A Multimodal Cooperative Damping Vibration Reduction Method and System for Main Girder of Long-Span Bridges

Abstract

This application relates to a multimodal collaborative damping vibration reduction method for the main girder of a long-span bridge, comprising the following steps: determining the type of the main girder of the long-span bridge and its corresponding structural characteristics; determining the target vibration reduction design requirements based on the main girder type, including the frequency range of vortex-induced vibration under different wind attack angles, the minimum damping ratio corresponding to each frequency under the vertical mode shape, and the minimum damping ratio corresponding to each frequency under the torsional mode shape; and determining the collaborative control scheme of the tower-beam dampers and tuned mass dampers installed on the long-span bridge for the multimodal vibration of the main girder based on the target vibration reduction design requirements. This application provides a multimodal collaborative damping vibration reduction method for the main girder of a long-span bridge, and simultaneously installs tower-beam dampers and tuned mass dampers on the main girder of the long-span bridge for combined use to complete the collaborative vibration reduction design, thereby achieving the purpose of improving the vibration reduction effect and full coverage of multimodal vibration frequencies, and solving the problem of vortex-induced vibration reduction of the main girder of a long-span bridge.

Description

Technical Field

[0001] This invention relates to the field of structural vibration control technology, specifically to a multimodal collaborative damping vibration reduction method and system for the main beam of a long-span bridge. Background Technology

[0002] Currently, cable-stayed bridges (such as cable-stayed bridges, suspension bridges, and cable-stayed suspension bridges) have become an important structural system for ultra-long-span bridges, characterized by low and dense vibration modes. Therefore, wind-induced vibration must be considered in the design, construction, and operation of long-span bridges, employing relevant structural, aerodynamic, or mechanical damping measures. Commonly used mechanical damping devices include viscous fluid dampers (VFDs) and tuned mass dampers (TMDs). Both types of dampers have their advantages and are widely used in vibration control of engineering structures.

[0003] For example, most bridges where vortex-induced vibration is observed use TMD dampers to suppress it. However, TMD dampers are effective at controlling a specific frequency, but their vibration reduction effect rapidly diminishes after the frequency shifts. Therefore, when using TMD dampers to control the multimodal vibration of the main beam of a long-span bridge, a TMD damper with a corresponding frequency needs to be set for each mode. This can lead to omissions in the overall bridge modal control or a large number of TMD dampers installed, resulting in a large additional mass and poor vibration reduction performance.

[0004] For example, when installing tower-beam dampers, such as torsional dampers or VFD dampers, between the main beam of a bridge and the bridge pier, the installation position of the dampers is limited, and the control effect of certain vibration modes is very poor when the displacement at the connection point between the main beam and the damper is very small. Summary of the Invention

[0005] The technical problems to be solved by this application are: when using tower-beam dampers alone, the installation position of the dampers is limited; when using TMD dampers alone, modal control is easily overlooked; and the large added mass leads to poor multimodal vibration performance.

[0006] This application provides a multimodal collaborative damping vibration reduction method for the main girder of a long-span bridge, including the following steps:

[0007] Determine the type of main girder and its corresponding structural characteristics for long-span bridges;

[0008] The target vibration reduction design requirements are determined based on the main beam type. The target vibration reduction design requirements include the frequency range of vortex-induced vibration under different wind attack angles, the minimum damping ratio corresponding to each frequency under the vertical mode mode, and the minimum damping ratio corresponding to each frequency under the torsional mode mode.

[0009] Based on the target vibration reduction design requirements, a collaborative control scheme for the multimodal vibration of the main beam using tower-beam dampers and tuned mass dampers installed on the long-span bridge is determined.

[0010] In one embodiment, the coordinated control scheme for the multimodal vibration of the main beam by the tower-beam dampers and tuned mass dampers installed on the long-span bridge, based on the target vibration reduction design requirements, includes:

[0011] Establish a tower-beam damper-tuned mass damper coupling system, determine the positions of the tower-beam damper and the tuned mass damper according to the target vibration reduction design requirements, and calculate the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes.

[0012] The damping ratio of each frequency under the vertical and torsional modes is controlled by the tower-beam damper.

[0013] When the damping ratio at certain frequencies does not meet the target vibration reduction design requirements, the tuned mass damper is used in a cross-coordination manner to control the damping ratio corresponding to those frequencies.

[0014] In one embodiment, the coordinated control scheme for the multimodal vibration of the main beam by the tower-beam dampers and tuned mass dampers installed on the long-span bridge, based on the target vibration reduction design requirements, includes:

[0015] Establish a tower-beam damper-tuned mass damper coupling system, determine the positions of the tower-beam damper and the tuned mass damper according to the target vibration reduction design requirements, and calculate the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes.

[0016] The damping ratio of the lower frequencies of the vertical and torsional modes is controlled by the tower-beam damper to achieve the target vibration reduction design requirements.

[0017] The tuned mass dampers are used in a complementary and coordinated manner to control the damping ratio of the residual frequency under the residual vibration mode, so as to achieve the target vibration reduction design requirements.

[0018] In one embodiment, determining the positions of the tower-beam damper and the tuned mass damper according to the target vibration reduction design requirements includes:

[0019] According to the target vibration reduction design requirements, the tower-beam damper is installed between the main beam of the bridge and the bridge pier tower. One end of the damper is connected to the bridge pier tower, and the other end is connected to the main beam of the bridge through a cantilever lever structure, so that the connection point between the tower-beam damper and the main beam of the bridge is close to the mid-span of the main beam of the bridge.

[0020] According to the target vibration reduction design requirements, the tuned mass damper is installed on the main beam of the bridge.

[0021] In one embodiment, calculating the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes includes:

[0022] The characteristic equations are established based on the tower-beam damper-tuned mass damper coupled system.

[0023] Solving the characteristic equation yields the relationship between different frequencies, different mode shapes, and damping ratios;

[0024] Based on the parameters and installation positions of the tower-beam damper and the tuned mass damper, as well as the aforementioned relationship, calculate the damping ratio provided by different dampers for different frequencies and vibration modes in the tower-beam damper-tuned mass damper coupling system.

[0025] In one embodiment, the method for determining the coordinated control scheme of the tower-beam damper and the tuned mass damper for the multimodal vibration of the main beam based on the target vibration reduction design requirements further includes:

[0026] Adjust the parameters and installation positions of the tower-beam damper and the tuned inertial mass damper, and calculate the target control satisfaction.

[0027] In one implementation, the calculation of target control satisfaction includes:

[0028] Define the satisfaction function of the tower-beam damper-tuned mass damper coupled system.

[0029] The expression for the satisfaction function is:

[0030] In the formula, w k These are the weighting coefficients determined based on the damping ratios of each mode. , where is the logarithmic decay rate threshold determined based on the damping ratio of each mode, and p is the confidence index;

[0031] The satisfaction level of the tower-beam damper-tuned mass damper coupled system under different operating conditions is calculated based on the satisfaction function.

[0032] In one embodiment, the tower beam damper includes an oil damper, a viscous damper, an eddy current damper, or an outrigger lever-type inertial mass damper.

[0033] In one embodiment, the tuned mass damper is a multi-tuned mass damper, a distributed tuned mass damper, or an inertial mass tuned damper.

[0034] This application also provides a multimodal collaborative damping vibration reduction system for the main girder of a long-span bridge, comprising:

[0035] The main girder determination module is used to determine the type of main girder and its corresponding structural characteristics for long-span bridges.

[0036] The target design module is used to determine the target vibration reduction design requirements based on the main beam type. The target vibration reduction design requirements include the frequency range of vortex-induced vibration under different wind attack angles, the minimum damping ratio corresponding to each frequency under the vertical mode mode, and the minimum damping ratio corresponding to each frequency under the torsional mode mode.

[0037] The collaborative control module is used to determine the collaborative control scheme of the tower-beam dampers and tuned mass dampers installed on the long-span bridge for the multimodal vibration of the main beam, based on the target vibration reduction design requirements.

[0038] The beneficial effects of the technical solutions provided in this application include:

[0039] This application provides a multimodal synergistic damping vibration reduction method for the main girder of a long-span bridge. Addressing the multimodal vibration control requirements of long-span bridges, it combines tower-beam dampers and tuned mass dampers installed on the main girder to achieve synergistic vibration reduction design. Through cross-synergistic or complementary synergistic control of these two dampers, the method aims to improve vibration reduction performance and achieve full coverage of multimodal vibration frequencies, thus solving the problem of vortex-induced vibration reduction in the main girder of long-span bridges. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart illustrating a multi-modal collaborative damping vibration reduction method for the main girder of a long-span bridge according to an embodiment of the present invention.

[0042] Figure 2 This is a schematic diagram of the installation of the tower-beam damper and the tuned mass damper on a long-span bridge according to one embodiment of the present invention.

[0043] Figure 3 This is a schematic diagram of the modeling of a suspension bridge-damper system in one embodiment of the present invention.

[0044] Figure 4 This is a schematic diagram of the analytical model of the tower-beam damper-tuned mass damper coupling system in one embodiment of the present invention.

[0045] In the diagram: 1. Tower beam damper; 12. Support bracket; 2. Tuned mass damper. Detailed Implementation

[0046] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0047] like Figure 1 As shown, Figure 1 This is a flowchart illustrating a multi-modal collaborative damping vibration reduction method for the main girder of a long-span bridge according to an embodiment of the present invention.

[0048] This embodiment provides a multi-modal collaborative damping vibration reduction method for the main girder of a long-span bridge, including the following steps:

[0049] Step S1: Determine the type of main girder and corresponding structural characteristics of long-span bridges;

[0050] Step S2: Determine the target vibration reduction design requirements based on the main beam type. The target vibration reduction design requirements include the frequency range of vortex-induced vibration under different wind attack angles, the minimum damping ratio corresponding to each frequency under the vertical mode mode, and the minimum damping ratio corresponding to each frequency under the torsional mode mode.

[0051] Step S3: Determine the coordinated control scheme for the multimodal vibration of the main beam by the tower-beam dampers and tuned mass dampers installed on the long-span bridge according to the target vibration reduction design requirements.

[0052] This embodiment provides a multimodal synergistic damping vibration reduction method for the main girder of a long-span bridge. Addressing the multimodal vibration control requirements of long-span bridges, it combines tower-beam dampers and tuned mass dampers installed on the main girder to achieve synergistic vibration reduction design. Through cross-synergistic or complementary synergistic control, it balances applicability and vibration reduction effect, effectively improving vibration reduction performance and achieving full coverage of multimodal vibration frequencies, thus solving the problem of vortex-induced vibration reduction for the main girder of long-span bridges.

[0053] The following is a detailed explanation and elaboration of each step.

[0054] Step S1: Determine the type of main girder and its corresponding structural characteristics for long-span bridges.

[0055] Specifically, determine whether the main girder type of a long-span bridge is a suspension bridge, cable-stayed bridge, or other types, and then determine the corresponding structural characteristics, such as the corresponding stiffness, mass, natural frequency, and mode shape.

[0056] This application is also applicable to the vibration reduction requirements of long-span structures such as the main girder of suspension bridges and the large cantilever of cable-stayed bridges during construction.

[0057] Step S2: Determine the target vibration reduction design requirements based on the main beam type. The target vibration reduction design requirements include the frequency range of vortex-induced vibration under different wind attack angles, the minimum damping ratio corresponding to each frequency under the vertical mode mode, and the minimum damping ratio corresponding to each frequency under the torsional mode mode.

[0058] Of course, in other embodiments, the target vibration reduction design requirement can be other parameters. The target vibration reduction design requirement can be determined by wind tunnel testing of long-span bridges or based on actual engineering needs.

[0059] Step S3: Determine the coordinated control scheme for the multimodal vibration of the main beam by the tower-beam dampers and tuned mass dampers installed on the long-span bridge according to the target vibration reduction design requirements.

[0060] In one embodiment, step S3, determining the coordinated control scheme for the multimodal vibration of the main beam by the tower-beam dampers and tuned mass dampers installed on the long-span bridge according to the target vibration reduction design requirements, includes:

[0061] Step S31: Establish the tower-beam damper-tuned mass damper coupling system. Determine the positions of the tower-beam damper and the tuned mass damper according to the target vibration reduction design requirements, and calculate the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes.

[0062] Step S32: Control the damping ratio of each frequency under vertical and torsional mode shapes using the tower-beam damper;

[0063] Step S33: When the damping ratio at some frequencies does not meet the target vibration reduction design requirements, a tuned mass damper is used for cross-coordination to control the damping ratio corresponding to that frequency.

[0064] The above scheme provides a cross-cooperative control scheme. Within the frequency range that needs to be controlled, the tower-beam damper covers the entire target frequency. The frequency part of the target vibration reduction design requirements that the damping ratio cannot reach, i.e., some missing modes, is filled by the tuned mass damper.

[0065] It should be noted that the omitted mode refers to the vibration mode in which the amplitude at the connection point between the damper and the main beam is very small or even zero. The vibration energy of this mode is difficult to be transmitted to the damper, thus the damping and vibration reduction of this mode cannot be achieved.

[0066] In one embodiment, step S3, determining the coordinated control scheme for the multimodal vibration of the main beam by the tower-beam dampers and tuned mass dampers installed on the long-span bridge according to the target vibration reduction design requirements, includes:

[0067] Step S31: Establish the tower-beam damper-tuned mass damper coupling system. Determine the positions of the tower-beam damper and the tuned mass damper according to the target vibration reduction design requirements, and calculate the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes.

[0068] Step S34: Use tower-beam dampers to control the damping ratio of the lower frequencies of the vertical and torsional modes in order to achieve the target vibration reduction design requirements.

[0069] Step S35: Use tuned mass dampers for complementary coordination to control the damping ratio of the residual frequency under the residual mode shape in order to achieve the target vibration reduction design requirements.

[0070] The above scheme provides a complementary and coordinated control scheme. Within the frequency range that needs to be controlled, the tower-beam damper controls most frequencies, while the tuned mass damper fills the gaps in the frequency range where the tower-beam damper's control effect is poor.

[0071] Cross-cooperative control schemes and complementary cooperative control schemes can be selected based on economic and safety considerations.

[0072] like Figure 2 As shown, Figure 2 This is a schematic diagram of the installation of the tower-beam damper and the tuned mass damper on a long-span bridge according to one embodiment of the present invention.

[0073] In one embodiment, step S31, determining the positions of the tower-beam damper and the tuned mass damper according to the target vibration reduction design requirements, includes:

[0074] According to the target vibration reduction design requirements, the tower-beam damper is installed between the main beam of the bridge and the bridge pier tower. One end of the damper is connected to the bridge pier tower, and the other end is connected to the main beam of the bridge through a cantilever lever structure, so that the connection point between the tower-beam damper and the main beam of the bridge is close to the mid-span of the main beam of the bridge.

[0075] Based on the target vibration reduction design requirements, tuned mass dampers are installed on the main beam of the bridge.

[0076] Specifically, the outrigger lever structure is similar to a seesaw, with one end extending under the main beam of the bridge, the middle support bracket 12 serving as the seesaw fulcrum, and the other end support bracket connecting to the tower-beam damper 1. The tower-beam damper 1 can be on the same side as the support bracket or on the opposite side.

[0077] The above scheme allows for the determination of the tower-beam damper's location. Without increasing the length of the corbel structure, the connection point between the tower-beam damper and the main beam is brought closer to the mid-span of the main beam using a cantilever lever structure. The closer to the mid-span, the greater the vertical displacement of the main beam, resulting in a larger installation location ratio, providing a higher additional damping ratio, and reducing the required damping coefficient, thus improving the additional damping effect. When determining the tuned mass damper, it can be installed at any location on the main beam (as long as it is not at the stagnation point of the target vibration mode), with fewer restrictions on the installation location. The method and location can be varied under different coordination requirements.

[0078] In one embodiment, the tower-beam damper includes an oil damper, a viscous damper, an eddy current damper, or an outrigger lever-type inertial mass damper. When the tower-beam damper is an outrigger lever-type inertial mass damper, the increased additional damping ratio allows for control of multiple vibration frequencies of the main beam, achieving better broadband control and multi-order high-frequency vibration control.

[0079] In one embodiment, the tuned mass damper is a multi-tuned mass damper, a distributed tuned mass damper, or an inertial mass tuned damper.

[0080] In one embodiment, step S31, calculating the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes includes:

[0081] The characteristic equation is established based on the tower-beam damper-tuned mass damper coupled system.

[0082] Solving the characteristic equation yields the relationship between different frequencies, different mode shapes, and damping ratios;

[0083] Based on the parameters and installation locations of the tower-beam damper and the tuned mass damper, as well as the relevant formulas, calculate the damping ratios provided by different dampers for different frequencies and vibration modes in the tower-beam damper-tuned mass damper coupled system.

[0084] Specifically, the characteristic equations of the tower-beam damper-tuned mass damper coupled system are established based on complex modal theory. Of course, other theories can also be used. Complex modal theory is a theoretical method for analyzing vibration systems with damping characteristics. In contrast to real modal theory, it is mainly used to handle non-proportional damped vibration systems, where the phase difference between vibration points is not necessarily zero or 180 degrees, resulting in complex modal coefficients. The core of complex modal theory lies in complex eigenvalues ​​and complex mode shapes. Complex eigenvalues ​​contain real and imaginary parts; the real part represents damping, and the imaginary part represents the angular frequency. If the real part is negative, it indicates that the mode is stable; if the real part is positive, it indicates that the mode is unstable. Complex mode shapes represent the conjugate of complex modal parameters and are used to derive response calculation formulas. Applications of complex modal theory include stability analysis of damped structures and random vibration analysis. For example, in the field of random vibration, complex modal theory can be used to analyze stationary random responses and study the statistical characteristics of random responses through time-domain analysis methods.

[0085] like Figure 3 As shown, Figure 3 This is a schematic diagram of the modeling of a suspension bridge-damper system in one embodiment of the present invention.

[0086] Taking a suspension bridge-damper composite vibration reduction system as an example, the simplified model is a tensioned string subjected to two lateral forces. Here, T, L, and m represent the common tension, length, and mass per unit length of the suspension cable and the main beam, respectively. Ignoring the common sag, bending stiffness, and inherent damping, the differential equation for the system's free vibration is expressed as:

[0087]

[0088] In the formula: y(x,t) is the lateral displacement of the cable; δ(·) represents the Dirac function; F j It means located at x = x j Lateral force at the location.

[0089] The differential equations for free vibration of the above system should satisfy the boundary conditions, i.e., y(0,t)=y(l,t)=0; the force equilibrium condition should be satisfied at the installation location of the damper.

[0090]

[0091] like Figure 4 As shown, Figure 4 This is a schematic diagram of the analytical model of the tower-beam damper-tuned mass damper coupling system in one embodiment of the present invention.

[0092] In the tower-beam damper-tuned mass damper coupled system, k ns and c nsLet m represent the stiffness coefficient and damping coefficient of the tower-beam damper (specifically, a viscous damper, or VD damper). An equivalent linearly tuned mass damper (TMD damper) is used for modeling, where m... dp ω dp and ζ dp Let represent the total tuning mass, angular frequency, and modal damping ratio, respectively. The lateral force amplitudes of the VD damper and TMD damper can be expressed as:

[0093] F1=(k ns +iωc ns )U(x),F2=(k d +iω dp ξ dp )U(x);

[0094] In the formula: U(x) is the mode shape function of the cable; F j denoted by j, the amplitude of the j-th transverse force; n is the complex characteristic frequency of the n-th mode of the coupled system. This represents the normalized dynamic stiffness of the damper. Substituting the lateral force amplitudes of the VD and TMD dampers into the aforementioned differential equation for free vibration of the system, we obtain:

[0095]

[0096] In the formula: The nth mode complex wave number represents the coupled system of tower-beam damper-tuned mass damper.

[0097] The solution to the above equation can be expressed as:

[0098]

[0099] This allows us to establish the characteristic equations for various types of tower-beam damper-tuned mass damper coupled systems. From this, we can obtain the tangent expression, i.e., the expression for the characteristic equation:

[0100]

[0101] The solution can be simplified by using Newton's iteration method or by approximating the independent variable based on the assumptions.

[0102] Then, based on the relationship between the complex eigenvalue frequency and the modal damping ratio of the tower-beam damper-tuned mass damper coupled system, the modal damping ratio is calculated.

[0103] For example, the modal frequency ω of each order n And modal damping ratio ξ n The relationship can be expressed as:

[0104]

[0105] It can be expressed as an expression for the complex mode frequency, or as a relation about the complex mode wavenumber.

[0106] Finally, based on the parameters and installation positions of the tower-beam damper and the tuned mass damper, as well as the relationship, the damping ratio provided by different dampers for different frequencies and vibration modes in the tower-beam damper-tuned mass damper coupling system is calculated.

[0107] While tower-beam dampers (such as viscous dampers) offer less effective vibration reduction than tuned mass dampers, they have a broad spectrum of effectiveness, providing damping for most modes. To achieve better vibration reduction while considering economic efficiency, tuned mass dampers are used to optimize and enhance the vibration reduction effect of each mode, building upon the viscous damper approach. The mass ratio of the tuned mass damper can be adjusted based on the effectiveness of the viscous damper. Based on the actual main beam boundary conditions and the installation positions of the tower-beam dampers and tuned mass dampers, single-mode damping effect calculations are performed on the tower-beam damper-tuned mass damper coupled system. Then, according to the structural target vibration reduction design requirements, multi-mode damping effect calculations are performed on the tower-beam damper-tuned mass damper coupled system.

[0108] In one embodiment, step S3, determining the coordinated control scheme of the tower-beam damper and the tuned mass damper for the multimodal vibration of the main beam based on the target vibration reduction design requirements, further includes:

[0109] Step S36: Adjust the parameters and installation positions of the tower beam damper and the tuned inertial mass damper, and calculate the target control satisfaction.

[0110] In one embodiment, step S36, calculating the target control satisfaction includes:

[0111] Define the satisfaction function of the tower-beam damper-tuned mass damper coupled system.

[0112] The expression for the satisfaction function is:

[0113] In the formula, w k These are the weighting coefficients determined based on the damping ratios of each mode. , where is the logarithmic decay rate threshold determined based on the damping ratio of each mode, and p is the confidence index;

[0114] The satisfaction level of the tower-beam damper-tuned mass damper coupled system under different operating conditions is calculated based on the satisfaction function.

[0115] Since different frequency vibration modes have varying sensitivities to wind speed, some modes are prone to vortex-induced vibration and require special consideration. The additional damping ratio should be increased accordingly, with different weights indicating different tendencies. The above scheme provides a performance evaluation method to facilitate the selection of parameter combinations for each damper.

[0116] This application also provides a multimodal collaborative damping vibration reduction system for the main girder of a long-span bridge, comprising:

[0117] The main girder determination module is used to determine the type of main girder and its corresponding structural characteristics for long-span bridges.

[0118] The target design module is used to determine the target vibration reduction design requirements based on the main beam type. The target vibration reduction design requirements include the frequency range of vortex-induced vibration under different wind attack angles, the minimum damping ratio corresponding to each frequency under the vertical mode mode, and the minimum damping ratio corresponding to each frequency under the torsional mode mode.

[0119] The collaborative control module is used to determine the collaborative control scheme for the multimodal vibration of the main beam by the tower-beam dampers and tuned mass dampers installed on long-span bridges, based on the target vibration reduction design requirements.

[0120] The functions of each module correspond to the steps in the method. The method has been explained in detail above and will not be repeated here.

[0121] Two specific examples are provided below to further illustrate cross-cooperative and complementary cooperative control schemes. Other details have been simplified.

[0122] The target control requirements for the main beam of a certain bridge require a control damping ratio of more than 1% for each frequency, as shown in Table 1.

[0123] Table 1

[0124] Mode shape First-order vertical bend Second-order vertical bend Third-order vertical bend Fourth-order vertical bend First-order torsion Second-order torsion Frequency (Hz) 0.118 0.157 0.227 0.286 0.315 0.412

[0125] If a complementary and coordinated control scheme is adopted, the control method is shown in Table 2.

[0126] Table 2

[0127]

[0128] If a cross-cooperative control scheme is adopted, the control method is shown in Table 3.

[0129] Table 3

[0130]

[0131] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application 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 application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" 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; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0132] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0133] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0134] The above are merely specific embodiments of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A multi-modal collaborative damping vibration reduction method for the main girder of a long-span bridge, characterized in that, Includes the following steps: Determine the type of main girder and its corresponding structural characteristics for long-span bridges; The target vibration reduction design requirements are determined based on the main beam type. The target vibration reduction design requirements include the frequency range of vortex-induced vibration under different wind attack angles, the minimum damping ratio corresponding to each frequency under the vertical mode mode, and the minimum damping ratio corresponding to each frequency under the torsional mode mode. Based on the target vibration reduction design requirements, a collaborative control scheme for the multimodal vibration of the main beam using tower-beam dampers and tuned mass dampers installed on the long-span bridge is determined. The coordinated control scheme includes: Establish a tower-beam damper-tuned mass damper coupling system, determine the positions of the tower-beam damper and the tuned mass damper according to the target vibration reduction design requirements, and calculate the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes. The damping ratio of each frequency under the vertical and torsional modes is controlled by the tower-beam damper. When the damping ratio at certain frequencies does not meet the target vibration reduction design requirements, the tuned mass damper is used in a cross-coordinated manner to control the damping ratio corresponding to that frequency. Alternatively, the cooperative control scheme may include: Establish a tower-beam damper-tuned mass damper coupling system, determine the positions of the tower-beam damper and the tuned mass damper according to the target vibration reduction design requirements, and calculate the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes. The damping ratio of the lower frequencies of the vertical and torsional modes is controlled by the tower-beam damper to achieve the target vibration reduction design requirements. The tuned mass dampers are used in a complementary and coordinated manner to control the damping ratio of the residual frequency under the residual vibration mode, so as to achieve the target vibration reduction design requirements.

2. The multi-modal collaborative damping vibration reduction method for the main girder of a long-span bridge as described in claim 1, characterized in that, Determining the positions of the tower-beam damper and the tuned mass damper based on the target vibration reduction design requirements includes: According to the target vibration reduction design requirements, the tower-beam damper is installed between the main beam of the bridge and the bridge pier tower. One end of the damper is connected to the bridge pier tower, and the other end is connected to the main beam of the bridge through a cantilever lever structure, so that the connection point between the tower-beam damper and the main beam of the bridge is close to the mid-span of the main beam of the bridge. According to the target vibration reduction design requirements, the tuned mass damper is installed on the main beam of the bridge.

3. The multi-modal collaborative damping vibration reduction method for the main girder of a long-span bridge as described in claim 1, characterized in that, The calculation of the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes includes: The characteristic equations are established based on the tower-beam damper-tuned mass damper coupled system. Solving the characteristic equation yields the relationship between different frequencies, different mode shapes, and damping ratios; Based on the parameters and installation positions of the tower-beam damper and the tuned mass damper, as well as the aforementioned relationship, calculate the damping ratio provided by different dampers for different frequencies and vibration modes in the tower-beam damper-tuned mass damper coupling system.

4. The multi-modal collaborative damping vibration reduction method for the main girder of a long-span bridge as described in claim 1, characterized in that, The coordinated control scheme for the multimodal vibration of the main beam by the tower-beam damper and the tuned mass damper, determined according to the target vibration reduction design requirements, also includes: Adjust the parameters and installation positions of the tower-beam damper and the tuned inertial mass damper, and calculate the target control satisfaction.

5. The multi-modal collaborative damping vibration reduction method for the main girder of a long-span bridge as described in claim 4, characterized in that, The calculated target control satisfaction includes: Define the satisfaction function of the tower-beam damper-tuned mass damper coupled system. The expression for the satisfaction function is: ; In the formula, These are the weighting coefficients determined based on the damping ratios of each mode. The threshold for logarithmic decay rate is determined based on the damping ratio of each mode. p As a confidence index; The satisfaction level of the tower-beam damper-tuned mass damper coupled system under different operating conditions is calculated based on the satisfaction function.

6. The multi-modal collaborative damping vibration reduction method for the main girder of a long-span bridge as described in claim 1, characterized in that, The tower beam damper includes an oil damper, a viscous damper, an eddy current damper, or an outrigger lever-type inertial mass damper.

7. The multi-modal collaborative damping vibration reduction method for the main girder of a long-span bridge as described in claim 1, characterized in that, The tuned mass damper is a multi-type tuned mass damper, a distributed tuned mass damper, or an inertial mass tuned damper.

8. A multi-modal collaborative damping vibration reduction system for the main girder of a long-span bridge, characterized in that, It includes: The main girder determination module is used to determine the type of main girder and its corresponding structural characteristics for long-span bridges. The target design module is used to determine the target vibration reduction design requirements based on the main beam type. The target vibration reduction design requirements include the frequency range of vortex-induced vibration under different wind attack angles, the minimum damping ratio corresponding to each frequency under the vertical mode mode, and the minimum damping ratio corresponding to each frequency under the torsional mode mode. The collaborative control module is used to determine the collaborative control scheme of the tower-beam dampers and tuned mass dampers installed on the long-span bridge for the multimodal vibration of the main beam, based on the target vibration reduction design requirements. The coordinated control scheme includes: Establish a tower-beam damper-tuned mass damper coupling system, determine the positions of the tower-beam damper and the tuned mass damper according to the target vibration reduction design requirements, and calculate the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes. The damping ratio of each frequency under the vertical and torsional modes is controlled by the tower-beam damper. When the damping ratio at certain frequencies does not meet the target vibration reduction design requirements, the tuned mass damper is used in a cross-coordinated manner to control the damping ratio corresponding to that frequency. Alternatively, the cooperative control scheme may include: Establish a tower-beam damper-tuned mass damper coupling system, determine the positions of the tower-beam damper and the tuned mass damper according to the target vibration reduction design requirements, and calculate the damping ratio provided by the tower-beam damper and the tuned mass damper for different frequencies and vibration modes. The damping ratio of the lower frequencies of the vertical and torsional modes is controlled by the tower-beam damper to achieve the target vibration reduction design requirements. The tuned mass dampers are used in a complementary and coordinated manner to control the damping ratio of the residual frequency under the residual vibration mode, so as to achieve the target vibration reduction design requirements.

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