be damped, and the middle part of the lever (1) is rotatably connected with the support frame (5).

3. The method of claim 2, wherein: the lever (1) is an L-shaped structure, the bending part of the L-shaped structure is rotatably connected with the support frame (5), and the L-shaped structure is divided into the power arm (11) and the resistance arm (12), and when there is no vibration, the resistance arm (12) is in a vertical state.

4. The method of claim 3, wherein: an installation plate (6) used for being arranged on the structure to be damped, and the support frame (5) is connected with the installation plate (6).

5. The method of claim 2, wherein: the super low frequency tuned lever-mass-inerter damper is designed with a mass ratio of the mass of the mass-inerter to the mass of the lever of 0.1 to 0.

5. the support frame (5) is a portal frame, the L-shaped structure comprises two L-shaped rods, the two L-shaped rods are arranged on two sides of the portal frame respectively, and the bending parts of the L-shaped rods are rotatably connected with the portal frame, and the L-shaped rods are divided into power rods and resistance rods.

6. The method of claim 5, wherein: the two ends of the rotating shaft (41) are rotatably connected with the power rods of the two L-shaped rods respectively.

7. The method of designing an ultra-low frequency tuned mass damper as recited in claim 6, wherein: the gear (42) is located in the middle of the rotating shaft (41).

8. The parameter design method for an ultra-low frequency tuned lever mass-inertia damper as described in claim 7, characterized in that: the flywheels (44) are arranged on the rotating shaft (41) at equal distances on both sides of the gear (42).

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