An arch bridge suspender tuned mass inertia damper and an optimization design method thereof

Abstract

The application discloses an arch bridge suspender tuned mass inertia damper and an optimization design method thereof, and the damper comprises a mass disc, an inertia disc, a middle shaft and a fastening mechanism, the mass disc is movably sleeved on the middle shaft, the inertia disc is sleeved on the middle shaft and can rotate relative to the middle shaft, a plurality of chiral metamaterial screws are connected between the mass disc and the inertia disc, the plurality of chiral metamaterial screws are arranged in a chiral manner in the circumferential direction of the center of the mass disc, and the end face of the mass disc away from the inertia disc is provided with compression elastic pieces, when the tuned mass inertia damper is connected with the suspender, the middle shaft is fixed on the suspender through the fastening mechanism, and the compression elastic pieces are arranged between the mass disc and the suspender. The application can efficiently suppress the vibration of the suspender, effectively reduce the mass and volume of the damper, improve the compactness of the device, and has the advantages of simple structure, convenient installation and maintenance.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of arch bridge suspender vibration suppression, and particularly relates to an arch bridge suspender tuned mass inertia damper and an optimization design method thereof. BACKGROUND

[0002] With the development of economy, people's demand for transportation engineering is increasing. In recent years, the construction of large-span bridges in China has ushered in a leap-forward development, and super projects across rivers and seas have emerged one after another. Under this background, arch bridges, with the unique advantages of strong span crossing ability and elegant and dignified appearance, have become the preferred bridge type for many urban river-crossing bridges and landmark bridges for tourism and travel. At present, the world's largest span arch bridge has broken through the 600-meter level (such as a certain three-bridge in Guangxi, with a span of 600 meters, which is the world's largest span steel pipe concrete arch bridge), and as the "lifeline" of the arch bridge, the suspender bears the core functions of transmitting the load of the bridge deck and coordinating the deformation of the main arch. The length of the suspender increases significantly with the increase of the span, and the longest suspender currently reaches more than 80 meters. However, such a suspender, as a typical slender flexible component, has characteristics such as large slenderness ratio, low natural frequency and weak damping characteristics. Under the external excitation of wind load and the like, it is easy to excite large vibration, which seriously threatens the long-term safety and use comfort of the structure, and therefore an efficient arch bridge suspender vibration suppression technology is urgently needed.

[0003] The current derrick vibration control scheme mainly includes two types of pneumatic and mechanical damping, the pneumatic measure generally adopts different size chamfering on the cross section of the derrick and digging lattice type hole around the original derrick to suppress the derrick vibration, however, its control effect is limited and a large number of wind tunnel tests are needed to find the optimal design. The mechanical measure mainly suppresses the vibration by adding damper (such as pendulum TMD, magnetic ring vibration absorber, liquid damper, etc.) on the derrick. The patent document (CN 110528381 A) discloses a four-line pendulum tuned mass damper for long derrick vibration reduction of large-span bridge and design method, the damping mode of the damper to realize vibration reduction includes feeding a control force opposite to the vibration direction of the derrick to the derrick through the damping pendulum, and dissipating energy through the universal rotating ball hinge at the connecting place of the pendulum and the support or / and the air damper between the derrick and the counterweight. The patent document (CN111637186 B) discloses a double-ring strong magnet array nonlinear dynamic vibration absorber for derrick vibration reduction and design method, the damping mode of the damper to realize vibration reduction includes feeding a control force opposite to the vibration direction of the derrick to the derrick, so that the derrick vibration energy is transferred to the vibration absorber and then less returned to the derrick, and dissipating energy through the friction between the universal wheel and the base, adding air damper and other measures. The patent document (CN 107657126 B) discloses a ring-shaped cylindrical tuned liquid damper for controlling long derrick vibration of large-span bridge and design method, the device dissipates energy by making the liquid in the box shake and uses the lateral force exerted by the liquid on the barrel wall to control the dynamic response of the derrick. The above-mentioned mechanical damping device has a large mass and size, which on the one hand will cause a strong fear to the personnel driving the vehicle on the bridge deck and has the risk of falling, and on the other hand will change the aerodynamic shape of the derrick and thus aggravate the derrick vibration phenomenon. In order to overcome this defect, some scholars propose to use inertial mass to reduce the size of the required installed mass, such as roller screw inertial container, gear rack inertial container, etc. However, although such inertial containers can reduce the mass of the mass block, they have defects such as large volume, non-compact device, high requirement for structural amplitude, etc. Moreover, the above patent documents are all for circular cross-section derricks installed on suspension bridges, and may not be applicable to H-shaped derricks of arch bridges. Therefore, it is urgent to develop a new type of damping device suitable for H-shaped derricks of arch bridges, which has good vibration characteristics and damping effect, small volume, high compactness, strong robustness, high durability and easy installation and maintenance. SUMMARY

[0004] The technical problem to be solved by the present application is to overcome the shortcomings of the prior art and provide an arch bridge derrick tuned mass inertial damper with compact structure, light weight, high energy dissipation and long-term stability, and an optimization design method thereof.

[0005] In the first aspect, to solve the above technical problems, the arch bridge derrick tuned mass inertial damper of the present application adopts the following technical scheme:

[0006] The chiral metamaterial-based arch bridge suspender tuned mass inertia damper comprises a mass disc, an inertia disc, a middle shaft and a fastening mechanism, the mass disc is movably sleeved on the middle shaft, the inertia disc is sleeved on the middle shaft and can rotate relative to the middle shaft, a plurality of chiral metamaterial screws are connected between the mass disc and the inertia disc, the plurality of chiral metamaterial screws are arranged in a chiral manner in the circumferential direction of the center of the mass disc, and the end face of the mass disc away from the inertia disc is provided with a compression elastic element.

[0007] Through the above technical scheme, when the suspender vibrates, the vibration is transmitted to the mass disc through the compression elastic element, and the mass disc is driven to move axially along the middle shaft; the movement of the mass disc is converted into the rotary movement of the inertia disc through the plurality of chiral metamaterial screws. This process utilizes the compression-torsion coupling effect of the chiral structure to efficiently convert linear vibration into rotary inertia movement, so that significant inertia amplification effect is achieved with a small physical mass, thereby significantly improving the inhibitory capacity of the damper for the vibration of the suspender while reducing the overall mass and volume of the damper, and enhancing the compactness and installation adaptability of the device.

[0008] As a further improvement of the above technical scheme, a shell is further arranged, the middle shaft is fixed in the shell, N-pole permanent magnets and S-pole permanent magnets are oppositely arranged on the inner wall of the shell, the mass disc is an electric conductor, and the mass disc, the N-pole permanent magnets and the S-pole permanent magnets constitute an eddy current damping unit.

[0009] As a further improvement of the above technical scheme, the inertia disc comprises an inner disc and an outer disc, the outer disc is sleeved on the outer periphery of the inner disc and can rotate relative to the inner disc, and the inner disc is fixedly sleeved on the middle shaft.

[0010] As a further improvement of the above technical scheme, a ring groove is arranged between the inner disc and the outer disc, and a plurality of ball bearings are arranged in the ring groove.

[0011] As a further improvement of the above technical scheme, an anti-collision pad block is arranged on the end face of the mass disc facing the inertia disc, or an anti-collision pad block is arranged on the end face of the inertia disc facing the mass disc.

[0012] As a further improvement of the above technical scheme, the fastening mechanism comprises a U-shaped seat, one end of the middle shaft away from the compression elastic element penetrates out of the shell and is fixedly connected with the inner side surface of the U-shaped seat, and the two ends of the U-shaped seat are fixedly connected with the suspender through bolts.

[0013] In the second aspect, to solve the above technical problem, an optimization design method of the arch bridge suspender tuned mass inertia damper adopts the following technical scheme:

[0014] The application discloses an optimization design method of a chiral metamaterial-based arch bridge suspender tuned mass damper.

[0015] S1, suspender parameter acquisition: the structural parameters and dynamic parameters of the arch bridge suspender to be controlled are acquired, and the dynamic parameters include the first-order bending natural frequency and the modal mass of the suspender;

[0016] S2, parameter design of the chiral metamaterial screw rod: the inertial mass amplification coefficient of the chiral metamaterial screw rod is acquired according to the initial angle and the helicity of the chiral metamaterial screw rod, the radius of the inertance disc and the moment of inertia of the inertance disc;

[0017] S3, target parameter optimization: the ratio of the damper installation position to the suspender length, the ratio of the mass disc to the suspender modal mass and the optimal inertial mass amplification coefficient are used as optimization variables, the first-order bending natural frequency and the modal mass of the suspender are used as inputs, and the optimal damper installation position, the optimal inertial mass amplification coefficient and the optimal mass ratio are calculated by using the fixed point method in combination with an optimization algorithm.

[0018] S4, eddy current damping parameter design: the optimal damping coefficient of the eddy current damping unit is calculated according to the optimal parameters obtained above, and the sizes of the N-pole permanent magnet, the S-pole permanent magnet and the mass disc are designed;

[0019] S5, tuning verification: the damping effect of the suspender system provided with the damper is verified by using a numerical simulation or an experimental method, so that the robustness of the suspender system is ensured when the frequency of the suspender (9) changes.

[0020] As a further improvement of the above technical solution, in the step S2, the inertial mass amplification coefficient is calculated according to the following formula:

[0021] wherein is the initial angle of the chiral metamaterial screw rod, is the helicity of the chiral metamaterial screw rod, is the radius of the inertance disc, is the moment of inertia of the inertance disc.

[0022] As a further improvement of the above technical solution, in the step S3, the analytical formula of the optimal frequency ratio and the optimal modal damping ratio after the damper is installed is obtained by using the fixed point method.

[0023] The optimal frequency ratio formula is: ,

[0024] The optimal modal damping ratio formula is: ,

[0025] wherein , is the ratio of the modal mass of the quality disc to the modal mass of the hanger, is the modal mass of the hanger after the modal shape is normalized at the damper installation position, is the first-order bending natural frequency of the hanger, is the design frequency of the damper, is referred to as the inertial mass ratio. is the ratio of the modal mass , and is referred to as the inertial mass ratio.

[0026] By adopting the above scheme, the three synergistic mechanisms of "chiral metamaterial (providing negative stiffness and motion conversion) + inertance disc (realizing inertial amplification) + eddy current (realizing efficient non-contact energy consumption)" are combined, and a set of "accurate design method based on model and global optimization" is combined, and the industry problem that "lightweight, high efficiency, robustness and durability" are difficult to balance in the arch bridge hanger vibration reduction is successfully solved, and reliable technical support is provided for the long-life safe operation of long-span arch bridges.

[0027] As a further improvement of the above technical scheme, in step S4, the calculation formula of the optimal damping coefficient of the eddy current damping unit is:

[0028] .

[0029] The core of the application is the innovative combination of chiral metamaterial screw, inertance disc and eddy current damping unit, which forms a triple synergistic vibration reduction mechanism of "mechanical conversion-inertial amplification-high efficiency energy consumption". Its working principle and effect are as follows:

[0030] Chiral metamaterial unit: the core of motion conversion and lightweight. Effect: using its unique compression-torsion coupling effect, the axial linear vibration of the mass disc is efficiently converted into the rotational motion of the inertance disc. This effect can produce macroscopic torsion under microscopic strain, providing negative stiffness characteristics for the system, effectively broadening the vibration reduction frequency band. This makes the device obtain strong restoring force without relying on large mass blocks, which is the cornerstone of realizing lightweight and miniaturization of the device.

[0031] Inertance vibration absorption unit: the key to realize inertial amplification. Effect: through the design of inner and outer disc structure and ball bearing, the torsional motion transmitted by the chiral metamaterial is converted into high-speed rotation of the outer disc. This mechanism can produce "apparent mass" much larger than its physical mass, typically 10-50 times. This means that a 1kg physical mass can produce a 10-50kg mass vibration reduction effect, which fundamentally breaks through the "mass barrier" of traditional TMD.

[0032] Eddy current damping unit: guarantee the persistent and stable energy consumption. Effect: the mass disc moves in the magnetic field of the permanent magnet, generates the eddy current, converts the vibration mechanical energy into the heat energy dissipation, the process is the non-contact energy consumption, completely eliminates the mechanical friction and fluid leakage, realizes the true maintenance-free and the stable performance in the whole life cycle, and the millisecond level response speed ensures the efficient dissipation of the wide frequency vibration energy.

[0033] The three synergies finally form a "low mass, small volume, strong robustness, high durability" composite damping system.

[0034] Compared with the prior art, the advantages of the present application are:

[0035] 1. Compared with the traditional linear TMD, the present application reduces the mass of the TMD through the chiral metamaterial unit and the inertial capacity vibration absorbing unit, improves the compactness of the device, widens the optimal vibration reduction parameter range, improves the robustness, and shows excellent vibration suppression capacity.

[0036] 2. The present application composites and integrates the chiral metamaterial unit, the inertial capacity vibration absorbing unit and the eddy current damping energy consumption unit through a specific structure, reduces the mass and volume requirements, realizes non-contact energy dissipation with the help of the eddy current damping, and the two synergistically form a "low mass, small volume, strong robustness" composite damping system, realizes efficient suppression of the boom vibration, significantly reduces the dynamic response amplitude, effectively reduces the required mass of the oscillator and the volume of the device, improves the compactness of the device, makes the structure relatively simple, and is convenient to install and maintain, has excellent durability, and is suitable for various boom sections (H-shaped, rectangular, circular).

[0037] 3. The eddy current damper of the present application has no fluid leakage risk, does not need regular maintenance, has strong weather resistance and durability; the response speed reaches the millisecond level, and can efficiently dissipate the wide frequency vibration energy. DETAILED DESCRIPTION

[0038] Figure 1 is the installation structure diagram of the arch bridge boom tuned mass inertia damper of the present application embodiment 1 on the boom.

[0039] Figure 2 is the cross-sectional view of the arch bridge boom tuned mass inertia damper of the present application embodiment 1.

[0040] Figure 3 is the internal structure diagram of the arch bridge boom tuned mass inertia damper of the present application embodiment 1 without the shell.

[0041] Figure 4 is the three-dimensional structure diagram of the inertial capacity disc in the present application embodiment 1.

[0042] Figure 5is a schematic diagram of the arrangement structure of the chiral metamaterial screw in embodiment 1 of the present application.

[0043] Figure 6 is a schematic diagram of the structure of the shell in embodiment 1 of the present application.

[0044] Figure 7 is a schematic diagram of the structure of the U-shaped seat in embodiment 1 of the present application.

[0045] The various reference signs in the drawings represent:

[0046] 1, shell; 11, N-pole permanent magnet; 12, S-pole permanent magnet; 2, mass disc; 3, inertial mass disc; 301, anti-collision pad; 31, inner disc; 32, outer disc; 33, ring groove; 34, ball bearing; 4, central shaft; 5, fastening mechanism; 51, U-shaped seat; 52, clamping groove; 53, screw hole; 6, linear bearing; 7, chiral metamaterial screw; 8, compression elastic member; 9, suspension rod. DETAILED DESCRIPTION

[0047] The present application is further described in detail below with the accompanying drawings and specific examples. Figures 1 to 7 The present application is further described in detail below with the accompanying drawings and specific examples.

[0048] In the description of the present application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship commonly used when the product of the present application is used, or the orientation or positional relationship commonly understood by those skilled in the art, and are only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the indicated device or element must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second", and the like are only used for differentiation in description and cannot be understood as indicating or implying relative importance.

[0049] In the description of the present application, it should also be noted that, unless otherwise explicitly specified and limited, the terms "arrangement", "installation", "connection", and "connection" should be broadly understood, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, or it can be connected inside 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.

[0050] Embodiment 1

[0051] As Figures 1 to 3As shown, the tuned mass inertia damper of the arch bridge suspender in the embodiment comprises a shell 1, a mass disc 2, an inertia disc 3, a central shaft 4 and a fastening mechanism 5. The shell 1 is a cylindrical structure, one end of which is open, the other end of which is closed, and the central shaft 4 is located in the shell 1 and fixedly connected to the closed end of the shell 1. The mass disc 2 and the inertia disc 3 are both sleeved on the central shaft 4, the mass disc 2 faces the opening, and the inertia disc 3 is located on the inner side of the mass disc 2. The mass disc 2 is axially movably sleeved on the central shaft 4 through a linear bearing 6, and the inertia disc 3 comprises an inner disc 31 and an outer disc 32, the outer disc 32 is sleeved on the outer periphery of the inner disc 31 and can rotate relative to the inner disc 31, the inner disc 31 is fixedly sleeved on the central shaft 4, and the outer disc 32 can rotate relative to the central shaft 4.

[0052] A chiral metamaterial screw 7 is connected between the mass disc 2 and the inertia disc 3, and a plurality of chiral metamaterial screws 7 are provided, and four chiral metamaterial screws 7 are provided in the embodiment. The plurality of chiral metamaterial screws 7 are arranged on the end face of the mass disc 2 facing the inertia disc 3, and are arranged in a circumferential direction with the center of the mass disc 2 as the center, as shown in the figure. Figure 5 As shown, a compression elastic element 8 is arranged on the end face of the mass disc 2 facing the opening of the shell 1. The compression elastic element 8 is preferably a compression spring. The inertia disc 3 and the mass disc 2 are both provided with a plurality of holes of a certain depth for placing both ends of the chiral metamaterial screw 7, and the inertia disc 3, the mass disc 2 and the chiral metamaterial screw 7 are fixedly connected through a related chemical adhesive (such as hot melt adhesive).

[0053] In the embodiment, the suspender 9 is specifically an H-shaped suspender, when the tuned mass inertia damper is connected with the suspender 9, the shell 1 is fixed on the suspender 9 through the fastening mechanism 5, the open end of the shell 1 is in contact with and adheres to the suspender 9, and the compression elastic element 8 is pressed between the mass disc 2 and the suspender 9, that is, the compression elastic element 8 has a certain pre-tightening force initially, which ensures the initial contact and the transmission of force, so that the vibration of the suspender 9 can be transmitted. When the arch bridge H-shaped suspender occurs bending vibration, the compression elastic element 8 acts on the mass disc 2, so that the mass disc 2 moves horizontally (vibrates) with the suspender 9, the horizontal movement of the mass disc 2 drives the outer disc 32 of the inertia disc 3 to rotate through the compression-torsion coupling effect of the chiral metamaterial screw 7, generates amplified torsion, and transfers the vibration energy of the suspender 9 to the inertia disc 3 to absorb, the vibration energy is converted into friction heat energy of the inertia disc 3, absorbs the vibration, and realizes high-efficiency energy dissipation. The structure adds the inertia vibration absorption unit composed of the chiral metamaterial unit and the inertia, forms a new type of vibration absorber, effectively reduces the physical mass of the vibrator and the volume of the device, and improves the damping performance, compactness and aesthetic appearance.

[0054] As shown in the figure, Figure 6As shown, in the embodiment, the N-pole permanent magnet 11 and the S-pole permanent magnet 12 are oppositely arranged on the inner wall of the shell 1, and the N-pole permanent magnet 11 and the S-pole permanent magnet 12 are annular bodies that can be attached to the inner wall of the cylindrical shell 1. The mass disc 2 is a conductor, preferably made of brass. The mass disc 2, the N-pole permanent magnet 11 and the S-pole permanent magnet 12 constitute an eddy current damping unit. When the mass disc 2 moves horizontally, the mass disc 2 as a conductor cuts the magnetic induction lines formed by the N-pole permanent magnet 11 and the S-pole permanent magnet 11 installed on the shell 1, thereby generating an eddy current and dissipating the energy of the bending vibration in the form of heat energy. This way has no risk of fluid leakage, no need for regular maintenance, strong weather resistance and durability; the response speed reaches milliseconds, and it can efficiently dissipate wideband vibration energy. Moreover, the chiral metamaterial unit, the inertial absorber unit and the eddy current damping energy dissipation unit are cleverly mechanically integrated and cooperatively act on the bending degree of freedom of the boom 9, so that the damper has the advantages of efficient, wideband and reliable vibration control.

[0055] In the embodiment, the end face of the inertial disc 3 facing the mass disc 2 is provided with a collision pad 301. The purpose of the collision pad 301 is to prevent the mass disc 2 from colliding with the inertial disc 3 when moving axially, wherein a flexible pad is arranged on the collision pad 301 to reduce the collision intensity. It should be noted that, in addition to the present embodiment, in other embodiments, the mass disc 2 can also be provided with a collision pad 301 on the end face facing the inertial disc 3, or both can be provided with a collision pad 301.

[0056] As shown in the figure, Figure 4 In the embodiment, a ring groove 33 is arranged between the inner disc 31 and the outer disc 32 of the inertial disc 3, the ring groove 33 is a through groove, and a plurality of ball bearings 34 are arranged in the ring groove 33 to realize the rotational connection between the inner disc 31 and the outer disc 32.

[0057] As shown in the figure, Figure 7 In the embodiment, the fastening mechanism 5 includes a U-shaped seat 51. The folded edges at both ends of the U-shaped seat 51 have clamping grooves 52, and screw holes 53 are further arranged on the folded edges. The middle shaft rod 4 passes out of the shell 1 from the open end away from the shell 1 and is fixedly connected to the inner side of the U-shaped seat 51. When the damper is fixed, the shell 1 is attached to the web of the boom 9, at this time the clamping grooves 52 on the two folded edges of the U-shaped seat 51 are clamped into the side edges of the boom 9, and finally the two ends of the U-shaped seat 51 are fixed on the boom 9 through bolts and screw holes 53, thereby realizing the installation of the damper on the boom 9. A non-slip pad is arranged between the clamping grooves 52 of the U-shaped seat 51 and the boom 9 to prevent damage to the boom 9 caused by excessive fastening force.

[0058] It should be noted that the boom 9 of the embodiment is taken as an example of an H-shaped boom, and in other embodiments, the boom 9 can also be rectangular or circular, and the shape of the fastening mechanism 5 and the shell 1 of the damper is modified adaptively to match different forms of the boom.

[0059] Embodiment 2

[0060] The design optimization method of the arch bridge boom tuned mass inertia damper of the embodiment is for the tuned mass inertia damper in embodiment 1, and the optimization method includes the following steps:

[0061] S1, boom parameter acquisition: the structural parameters and dynamic parameters of the controlled arch bridge boom 9 are acquired, and the dynamic parameters include the first-order bending natural frequency and modal mass of the boom 9.

[0062] Specifically, the key parameters of the controlled boom 9 are acquired through field testing or consulting design data, the structural parameters include cross-sectional parameters, Poisson's ratio, length, density, torsional stiffness, elastic modulus and axial force, and the first-order bending natural frequency and modal mass are calculated by using finite element analysis (such as ANSYS simulation) or analytical formula to ensure the accuracy of the parameters.

[0063] S2, parameter design of chiral metamaterial screw rod: the inertia amplification coefficient of the chiral metamaterial screw rod 7 is acquired according to the initial angle and helicity of the chiral metamaterial screw rod 7, the radius of the inertial disk 3 and the moment of inertia of the inertial disk 3.

[0064] Specifically, the inertia amplification coefficient is calculated by the formula: .

[0065] Wherein, is the initial angle of the chiral metamaterial screw rod 7, is the helicity of the chiral metamaterial screw rod 7, is the radius of the inertial disk 3, is the moment of inertia of the inertial disk 3.

[0066] S3, target parameter optimization: the ratio of the damper installation position to the length of the boom 9, the ratio of the mass disk 2 to the modal mass of the boom 9, and the optimal inertia amplification coefficient are taken as optimization variables, the first-order bending natural frequency and modal mass of the boom 9 are taken as input, and the optimal damper installation position, the optimal inertia amplification coefficient and the optimal mass ratio are calculated by the fixed point method combined with the optimization algorithm.

[0067] Specifically, the analytical formula of the optimal frequency ratio and the optimal modal damping ratio after installing the damper is obtained by the fixed point method:

[0068] The optimal frequency ratio formula is: .

[0069] The optimal modal damping ratio formula is: .

[0070] wherein, , is the ratio of the modal mass of the mass disc 2 to the boom 9, is the modal mass of the boom 9 after the modal shape is normalized at the damper installation position, is the first-order bending natural frequency of the boom 9, is the design frequency of the damper, refers to the ratio of the inertial mass amplification coefficient (inertance) to the modal mass , which is referred to as the inertial mass ratio. In addition, the damper installation position, the inertial mass amplification coefficient, and the mass ratio are determined according to the actual structure and the on-site installation condition.

[0071] S4, eddy current damping parameter design: according to the optimal parameters obtained above, the optimal damping coefficient of the eddy current damping unit is calculated, and the sizes of the N-pole permanent magnet 11, the S-pole permanent magnet 12, and the mass disc 2 are designed.

[0072] Specifically, the calculation formula of the optimal damping coefficient of the eddy current damping unit is: .

[0073] S5, tuning verification: the vibration reduction effect of the boom system with the damper installed is verified by using numerical simulation or experimental method, so as to ensure that the boom system remains robust when the frequency of the boom 9 changes. The boom system refers to the entire system of the boom + arch bridge boom tuning mass inertial damper.

[0074] Finally, the components are processed according to the final parameters, and the installation is carried out by using modular installation: the transmission disc, the dynamic damping disc, and the inertance disc are fixed on the boom first, then the transmission disc and the external shell are assembled, and finally the eddy current unit is debugged to complete the installation.

[0075] The core effect of the optimal design method of the application is that it changes an experience-dependent trial-and-error process into a precise and predictable system engineering. By correlating the physical parameters (inertial mass amplification coefficient ) of the chiral metamaterial and the inertance disc with the characteristics (modal mass ) of the boom as the relative inertial mass ratio , and using the fixed point method formula and the particle swarm optimization algorithm, the coupling optimization problem of multiple parameters such as the installation position, the mass ratio, and the inertial mass ratio is systematically solved, so as to output a set of globally optimal design parameters for a specific boom. This not only ensures that the damper is "processed into an excellent product", realizes precise matching and performance prediction with the target boom, but also, due to the design kernel based on the model, gives the device strong robustness to the change of the boom frequency, and guarantees long-term, efficient, and reliable vibration reduction effect from the design source.

[0076] While the present application has been disclosed in its preferred embodiments with reference to the drawings, it is to be understood that the application is not limited to the above- described embodiments. Any person skilled in the art, without departing from the scope of the application, can make many possible variations and modifications of the application, or equivalent embodiments, by utilizing the above-described technical content of the application. Therefore, any simple modification, equivalent change and modification of the above embodiments, without departing from the content of the application, according to the technical essence of the application, should fall within the scope of protection of the application.

Claims

1. A tuned mass-inertia damper for an arch bridge suspender, characterized in that, The device includes a mass disk (2), an inertia disk (3), a central shaft (4), and a fastening mechanism (5). The mass disk (2) is movably mounted on the central shaft (4), and the inertia disk (3) is mounted on the central shaft (4) and can rotate relative to the central shaft (4). Multiple chiral metamaterial screws (7) are connected between the mass disk (2) and the inertia disk (3). The multiple chiral metamaterial screws (7) are arranged chirally in the circumferential direction with the center of the mass disk (2). A compression elastic element (8) is provided on the end face of the mass disk (2) away from the inertia disk (3). When the tuned mass-inertia damper is connected to the boom (9), the central shaft (4) is fixed on the boom (9) by the fastening mechanism (5). The compression elastic element (8) is abutted between the mass disk (2) and the boom (9).

2. The tuned mass-inertia damper for arch bridge hangers according to claim 1, characterized in that, It also includes a housing (1), the central shaft (4) is fixed inside the housing (1), and N-pole permanent magnets (11) and S-pole permanent magnets (12) are arranged opposite to each other on the inner wall of the housing (1). The mass disk (2) is a conductor, and the mass disk (2), N-pole permanent magnets (11) and S-pole permanent magnets (12) constitute an eddy current damping unit.

3. The tuned mass-inertia damper for arch bridge hangers according to claim 2, characterized in that, The inertial container (3) includes an inner disk (31) and an outer disk (32). The outer disk (32) is fitted around the outer periphery of the inner disk (31) and the two can rotate relative to each other. The inner disk (31) is fixedly fitted onto the central shaft (4).

4. The tuned mass inertia damper for arch bridge hangers according to claim 3, characterized in that, An annular groove (33) is provided between the inner disk (31) and the outer disk (32), and multiple ball bearings (34) are provided in the annular groove (33).

5. The tuned mass-inertia damper for arch bridge hangers according to claim 2, characterized in that, The end face of the mass disk (2) facing the inertia disk (3) is provided with anti-collision pads (301); or, the end face of the inertia disk (3) facing the mass disk (2) is provided with anti-collision pads (301).

6. The tuned mass-inertia damper for arch bridge suspenders according to any one of claims 2 to 5, characterized in that, The fastening mechanism (5) includes a U-shaped seat (51), the central shaft (4) extends out of the housing (1) away from the compression elastic element (8) and is fixedly connected to the inner side of the U-shaped seat (51), and the two ends of the U-shaped seat (51) are fixedly connected to the hanging rod (9) by bolts.

7. An optimized design method for a tuned mass-inertia damper for an arch bridge suspender as described in any one of claims 2 to 6, characterized in that, Includes the following steps: S1. Obtaining the parameters of the suspender: Obtain the structural and dynamic parameters of the suspender (9) of the arch bridge to be controlled. The dynamic parameters include the first-order bending natural frequency and modal mass of the suspender (9). S2. Parameter design of chiral metamaterial screw: The inertial mass amplification factor of chiral metamaterial screw (7) is obtained based on the initial included angle and helix of chiral metamaterial screw (7), the radius of inertial disk (3), and the moment of inertia of inertial disk (3). S3. Target parameter optimization: The ratio of the damper installation position to the length of the rod (9), the ratio of the modal mass of the mass disk (2) to the rod (9), and the optimal inertial mass amplification factor are used as optimization variables. The first-order bending natural frequency and modal mass of the rod (9) are used as inputs. The optimal damper installation position, optimal inertial mass amplification factor, and optimal mass ratio are calculated by combining the fixed point method with the optimization algorithm. S4. Eddy current damping parameter design: Based on the optimal parameters obtained above, the optimal damping coefficient of the eddy current damping unit is calculated, and the dimensions of the N-pole permanent magnet (11), S-pole permanent magnet (12) and mass disk (2) are designed accordingly. S5. Tuning verification: The vibration reduction effect of the rod system with dampers is verified by numerical simulation or experimental methods to ensure that the rod system remains robust when the frequency of the rod (9) changes.

8. The optimization design method according to claim 7, characterized in that, In step S2, the inertial mass amplification factor The calculation formula is: ,in, Let be the initial included angle of the chiral metamaterial screw (7). The helixity of the chiral metamaterial screw (7) is given by... Let the radius of the inertial disk (3) be , Let be the moment of inertia of the inertial container (3).

9. The optimization design method according to claim 8, characterized in that, In step S3, the analytical formulas for the optimal frequency ratio and the optimal modal damping ratio after installing the damper are obtained using the fixed-point method: The formula for the optimal frequency ratio is: , The formula for the optimal modal damping ratio is: , in , The ratio of the modal mass of the mass disk (2) to that of the boom (9) is given. The modal mass of the suspension rod (9) is obtained by normalizing the modal vibration mode at the damper installation location. Let the first-order bending natural frequency of the rod (9) be , For the design frequency of the damper, This refers to the inertia magnification factor. With modal mass The ratio of inertia to mass is called the inertia-mass ratio.

10. The optimization design method according to claim 9, characterized in that, In step S4, the formula for calculating the optimal damping coefficient of the eddy current damping unit is as follows: .

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