Tuned mass inertial torsional damper for rigid suspender of arch bridge and optimization design method thereof

Abstract

The invention discloses an arch bridge rigid suspender tuned mass inertial torsion damper and an optimization design method thereof.The damper comprises a transmission disc, a dynamic damping disc, a transmission disc and an inerter disc, the transmission disc is fixedly connected with a suspender, the dynamic damping disc is rotatably connected to the suspender, a pre-pressure mechanism is arranged on the transmission disc, and the transmission disc is connected with the inerter disc; the dynamic damping disc is provided with a transmission block which is used for being connected with a pre-pressure mechanism so that rotation of the transmission disc can drive the dynamic damping disc to rotate, the transmission disc is connected to the hanging rod in a sliding mode, a plurality of first chiral metamaterial screws are connected between the transmission disc and the dynamic damping disc, and the first chiral metamaterial screws are arranged in a chiral mode. The inerter disc is rotatably connected to the hanging rod, a plurality of second chiral metamaterial screws are connected between the transmission disc and the inerter disc, and the second chiral metamaterial screws are arranged in a chiral mode. The problems that a traditional inerter is large in size, sensitive to amplitude and difficult to adapt to the degree of freedom of torsion are solved, and efficient, broadband and reliable vibration control is achieved.

Description

Technical Field

[0001] This invention relates to the field of vibration suppression of arch bridge hangers, and more particularly to a tuned mass-inertia torsional damper for rigid arch bridge hangers and its optimization design method. Background Technology

[0002] With economic development, the demand for transportation engineering is increasing. In recent years, the construction of long-span bridges has developed rapidly, with large-scale projects such as those spanning rivers and seas being completed one after another. Currently, the world's largest span arch bridge has exceeded 600 meters. As the "lifeline" of arch bridges, the suspenders bear the core function of transmitting bridge deck loads and coordinating the deformation of the main arch. Their length increases significantly with the span, and the longest suspender currently reaches over 80 meters. However, as typical slender and flexible components, these suspenders have characteristics such as a large slenderness ratio, low natural frequency, and weak damping characteristics. Under external excitations such as wind loads, they are prone to large-amplitude vibrations, especially torsional vibrations and bending-torsional coupled vibrations. Compared with bending vibrations, the torsional vibrations of suspenders have strong nonlinearity, multimodal coupling, and are more sensitive to local stress concentrations.

[0003] Existing mechanical vibration reduction technologies (such as pendulum TMDs, magnetic ring vibration absorbers, and liquid dampers) have significant limitations in suppressing torsional vibration of suspension booms. Specifically, patent document (CN110528381A) discloses a four-line pendulum tuned mass damper and its design method for vibration reduction of long suspension booms in long-span bridges. This damper achieves vibration reduction by feeding back a control force to the suspension boom through the damper's oscillation, opposite to the direction of the boom's vibration, and by dissipating energy through a universal rotating ball joint at the connection between the pendulum and the support, or / and an air damper between the suspension boom and the counterweight. However, this device has the following limitations: Firstly, torsional vibration of the suspension boom is often accompanied by geometric nonlinearity (at large amplitudes). sinθ ≠ θThis leads to parameter mismatch. Furthermore, although multi-directional oscillation is achieved through a universal ball joint, a dedicated torsional degree-of-freedom tuning mechanism is not designed. It relies solely on the inertia of the mass block to suppress horizontal vibration, resulting in limited control over the midpoint of the boom with the largest torsional mode displacement. Patent document (CN111637186B) discloses a nonlinear dynamic vibration absorber with a double-ring strong magnet array for boom vibration reduction and its design method. This damper achieves vibration reduction by transferring the boom's vibration energy to the absorber through feedback of a control force opposite to the boom's vibration direction, thereby reducing energy return to the boom, and by dissipating energy through friction between the universal wheels and the base, and by adding air dampers. However, this device has the following limitations: firstly, the device requires precise design of the number of magnetic tiles, central angle, and electromagnetic parameters of the inner and outer magnetic ring arrays, demanding high processing precision and significantly increasing manufacturing costs; secondly, precise tuning is difficult to achieve on-site. Patent document (CN107657126B) discloses a ring-shaped cylindrical tuned liquid damper and its design method for controlling the vibration of long suspension rods in long-span bridges. This device controls the dynamic response of the suspension rod by dissipating energy through liquid sloshing within the container and applying lateral force to the container wall using the liquid sloshing. However, this device has the following limitations: Firstly, it requires strict matching with the first-order natural frequency of the suspension rod, but the first-order bending and torsional natural frequencies are different, making it impossible to simultaneously suppress bending and torsional vibrations. Furthermore, the energy dissipation efficiency of the liquid sloshing for torsional vibration is low, and the damping mechanism is not optimized for the torsional degree of freedom. Secondly, the suspension rod is prone to frequency drift due to tension changes and aging during service; once detuned, the vibration reduction effect significantly decreases. Patent document (CN112942103B) discloses a cable vibration damping device, which achieves vibration reduction of the cable primarily through the friction between friction components. However, this device has issues such as pre-deformation of the reserved track when the torsional vibration angle is large. Patent document (CN102409604B) discloses a vibration reduction and protection device for bridge suspenders. This invention uses lateral damping tubes to replace the suspenders in bearing wind loads, while the vibration energy of the lateral damping tubes under wind loads is dissipated through damping material inside the device. However, this device suffers from unstable durability of the damping material. Patent document (CN113638306B) discloses a bridge suspender damping cable vibration reduction device. This invention forms a standard damping segment by combining every two transverse main and auxiliary cables with two longitudinal main and auxiliary cables, thereby simultaneously suppressing the vibration of four adjacent suspenders in any direction. Finally, by connecting the damping segments sequentially, the vibration of the entire bridge suspenders is suppressed.

[0004] The existing mechanical vibration reduction technologies generally suffer from the following problems: First, traditional technologies mostly follow the approach of controlling bending vibration, rarely designing dedicated inertial mass units for torsional degrees of freedom, relying solely on the inertia of mass blocks or fluid energy dissipation, resulting in extremely low efficiency in phase control and energy dissipation for torsional vibrations; Second, they have weak adaptability to torsional vibrations with prominent nonlinear characteristics (such as parameter mismatch caused by geometric nonlinearity under large amplitude); Third, they suffer from problems such as high tuning difficulty, high manufacturing cost, and inability to simultaneously suppress bending-torsional coupled vibrations; Fourth, most are designed for circular cross-sections, making it difficult to directly adapt to H-shaped booms. Therefore, there is an urgent need to develop a new type of damping device that addresses the torsional vibration characteristics of booms, integrates inertial mass technology, has high vibration reduction efficiency, a compact structure, easily tuned parameters, strong robustness, and is easy to install and maintain. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a tuned mass inertia torsional damper for rigid hangers of arch bridges and its optimization design method.

[0006] Firstly, to solve the above-mentioned technical problems, the present invention adopts the following technical solution: A tuned mass-inertia torsional damper for a rigid suspender of an arch bridge includes a transmission disc, a dynamic damping disc, a transmission disc, and an inertia-capacity disc. The transmission disc, dynamic damping disc, transmission disc, and inertia-capacity disc are sequentially and coaxially sleeved on the suspender. The transmission disc is fixedly connected to the suspender. The dynamic damping disc is rotatably connected to the suspender. A preload mechanism is provided on the end face of the transmission disc facing the dynamic damping disc. The dynamic damping disc has a transmission block for connecting to the preload mechanism so that rotation of the transmission disc can drive rotation of the dynamic damping disc. The transmission disc is slidably connected to the suspender. Multiple chiral metamaterial screws (first type) are connected between the transmission disc and the dynamic damping disc. Each chiral metamaterial screw (first type) is circumferentially distributed around the center of the dynamic damping disc and arranged in a chiral manner. The inertia-capacity disc is rotatably connected to the suspender. Multiple chiral metamaterial screws (second type) are connected between the transmission disc and the inertia-capacity disc. Each chiral metamaterial screw (second type) is circumferentially distributed around the center of the transmission disc and arranged in a chiral manner.

[0007] Through the above scheme, when the suspender experiences torsional vibration, the transmission disc fixed to it rotates synchronously, driving the dynamic damping disc to rotate accordingly via a preload mechanism. This rotational motion, through multiple chiral metamaterial screws arranged circumferentially and chirally, transforms its unique compression-torsional coupling effect into precise sliding of the transmission disc along the suspender's axial direction. This axial sliding further drives a second set of chiral metamaterial screws, again utilizing their coupling effect to restore and amplify the linear motion into the rotational motion of the inertial volume disc. Through the above two-stage motion transformation and inertial mass amplification—"rotation → linear → amplified rotation"—this setup can efficiently extract, transmit, and ultimately converge the torsional vibration energy of the suspender onto the inertial volume disc, applying a reverse inertial force in the form of amplified "apparent mass," thereby achieving highly targeted and efficient suppression of the torsional vibration of the rigid suspender of the arch bridge.

[0008] As a further improvement to the above technical solution, it also includes a housing, in which the transmission disk, dynamic damping disk, transfer disk and inertia disk are all located. The inner wall of the housing is provided with annular N-pole permanent magnets and annular S-pole permanent magnets, with a gap between the N-pole permanent magnets and the S-pole permanent magnets. The outer damping disk is provided with a conductor, which extends into the gap. The dynamic damping disk, the N-pole permanent magnets and the S-pole permanent magnets constitute an eddy current damping unit.

[0009] The above solution adds a highly efficient, contactless, and maintenance-free damping energy dissipation mechanism. When the dynamic damping disc drives the conductive body to rotate within the gap of the permanent magnet, eddy currents are generated, directly converting the mechanical energy of vibration into heat energy for dissipation. The advantages of this solution are: stable damping performance, unaffected by temperature or aging; no friction or wear, long lifespan, and virtually maintenance-free; rapid response, effectively suppressing broadband vibrations; and a compact structure, easily integrated into the housing. This approach combines the core structure with the key energy dissipation unit, enhancing the practicality and vibration reduction efficiency of the solution.

[0010] As a further improvement to the above technical solution, the dynamic damping disc includes an inner damping disc and an outer damping disc that is rotatably fitted around the inner damping disc. The inner damping disc is fixed on the suspension rod, the transmission block is disposed on the outer damping disc, and the chiral metamaterial screw is connected to the outer damping disc.

[0011] As a further improvement to the above technical solution, the inertial volume disk includes an inner inertial volume disk and an outer inertial volume disk rotatably fitted outside the inner inertial volume disk. The inner inertial volume disk is fixed on the lifting rod, and the chiral metamaterial screw is connected to the outer inertial volume disk.

[0012] As a further improvement to the above technical solution, the pre-pressure mechanism includes a base and two upright plates fixed on the base, with a horizontally arranged spring installed on each upright plate, and the transmission block is clamped between the two springs.

[0013] As a further improvement to the above technical solution, the pre-pressure mechanism is provided in multiple sets, and the multiple sets of pre-pressure mechanisms are arranged circumferentially along the center of the transmission disc, and the transmission block is provided in multiple sets accordingly.

[0014] As a further improvement to the above technical solution, the housing, transmission disk, dynamic damping disk, transfer disk, and inertia disk are all formed by splicing together two halves of a circular arc.

[0015] As a further improvement to the above technical solution, the inner wall of the shock-absorbing outer disc is connected to multiple hubs 1, and the outer wall of the shock-absorbing inner disc is provided with a slot 1, in which the hub 1 can be rolled and locked in the slot 1; the inner wall of the inertial capacity outer disc is connected to multiple hubs 2, and the outer wall of the inertial capacity inner disc is provided with a slot 2, in which the hub 2 can be rolled and locked in the slot 2.

[0016] Secondly, to solve the above-mentioned technical problems, the present invention adopts the following technical solution: An optimized design method for a rigid hanger tuned mass-inertia torsional damper for an arch bridge, as described above, includes the following steps: S1. Obtaining the parameters of the boom: Obtain the key parameters of the boom to be controlled, including cross-sectional parameters, Poisson's ratio, length, density, torsional stiffness, elastic modulus and axial force, and calculate the first torsional natural frequency of the boom based on the key parameters; S2. Mass ratio setting: Based on the preset optimization target, set the mass ratio between the total mass of the damper and the mass of the boom; S3. Design steps for two-stage inertial mass amplification factor: Based on the configuration parameters of the first-stage chiral metamaterial screw one and the configuration parameters of the second-stage chiral metamaterial screw two, as well as the radii of the dynamic damping disk and the inertial capacity disk, determine the comprehensive inertial mass amplification factor of the damper. S4. Parameter optimization steps: Based on the control objective, through optimization algorithms or finite element simulation, simultaneously optimize the mass ratio, inertia-mass ratio, damper installation position, chiral metamaterial screw 1-81 configuration parameters, and chiral metamaterial screw 2-82 configuration parameters, so that optimal performance can be achieved by installing a lower mass block at a relatively low position. S5. Eddy current damping design: Based on the optimal parameters obtained in step S4, calculate the required optimal damping coefficient, and design the strength of the N-pole permanent magnet and the S-pole permanent magnet, as well as the size of the conductor accordingly. S6. System Integration and Tuning: The various units are integrated into a whole damper. Through numerical simulation, the displacement time history response and frequency domain response of the boom and the tuned mass-inertia torsional damper are calculated. By comparing with the first-order torsional natural frequency and displacement time history of the boom, the vibration reduction effect is comprehensively verified. Based on this, the parameters are fine-tuned to ensure that the system remains robust when the boom frequency changes.

[0017] As a further improvement to the above technical solution: The inertial mass amplification factor The calculation formula is: .

[0018] The initial included angle of the chiral metamaterial screw is given. The initial included angle of the chiral metamaterial screw two is... The helix degree of the chiral metamaterial screw. For the helixity of the chiral metamaterial screw II, The radius of the dynamic damping disc. Let be the radius of the inertial disk.

[0019] Compared with the prior art, the advantages of the present invention are as follows: (1) This invention is the first to create an innovative architecture for a chiral metamaterial as the core inertial container. It utilizes the geometric nonlinear deformation characteristics of the artificial topology of chiral metamaterials to directly excite a coordinated torsional response through axial compression / tension motion, efficiently converting linear motion into torsional inertial force output. It constructs a lightweight and compact torsional inertial container from the intrinsic material level, completely solving the problems of large volume, sensitivity to amplitude and difficulty in adapting to torsional degrees of freedom of traditional inertial containers. It achieves efficient, wide-frequency and reliable vibration control, and at the same time realizes the provision of strong restoring force without relying on large mass blocks. It effectively breaks through the limitation of traditional tuned mass dampers (TMDs) that "the larger the mass, the better the vibration reduction effect", reduces the dependence on physical mass blocks, and provides a key material basis for reducing the physical mass of the oscillator and the volume of the device.

[0020] (2) The present invention integrates chiral metamaterial unit, inertial capacitance vibration absorption unit and eddy current damping energy dissipation unit through a specific structure to achieve efficient suppression of torsional vibration of the suspension rod and significantly reduce the dynamic response amplitude; at the same time, it can effectively reduce the physical mass of the required oscillator and the volume of the device, improve compactness, make the structure simpler, installation and maintenance more convenient, and have excellent durability.

[0021] (3) The present invention has the performance of effectively suppressing torsional vibration: it is specifically designed for the torsional degree of freedom of the boom, and through a composite mechanism, it efficiently absorbs and dissipates torsional vibration energy, significantly reduces the torsional response amplitude of the boom, and effectively alleviates fatigue damage.

[0022] (4) The present invention has high robustness and wide frequency adaptability: the chiral metamaterial combined with the "apparent quality" amplification effect of the inertial container makes the system exhibit beneficial nonlinear characteristics. This greatly expands the optimal vibration reduction frequency range of the damper, making it highly adaptable to the deviation of the rod frequency caused by environmental changes, aging or detuning, and maintaining a stable and efficient vibration reduction effect.

[0023] (5) The present invention has the advantages of easy parameter tuning and long-lasting effect: the inertial container and eddy current unit are not easily affected by environmental aging and fatigue, and the damping characteristics are stable. The structural characteristics of the negative stiffness unit are also relatively stable. Compared with the traditional TMD that relies on springs, the device parameters of the present invention are easier to keep stable, the long-term vibration reduction effect is more reliable, and the maintenance cycle and service life are significantly extended.

[0024] (6) This invention features a compact structure and convenient installation: the split-type ring design facilitates on-site installation and fixing of the hangers, minimizing impact on the bridge landscape. It also boasts wide applicability: the design method is clear and can be customized according to different hanger parameters, suitable for various hanger cross-sections (H-shaped, rectangular, circular). Furthermore, it offers good durability and low maintenance costs: primarily using durable materials such as metals and composite materials, the core energy-consuming units (eddy current, friction) have no fluid leakage issues, the structure is simple and reliable, significantly reducing subsequent maintenance needs and costs. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the installation structure of the tuned mass inertia torsional damper for the rigid hanger of an arch bridge according to Embodiment 1 of the present invention.

[0026] Figure 2 yes Figure 1 Cross-sectional view.

[0027] Figure 3 This is a schematic diagram (excluding the housing) of the tuned mass inertia torsional damper for the rigid hanger of an arch bridge according to Embodiment 1 of the present invention.

[0028] Figure 4 This is a schematic diagram of the transmission disc in Embodiment 1 of the present invention.

[0029] Figure 5 This is a schematic diagram of the dynamic damping disc in Embodiment 1 of the present invention.

[0030] Figure 6 This is a schematic diagram of the transfer disk in Embodiment 1 of the present invention.

[0031] Figure 7 This is a schematic diagram of the inertial capacity disk in Embodiment 1 of the present invention.

[0032] Figure 8 This is a schematic diagram of the shell structure in Embodiment 1 of the present invention.

[0033] Figure 9 This is a schematic diagram of the structure of hub one in Embodiment 1 of the present invention.

[0034] The labels in the diagram represent: 1. Shell; 11. N-pole permanent magnet; 12. S-pole permanent magnet; 13. Semi-cylindrical split; 14. Clearance groove; 2. Transmission disc; 21. Transmission semi-circular block; 22. Connecting plate one; 3. Dynamic damping disc; 302. Connecting plate two; 31. Inner damping disc; 311. Inner damping semi-circular block; 32. Outer damping disc; 321. Outer damping semi-circular block; 33. Transmission block; 34. Conductor; 4. Transfer disc; 41. Anti-collision block; 42. Transmission semi-circular block; 43. Connecting plate three; 5. 51. Inertia plate; 51. Inner inertia plate; 511. Inner semicircular block of inertia; 52. Outer inertia plate; 521. Outer semicircular block of inertia; 53. Connecting plate four; 6. Hanging rod; 61. Web plate; 62. Side plate; 63. Long groove; 7. Preload mechanism; 71. Base; 72. Vertical plate; 73. Spring; 81. Chiral metamaterial screw one; 82. Chiral metamaterial screw two; 91. Hub one; 92. Hub two; 100. Bolt; 200. Bolt hole; 300. Smooth bolt. Detailed Implementation

[0035] The following is in conjunction with the instruction manual. Figures 1 to 9 The present invention will be further described in detail with reference to specific embodiments.

[0036] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this invention is in use, or the orientation or positional relationship commonly understood by those skilled in the art. They are only used for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. In addition, the terms "first," "second," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0037] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0038] Example 1 like Figures 1 to 3As shown, the tuned mass-inertia torsional damper for the rigid hanger of the arch bridge in this embodiment includes a housing 1 and a transmission disc 2, a dynamic damping disc 3, a transmission disc 4, and an inertia volume disc 5 disposed within the housing 1. The transmission disc 2, the dynamic damping disc 3, the transmission disc 4, and the inertia volume disc 5 are sequentially and coaxially sleeved around the hanger 6. The housing 1 is mounted on the hanger 6 to protect the transmission disc 2, the dynamic damping disc 3, the transmission disc 4, and the inertia volume disc 5.

[0039] The transmission disc 2 is located at the bottom and is fixedly connected to the suspension rod 6. The end face (i.e., the upper end face) of the transmission disc 2 facing the dynamic damping disc 3 is provided with a preload mechanism 7. The function of the transmission disc 2 is to directly sense and follow the torsional vibration of the suspension rod 6, and convert the torsional angular displacement into a drive for the dynamic damping disc 3.

[0040] The dynamic damping disc 3 includes an inner damping disc 31 and an outer damping disc 32. The outer damping disc 32 is rotatably fitted over the inner damping disc 31. The inner damping disc 31 is fixed on the hanger 6. The outer damping disc 32 has a transmission block 33 on its end face (i.e., lower end face) facing the transmission disc 2. The transmission block 33 is used to connect with the preload mechanism 7 so that the rotation of the transmission disc 2 can drive the rotation of the outer damping disc 32.

[0041] The transfer disk 4 is slidably mounted on the boom 6. Multiple chiral metamaterial screws 81 connect the transfer disk 4 to the shock-absorbing outer disk 32; this embodiment uses four chiral metamaterial screws 81 as an example. Each chiral metamaterial screw 81 is circumferentially distributed around the center of the shock-absorbing outer disk 32 and arranged chirally. Both the shock-absorbing outer disk 32 and the transfer disk 4 have multiple holes of a certain depth. The positions of the holes are designed according to the initial rotation angle of the chiral metamaterial screws 81. During connection, the two ends of the chiral metamaterial screws 81 are first placed into the corresponding holes, and then the shock-absorbing outer disk 32, the transfer disk 4, and the chiral metamaterial screws 81 are fixed together using a relevant chemical adhesive (such as hot melt adhesive). When the shock-absorbing outer disk 32 rotates, the torsional motion of the shock-absorbing outer disk 32, through the compression-torsional coupling effect of the chiral metamaterial screws 81, drives the transfer disk 4 to move up and down along the axial direction of the boom 6 without rotation. The function of the transmission disk 4 is to convert the rotational motion of the shock-absorbing outer disk 32 into the precise up-and-down linear motion of the transmission disk 4 itself through the coupling effect of the chiral screw, thereby providing input energy for the rotational motion of the inertial container disk 5.

[0042] The inertial volume disk 5 includes an inner inertial volume disk 51 and an outer inertial volume disk 52. The outer inertial volume disk 52 is rotatably fitted over the inner inertial volume disk 51, and the inner inertial volume disk 51 is fixed to the lifting rod 6. Multiple chiral metamaterial screws 82 are connected between the transfer disk 4 and the outer inertial volume disk 52; this embodiment uses four as an example. The four chiral metamaterial screws 82 are distributed circumferentially around the center of the transfer disk 4 and arranged in a chiral manner. Similar to the fixing method of the chiral metamaterial screw 81, both the outer inertial volume disk 52 and the transfer disk 4 have multiple holes of a certain depth. The positions of the holes are designed according to the initial rotation angle of the chiral metamaterial screws 82. During connection, the two ends of the chiral metamaterial screws 82 are first inserted into the corresponding holes, and the outer inertial volume disk 52, the transfer disk 4, and the chiral metamaterial screws 82 are then fixed together using a relevant chemical adhesive (such as hot melt adhesive). When the transfer disk 4 compresses the chiral metamaterial screw 82 through its up-and-down motion, the outer inertial volume disk 52 can rotate independently of the inner inertial volume disk 51 due to the unique compression-torsional coupling effect of the chiral metamaterial screw 82, but it will not move up and down. The function of the inertial volume disk 5 is based on the unique compression-torsional coupling effect of the chiral metamaterial, converting the linear motion of the transfer disk 4 into the high-speed rotational motion of the outer disk. This mechanism can generate an "apparent mass" much larger than its physical mass, greatly amplifying the inertial effect, thereby efficiently absorbing vibrational energy.

[0043] When the arch bridge suspender 6 undergoes constrained torsion, the transmission disk 2, installed at the midpoint of the suspender 6 (where the torsional vibration mode displacement is maximum), rotates with the suspender 6, driving the damping outer disk 32 to undergo torsional motion through the preload mechanism 7. The torsional motion of the damping outer disk 32, through the compression-torsional coupling effect of the chiral metamaterial screw 81, drives the transmission disk 4 to move upward along the axial direction of the suspender 6. The displacement of the transmission disk 4 further compresses the chiral metamaterial screw 82, causing the inertial volume outer disk 52 to generate amplified torsion (the inertial volume outer disk 52 rotates), transferring the vibration energy of the suspender 6 to the inertial volume disk 5 for absorption. In the above process, energy is converted into frictional heat energy of the inertial volume disk, achieving efficient energy dissipation. Compared with traditional linear TMD, the nonlinear characteristics of this invention (introduced by the negative stiffness element) broaden the range of optimal vibration reduction parameters, improve robustness, and exhibit excellent vibration suppression capabilities.

[0044] In this embodiment, to further improve vibration reduction performance, an annular N-pole permanent magnet 11 and an annular S-pole permanent magnet 12 are provided on the inner wall of the housing 1, with a gap between the N-pole permanent magnet 11 and the S-pole permanent magnet 12. A conductor 34 is provided on the damping outer disk 32, extending into the gap. The damping outer disk 32, the N-pole permanent magnet 11, and the S-pole permanent magnet 12 constitute an eddy current damping unit. When the damping outer disk 32 rotates, the conductor 34 on its outer side cuts the magnetic field lines formed by the permanent magnets (N and S poles). The conductor 34 moves relative to the magnetic field, generating eddy currents, thereby dissipating the vibration kinetic energy as heat. This method eliminates the risk of fluid leakage, requires no regular maintenance, and has excellent weather resistance and durability; the response speed is at the millisecond level, efficiently dissipating broadband vibration energy. Furthermore, the chiral metamaterial unit, the inertial capacitive vibration absorption unit, and the eddy current damping energy dissipation unit are ingeniously integrated through a composite mechanical structure, thereby enabling the damper to achieve the advantages of efficient, wide-bandwidth, and reliable vibration control.

[0045] In this embodiment, the conductor 34 is a fan-shaped block sleeved on the outside of the shock-absorbing outer disk 32. Multiple fan-shaped blocks are provided and evenly arranged around the circumference of the shock-absorbing outer disk 32. The conductor 34 is preferably made of brass.

[0046] In this embodiment, the preload mechanism 7 includes a base 71 and two upright plates 72 fixed on the base 71. A horizontally arranged spring 73 is mounted on each upright plate 72, and a transmission block 33 is sandwiched between the two springs 73. When the transmission disc 2 rotates clockwise, it compresses the right-side spring 73, which transmits force to the transmission block 33, causing the shock-absorbing outer disc 32 to rotate clockwise. When the transmission disc 2 rotates counterclockwise, it compresses the left-side spring 73, which transmits force to the transmission block 33, causing the shock-absorbing outer disc 32 to rotate counterclockwise. Regardless of the direction of rotation of the transmission disc 2, one spring is always compressed to transmit power. This design avoids rigid contact between the transmission block 33 and the vertical plate 72, achieving zero-backlash transmission with extremely rapid and smooth response. Furthermore, the spring can be pre-compressed during installation, applying a continuous preload to the transmission block 33. In a static state, the stop block is stably clamped in the center position, preventing wobbling from minor disturbances. The spring 73 can also absorb and buffer high-frequency impacts and large-amplitude vibrations transmitted from the boom 6, thus protecting the chiral metamaterial screws and inertial disks from sudden large loads. Four sets of preload mechanisms 7 are arranged circumferentially along the center of the transmission disk 2, with multiple sets corresponding to the transmission block 33.

[0047] In this embodiment, the hanger 6 is an example of an H-shaped hanger for an arch bridge. The H-shaped hanger includes a web 61 and two side plates 62. For ease of installation, the transmission disc 2, dynamic damping disc 3, transmission disc 4, and inertia disc 5 are all formed by splicing two halves of a circular arc.

[0048] like Figure 8 As shown, specifically, the housing 1 includes two hollow semi-cylindrical sections 13, which are connected by bolts 100 and bolt holes 200. Each semi-cylindrical section 13 has a clearance groove 14 on its two semi-circular end faces, which is used to avoid the side plate 62, allowing the semi-cylindrical section 13 to be inserted into the side plate 62. The two semi-cylindrical sections 13 are clamped onto the side plate 62 of the lifting rod 6 to form a fixed installation.

[0049] like Figure 4 As shown, the transmission disc 2 includes two transmission semicircular blocks 21, which are connected by bolts 100 and bolt holes 200. Each transmission semicircular block 21 has a flat connecting plate 22 near the joint on its inner wall. The connecting plates 22 are arranged in pairs. When the two transmission semicircular blocks 21 are fitted onto the suspension rod 6, the pairs of connecting plates 22 clamp the side plate 62 of the suspension rod 6 and are locked in place by bolts 100. Each transmission semicircular block 21 has a pair of connecting plates 22 at both ends, and four pairs of connecting plates 22 are provided. Anti-slip washers are provided between the connecting plates 22 and the side plate 62.

[0050] like Figure 5 As shown, the inner damping disc 31 and outer damping disc 32 of the dynamic damping disc 3 are both split structures. The two inner damping semicircular blocks 311 of the inner damping disc 31 are connected by bolts 100 and bolt holes 200, and the two outer damping semicircular blocks 321 of the outer damping disc 32 are connected by bolts 100 and bolt holes 200. Each inner wall of the inner damping semicircular block 311 has a flat connecting plate 302 near the joint. The connecting plates 302 are arranged in pairs. When the two inner damping semicircular blocks 311 are fitted onto the hanger 6, the pairs of connecting plates 302 clamp the side plate 62 of the hanger 6 and lock it in place with bolts 100. Each inner damping semicircular block 311 has a pair of connecting plates 302 at both ends, and four pairs of connecting plates 302 are provided. Anti-slip washers are provided between the connecting plates 302 and the side plate 62. Multiple wheel hubs 91 are connected to the inner wall of the outer damping disc 32, such as... Figure 9 As shown, the outer wall of the inner shock absorber 31 is provided with a groove, and the hub 91 is rotatably engaged in the groove. The outer shock absorber 32 and the inner shock absorber 31 are rotatably connected through the hub 91 and the groove. It should be noted that, in addition to using a hub to achieve a rotatable connection between the inner shock absorber 31 and the outer shock absorber 32, other rotatable connection structures, such as ball bearings, can also be used in other embodiments of this invention.

[0051] like Figure 6As shown, the transfer disk 4 includes two transfer semicircular blocks 42, which are connected by bolts 100 and bolt holes 200. Each transfer semicircular block 42 has a flat connecting plate 3 43 near the joint on its inner wall. The connecting plates 3 43 are arranged in pairs. The hanger 6 has an elongated groove 63, within which a smooth bolt 300 is fitted. When the two transfer semicircular blocks 42 are fitted onto the hanger 6, the paired connecting plates 3 43 are clamped onto the side plate 62 of the hanger 6. The smooth bolt 300 passes through the connecting plates 3 43 and the elongated groove 63, locking the paired connecting plates 3 43 in place. The smooth bolt 300 can slide up and down within the elongated groove 63. Anti-collision blocks 41 are provided on both the upper and lower end faces of the transfer disk 4. The anti-collision blocks 41 prevent the transfer disk 4 from colliding with the dynamic damping disk 3 and the inertia disk 5 during its upward and downward sliding motion.

[0052] like Figure 7 As shown, the outer inertia plate 52 and the inner inertia plate 51 of the inertia plate 5 are both separately configured. The two inner semicircular blocks 511 of the inner inertia plate 51 are connected by bolts 100 and bolt holes 200, and the two outer semicircular blocks 521 of the outer inertia plate 52 are connected by bolts 100 and bolt holes 200. Each inner semicircular block 511 has a flat connecting plate 4 53 near the joint on its inner wall surface. The connecting plates 4 53 are arranged in pairs. When the two inner semicircular blocks 511 are fitted onto the hanger 6, the pairs of connecting plates 4 53 clamp the side plate 62 of the hanger 6 and are locked with bolts 100. Each inner semicircular block 511 has a pair of connecting plates 4 53 at both ends, and there are four pairs of connecting plates 4 53. Anti-slip washers are provided between the connecting plates 4 53 and the side plate 62. Multiple hubs 92 are connected to the inner wall of the outer inertial container 52, and the outer wall of the inner inertial container 51 is provided with a slot, in which the hubs 92 can be rolled and locked. The outer inertial container 52 and the inner inertial container 51 are rotatably connected through the hubs 92 and the slots.

[0053] Example 2 The optimization design method for the tuned mass inertial torsional damper of the rigid suspender of the arch bridge in this embodiment is aimed at the tuned mass inertial damper in Embodiment 1. The optimization method includes the following steps: S1. Acquisition of hanger parameters: Acquire the key parameters of the hanger 6 to be controlled, including cross-sectional parameters, Poisson's ratio, length, density, torsional stiffness, elastic modulus and axial force, and calculate the first torsional natural frequency of hanger 6 through finite element modeling based on the key parameters. It should be noted that these key parameters will be designed in the initial stage of bridge design. S2. Mass ratio setting: Based on the preset optimization target, set the mass ratio between the total mass of the damper and the mass of the boom 6; S3. Two-stage mass amplification factor design: Based on the configuration parameters of the first-stage chiral metamaterial screw 81 and the second-stage chiral metamaterial screw 82, as well as the radii of the dynamic damping disk 3 and the inertial volume disk 5, the overall mass amplification factor of the damper is determined. This mass amplification factor applies to the entire system from the outer damping disk 32 to the chiral metamaterial screw 81, the transfer disk 4, the chiral metamaterial screw 82, and the inertial volume disk 5. There is only one such mass amplification factor. The calculation formula is: ,in, The initial included angle of the chiral metamaterial screw-81. The initial included angle of the chiral metamaterial screw 282. The helix degree of the chiral metamaterial screw-81 For the helixity of chiral metamaterial screw 282, The radius of the dynamic damping disc 3, Let be the radius of the inertial disk 5; S4. Parameter optimization: Based on the control objective, the mass ratio, inertia-mass ratio, damper installation position, chiral metamaterial screw 1-81 configuration parameters and chiral metamaterial screw 2-82 configuration parameters are optimized simultaneously through optimization algorithms or finite element simulation, so that the optimal performance can be achieved by installing a lower mass block at a relatively low position. S5. Eddy current damping design: Based on the optimal parameters obtained in step S4, calculate the required optimal damping coefficient, and design the strength of N-pole permanent magnet 11 and S-pole permanent magnet 12 and the size of conductor 34 accordingly. S6. System Integration and Tuning: The various units are integrated into a single damper. Through numerical simulation, the displacement-time history response and frequency domain response of the boom 6 and the tuned mass-inertia torsional damper are calculated. The vibration reduction effect is comprehensively verified by comparing these responses with the first-order torsional natural frequency and displacement-time history of the boom 6. Based on this, parameter fine-tuning is performed to ensure the boom system remains robust when the frequency of the boom 6 changes. Here, "system" refers to the entire boom + damper system. The goal is to obtain optimal parameters, which require optimization algorithms and numerical simulations to determine.

[0054] This invention's optimized design method, through a systematic multi-step process, provides for the first time a complete parametric design path for torsional dampers: starting with the acquisition of key rod parameters and the calculation of the first-order torsional frequency, setting the mass ratio, and innovatively establishing an inertial-mass amplification factor model based on the geometric configuration parameters of a two-stage chiral metamaterial screw, and simultaneously tuning the mass, position, and screw parameters through a collaborative optimization algorithm, ultimately matching and designing the eddy current damping unit. This method achieves a seamless transition from theoretical modeling to engineering implementation, enabling the damper to maintain lightweight and compactness while possessing efficient control capabilities for torsional vibrations, wide frequency adaptability, and strong robustness.

[0055] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the present invention, should fall within the protection scope of the present invention.

Claims

1. A tuned mass-inertia torsional damper for a rigid hanger of an arch bridge, characterized in that, The device includes a transmission disc (2), a dynamic damping disc (3), a transmission disc (4), and an inertia disc (5). The transmission disc (2), the dynamic damping disc (3), the transmission disc (4), and the inertia disc (5) are coaxially sleeved on the outside of the boom (6). The transmission disc (2) is fixedly connected to the boom (6). The dynamic damping disc (3) is rotatably connected to the boom (6). The end face of the transmission disc (2) facing the dynamic damping disc (3) is provided with a preload mechanism (7). The dynamic damping disc (3) is provided with a preload mechanism (7) for connecting to the dynamic damping disc (7) so that the rotation of the transmission disc (2) can drive the dynamic damping disc (3). The rotating transmission block (33) is slidably connected to the transmission disk (4) on the boom (6). Multiple chiral metamaterial screws (81) are connected between the transmission disk (4) and the dynamic damping disk (3). Each chiral metamaterial screw (81) is distributed circumferentially around the center of the dynamic damping disk (3) and arranged in a chiral manner. The inertial capacity disk (5) is rotatably connected to the boom (6). Multiple chiral metamaterial screws (82) are connected between the transmission disk (4) and the inertial capacity disk (5). Each chiral metamaterial screw (82) is distributed circumferentially around the center of the transmission disk (4) and arranged in a chiral manner.

2. The tuned mass-inertia torsional damper for rigid hangers of arch bridges according to claim 1, characterized in that, It also includes a housing (1), and the transmission disk (2), dynamic damping disk (3), transmission disk (4) and inertia disk (5) are all located inside the housing (1). The inner wall of the housing (1) is provided with an annular N-pole permanent magnet (11) and an annular S-pole permanent magnet (12). There is a gap between the N-pole permanent magnet (11) and the S-pole permanent magnet (12). The dynamic damping disk (3) is provided with a conductor (34), which extends into the gap. The dynamic damping disk (3), the N-pole permanent magnet (11) and the S-pole permanent magnet (12) constitute an eddy current damping unit.

3. The tuned mass-inertia torsional damper for rigid hangers of arch bridges according to claim 2, characterized in that, The dynamic damping disc (3) includes an inner damping disc (31) and an outer damping disc (32) rotatably fitted outside the inner damping disc (31). The inner damping disc (31) is fixed on the hanger (6), the transmission block (33) is set on the outer damping disc (32), and the chiral metamaterial screw (81) is connected to the outer damping disc (32).

4. The tuned mass-inertia torsional damper for rigid hangers of arch bridges according to claim 3, characterized in that, The inertial volume disk (5) includes an inner inertial volume disk (51) and an outer inertial volume disk (52) rotatably fitted outside the inner inertial volume disk (51). The inner inertial volume disk (51) is fixed on the lifting rod (6), and the chiral metamaterial screw two (82) is connected to the outer inertial volume disk (52).

5. The tuned mass-inertia torsional damper for rigid hangers of arch bridges according to any one of claims 2 to 4, characterized in that, The preload mechanism (7) includes a base (71) and two upright plates (72) fixed on the base (71). A horizontally arranged spring (73) is installed on each upright plate (72), and the transmission block (33) is sandwiched between the two springs (73).

6. The tuned mass-inertia torsional damper for rigid hangers of arch bridges according to any one of claims 2 to 4, characterized in that, The pre-pressure mechanism (7) is provided in multiple sets, and the multiple sets of pre-pressure mechanisms (7) are arranged around the center of the transmission disc (2). The transmission block (33) is provided in multiple sets accordingly.

7. The tuned mass-inertia torsional damper for rigid hangers of arch bridges according to any one of claims 2 to 4, characterized in that, The shell (1), transmission disk (2), dynamic damping disk (3), transmission disk (4) and inertia disk (5) are all formed by splicing together two half-circular arcs.

8. The tuned mass-inertia torsional damper for rigid hangers of arch bridges according to claim 4, characterized in that, The inner wall of the shock-absorbing outer disc (32) is connected to multiple hubs (91), and the outer wall of the shock-absorbing inner disc (31) is provided with a slot, and the hubs (91) can be rolled and locked in the slots. The inner wall of the inertial capacity outer disc (52) is connected to multiple hubs (92), and the outer wall of the inertial capacity inner disc (51) is provided with a slot, and the hubs (92) can be rolled and locked in the slots.

9. An optimized design method for a tuned mass-inertia torsional damper for a rigid hanger of an arch bridge as described in any one of claims 2 to 8, characterized in that, Includes the following steps: S1. Obtaining the parameters of the rod: Obtain the key parameters of the rod to be controlled (6), including the cross-sectional parameters, Poisson's ratio, length, density, torsional stiffness, elastic modulus and axial force, and calculate the first torsional natural frequency of the rod (6) based on the key parameters. S2, Mass ratio setting: Based on the preset optimization target, set the mass ratio between the total mass of the damper and the mass of the rod (6); S3, Design of two-stage mass amplification factor: Based on the configuration parameters of the first-stage chiral metamaterial screw one (81) and the configuration parameters of the second-stage chiral metamaterial screw two (82), as well as the radii of the dynamic damping disk (3) and the inertial capacity disk (5), the mass amplification factor of the damper is determined. S4. Parameter optimization: Based on the control objective, the mass ratio, inertia-mass ratio, damper installation position, chiral metamaterial screw 1-81 configuration parameters and chiral metamaterial screw 2-82 configuration parameters are optimized simultaneously through optimization algorithms or finite element simulation, so that the optimal performance can be achieved by installing a lower mass block at a relatively low position. S5. Eddy current damping design: Based on the optimal parameters obtained in step S4, calculate the required optimal damping coefficient, and design the strength of the N-pole permanent magnet (11) and the S-pole permanent magnet (12) and the size of the conductor (34) accordingly. S6. System integration and tuning: The units are integrated into an overall damper. The displacement time history response and frequency domain response of the rod (6) and the tuned mass inertial torsional damper are calculated through numerical simulation. The vibration reduction effect is verified by comparing the first-order torsional natural frequency and displacement time history of the rod (6). The parameters are then fine-tuned to ensure that the system remains robust when the frequency of the rod (6) changes.

10. The optimization design method according to claim 9, characterized in that, In step S3, the inertial mass amplification factor The calculation formula is: ， in ， The initial included angle of the chiral metamaterial screw (81) is given. The initial included angle of the chiral metamaterial screw two (82) is given. The helixity of the chiral metamaterial screw (81) is given. For the helixity of the chiral metamaterial screw 2 (82), The radius of the dynamic damping disc (3) is... Let be the radius of the inertial disk (5).

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