Bridge multi-mode vibration control method and system

Abstract

The invention relates to a bridge multi-mode vibration control method and system, and the method comprises the steps: building a suspension bridge space finite element model, and recognizing a key vertical bending mode of a bridge and the frequency and vibration mode of the key vertical bending mode through modal analysis; determining a main beam vibration mode displacement peak value position based on the vibration mode, applying a simple harmonic load consistent with the modal frequency to the main beam vibration mode displacement peak value position, and determining a first speed section damping parameter; selecting seismic waves meeting bridge site conditions as input excitation, and determining a second speed section parameter through nonlinear time-history analysis; and the first speed section parameter and the second speed section parameter are integrally arranged in the longitudinal damper, and the use parameter of the longitudinal damper is switched between the first speed section damping parameter and the second speed section parameter based on the relative speed of the two ends of the longitudinal damper. The single damper can adapt to the vibration characteristics of two working conditions at the same time, and special devices do not need to be installed for vibration in different directions.

Description

Technical Field

[0001] This application relates to the field of bridge vibration reduction design, specifically to a method and system for controlling multimodal vibration of bridges. Background Technology

[0002] Long-span suspension bridges, as key nodes in modern transportation infrastructure, are highly sensitive to dynamic loads such as wind, earthquakes, and vehicles due to their large spans and flexible structures. Traditional bridge dynamic response analysis and control often treat longitudinal (longitudinal) and vertical vibrations separately, forming relatively independent research and practice systems.

[0003] In fact, long-span suspension bridges are highly susceptible to vertical multimodal vibrations (such as vortex-induced vibration and buffeting) under wind loads, including antisymmetric and symmetrical vertical bending. These vertical vibrations not only affect the comfort and safety of driving, but also lead to structural fatigue over time, threatening the long-term service performance and lifespan of the bridge.

[0004] Current mainstream solutions separate longitudinal vibration control from vertical vibration control: longitudinal vibration requires a dedicated longitudinal damper, while vertical vibration relies on devices such as a vertical tuned mass damper (TMD), resulting in the need to install two independent vibration reduction devices, which significantly increases construction costs and the complexity of subsequent maintenance. Summary of the Invention

[0005] This application provides a method and system for multimodal vibration control of bridges, which can solve the problem that the vertical and longitudinal vibration control of long-span suspension bridges has long relied on two independent devices, resulting in complex systems and poor economic efficiency.

[0006] In a first aspect, embodiments of this application provide a method for controlling multimodal vibration of a bridge, comprising: A spatial finite element model of the suspension bridge was established, and the key vertical bending modes of the bridge, as well as the frequencies and mode shapes of the key vertical bending modes, were identified through modal analysis. Based on the vibration mode, the peak position of the main beam vibration mode displacement is determined, and a simple harmonic load with the same frequency as the mode is applied at the peak position of the main beam vibration mode displacement to determine the damping parameters of the first velocity segment. Seismic waves that meet the site conditions of the bridge are selected as input excitation, and the parameters of the second velocity segment are determined through nonlinear time history analysis. The first speed segment parameter and the second speed segment parameter are integrated into the longitudinal damper, and the operating parameters of the longitudinal damper are switched between the first speed segment damping parameter and the second speed segment parameter based on the relative velocity at both ends of the longitudinal damper.

[0007] In conjunction with the first aspect, in one implementation, a spatial finite element model of the suspension bridge is established, and key vertical bending modes of the bridge, as well as the frequencies and mode shapes of the key vertical bending modes, are identified through modal analysis. Specifically, this includes: A spatial finite element model of a suspension bridge was established, and the dominant vertical vibration modes of the bridge were identified through modal analysis. The vertical bending modes within the wind-sensitive frequency band are identified as the key vertical bending modes; Determine the frequency and mode shape of each key vertical bending mode.

[0008] In conjunction with the first aspect, in one implementation, the operating parameters of the longitudinal damper are switched between first-speed damping parameters and second-speed damping parameters based on the relative velocities at both ends of the longitudinal damper, specifically including: The first speed range parameter is used when the relative velocity between the two ends of the longitudinal damper is within the first threshold range. The second speed range parameter is used when the relative velocity between the two ends of the longitudinal damper is within the second threshold range.

[0009] In conjunction with the first aspect, in one embodiment, a simple harmonic load with the same modal frequency is applied at the peak position of the main beam's vibration mode displacement to determine the damping parameters of the first velocity segment, specifically including: A simple harmonic load with the same modal frequency is applied at the peak position of the main beam vibration mode displacement, and the time history data of the structural displacement are obtained. The additional damping ratio of the vertical bending mode is calculated using the structural displacement time history data, and the optimal damping coefficient is determined. Under the condition that the optimal damping coefficient remains unchanged, the speed index of the longitudinal damper is changed to determine the optimal speed index; The optimal damping coefficient and optimal velocity index are used as the damping parameters for the first velocity segment so that the damping ratio of the vertical bending mode reaches the target value.

[0010] In conjunction with the first aspect, in one implementation, the additional damping ratio of the vertical bending mode is calculated using the structural displacement time history data, and the optimal damping coefficient is determined, specifically including: Based on the structural displacement time history data, the additional damping ratio of the vertical bending mode corresponding to multiple different damping coefficients is calculated, and the relationship curve between the additional damping ratio of the vertical bending mode and the damping coefficient is determined. Determine the damping coefficient corresponding to the maximum additional damping ratio of the vertical bending mode from the aforementioned relationship curve; This damping coefficient is taken as the optimal damping coefficient.

[0011] In conjunction with the first aspect, in one implementation, under the condition that the optimal damping coefficient remains unchanged, the velocity index of the longitudinal damper is changed to determine the optimal velocity index, specifically including: Under the condition that the optimal damping coefficient remains unchanged, the velocity index of the longitudinal damper is changed; Based on the structural displacement time history data, the additional damping ratio of the vertical bending mode corresponding to different velocity indices is calculated, and the relationship curve between the additional damping ratio of the vertical bending mode and the velocity index is determined. Determine the velocity index corresponding to the maximum additional damping ratio of the vertical bending mode from the aforementioned relationship curve; This speed index is taken as the optimal speed index.

[0012] In conjunction with the first aspect, in one implementation method, a seismic wave that meets the site conditions of the bridge location is selected as the input excitation, and the parameters of the second velocity segment are determined through nonlinear time history analysis, specifically including: Seismic waves that meet the site conditions of the bridge were selected as the input excitation for nonlinear time history analysis. Based on the nonlinear time history analysis results, the damping coefficient and velocity index that satisfy the constraints of maximum relative displacement between the tower and beam, internal forces of the structure, and output force of the damper are determined. The damping coefficient and speed index are used as parameters for the second speed range.

[0013] In conjunction with the first aspect, in one embodiment, the method further includes: The additional damping ratio contribution of the longitudinal damper to the vertical bending mode of the bridge target was obtained by using a steady-state excitation test method.

[0014] In conjunction with the first aspect, in one implementation method, a steady-state excitation test method is used to obtain the additional damping ratio contribution of the longitudinal damper to the target vertical bending mode of the bridge, specifically including: By applying harmonic excitation at the target vertical bending mode resonance frequency, the inherent damping ratio of the uncontrolled state is obtained. Install longitudinal dampers on the bridge to obtain the controlled state damping ratio; Based on the inherent damping ratio in the uncontrolled state and the damping ratio in the controlled state, the additional damping ratio increment and the damping effect improvement rate are calculated to obtain the additional damping ratio contribution of the longitudinal damper to the target vertical bending mode of the bridge.

[0015] Secondly, embodiments of this application provide a bridge multimodal vibration control system, comprising: a first module, a second module, a third module, and a fourth module. The first module is used to: establish a spatial finite element model of the suspension bridge and identify the key vertical bending modes of the bridge, as well as the frequencies and mode shapes of the key vertical bending modes, through modal analysis. The second module is used to: determine the peak displacement position of the main beam mode shape based on the mode shape, and apply a harmonic load consistent with the mode frequency at the peak displacement position of the main beam mode shape to determine the first velocity segment damping parameters. The third module is used to: select seismic waves that meet the site conditions of the bridge as input excitation and determine the second velocity segment parameters through nonlinear time history analysis. The fourth module is used to: integrate the first and second velocity segment parameters into a longitudinal damper, and switch the operating parameters of the longitudinal damper between the first and second velocity segment parameters based on the relative velocity at both ends of the longitudinal damper. The beneficial effects of the technical solutions provided in this application include: This application provides a method and system for controlling multimodal vibration of a bridge. By establishing a spatial finite element model of the suspension bridge and identifying key vertical bending modes and their frequency modes, the damper parameters are optimized based on actual vibration characteristics rather than empirical formulas, thus ensuring accurate matching between the longitudinal damper and the bridge's vibration characteristics. A harmonic load consistent with the target mode frequency is applied at the peak displacement position of the main beam mode shape, achieving efficient energy transfer at the mode shape peak. This ensures that the calculated additional damping ratio of the vertical bending mode truly reflects the damper's control capability over the target mode. The separate design of the first and second velocity parameters allows the longitudinal damper to be specifically optimized for wind-induced vibration (medium-to-low speed vibration) and earthquake vibration (high-speed vibration), avoiding the inaccurate control effect caused by parameter mixing in traditional schemes. Integrating the first and second velocity parameters into the longitudinal damper and automatically switching them by relative velocity allows a single damper to adapt to the vibration characteristics of both working conditions simultaneously, eliminating the need for separate dedicated devices for vibrations in different directions. This significantly simplifies the structural system while ensuring control effectiveness, reducing construction costs and maintenance complexity. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the bridge multimodal vibration control method of this application. Detailed Implementation

[0017] 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.

[0018] This application provides a method and system for multimodal vibration control of bridges, which can solve the problem that the vertical and longitudinal vibration control of long-span suspension bridges has long relied on two independent devices, resulting in complex systems and poor economic efficiency.

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0020] In a first aspect, embodiments of this application provide a method for controlling multimodal vibration of a bridge, comprising: 101: Establish a spatial finite element model of the suspension bridge, and identify the key vertical bending modes of the bridge, as well as the frequencies and mode shapes of the key vertical bending modes, through modal analysis; 102: Determine the peak position of the main beam's mode displacement based on the mode shape, and apply a simple harmonic load with the same frequency as the mode at the peak position of the main beam's mode displacement to determine the damping parameters of the first velocity segment; 103: Select seismic waves that meet the site conditions of the bridge site as input excitation, and determine the parameters of the second velocity segment through nonlinear time history analysis; 104: Integrate the first speed segment parameter and the second speed segment parameter into the longitudinal damper, and switch the operating parameters of the longitudinal damper between the first speed segment damping parameter and the second speed segment parameter based on the relative velocity at both ends of the longitudinal damper.

[0021] In this application, by establishing a spatial finite element model of the suspension bridge and identifying key vertical bending modes and their frequency modes, the damper parameter optimization is based on actual vibration characteristics rather than empirical formulas, thus ensuring accurate matching between the longitudinal damper and the bridge's vibration characteristics. Applying a simple harmonic load consistent with the target mode frequency at the peak displacement position of the main beam mode shape achieves efficient energy transfer at the mode shape peak, ensuring that the calculated result of the additional damping ratio of the vertical bending mode truly reflects the longitudinal damper's control capability over the target mode. The separate design of the first and second velocity parameters allows the longitudinal damper to be specifically optimized for wind-induced vibration (medium-to-low speed vibration) and earthquake vibration (high-speed vibration), avoiding the inaccurate control effect caused by parameter mixing in traditional schemes. Integrating the first and second velocity parameters into the longitudinal damper and automatically switching them by relative velocity allows a single damper to adapt to the vibration characteristics of both working conditions simultaneously, eliminating the need for separate dedicated devices for vibrations in different directions. This significantly simplifies the structural system while ensuring control effectiveness, reducing construction costs and maintenance complexity.

[0022] It should be noted that the parameters for the first speed range are for the low-to-medium speed range; the parameters for the second speed range are for the high-speed range.

[0023] In the damper parameter design of this application, the first velocity range parameters specifically refer to the damping coefficient C1 and velocity index α1 in the low-to-medium velocity range. This parameter combination is used to optimize the control of vertical multimodal vibrations (such as vortex-induced vibration and buffeting under wind load), and its effective velocity range covers the typical vibration velocities of bridges under wind-induced vibration conditions. The second velocity range parameters specifically refer to the damping coefficient C2 and velocity index α2 in the high-velocity range. This parameter combination is used to optimize vibration control under seismic loading, and its effective velocity range covers the high-velocity conditions caused by seismic loading. The seismic performance is verified through nonlinear time history analysis to ensure that the longitudinal damper provides sufficient energy dissipation capacity under seismic impact.

[0024] Based on the above embodiments, in this embodiment, a spatial finite element model of the suspension bridge is established, and the key vertical bending modes of the bridge, as well as the frequencies and mode shapes of the key vertical bending modes, are identified through modal analysis. Specifically, this includes: first, establishing a spatial finite element model of the suspension bridge and identifying the dominant vertical vibration modes of the bridge through modal analysis; then, determining the vertical bending modes in the wind-sensitive frequency band as key vertical bending modes; and finally, determining the frequencies and mode shapes of each key vertical bending mode.

[0025] In the implementation of this application, the spatial finite element model of the suspension bridge is also called the refined spatial finite element model of the suspension bridge. Its establishment is a core foundational step. The model includes the main structure such as the main beam, main cable, suspension cable, and bridge tower, as well as reasonable boundary conditions (such as bridge tower foundation constraints and anchorage connections) to ensure that the longitudinal and vertical dynamic response characteristics of the bridge under wind load and seismic action can be accurately simulated.

[0026] After extracting all vibration modes through modal analysis, the system first selects the vertical bending mode.

[0027] Subsequently, based on the bridge design parameters and wind vibration characteristics, the wind-sensitive frequency band (i.e. the frequency range in which the bridge is prone to resonance under typical wind speeds, usually covering the vertical natural frequency range of the bridge) was determined, and the vertical bending modes in this frequency band were listed as key modes, such as the first-order symmetrical vertical bending mode (the bridge deck vibrates symmetrically from top to bottom, and the mode shape shows that the displacement at the midpoint is the largest and the two ends are close to zero) and the first-order antisymmetric vertical bending mode (the bridge deck bends asymmetrically from left to right, and the mode shape shows that the bridge deck has opposite displacements on the left and right sides).

[0028] For each key mode, its frequency value and mode shape characteristics are recorded. The mode shape describes the deformation pattern and displacement distribution law of the structure during vibration. For example, the peak displacement of the symmetrical vertical bending mode is located at the mid-span of the bridge deck, while the peak displacement of the antisymmetric vertical bending mode usually appears in the regions on both sides of the bridge deck. These data are directly used to apply vertical harmonic loads at the peak displacement of the mode shape to optimize the damping parameters, ensuring that the damper can act on the key points of vibration energy dissipation, and providing a reliable input basis for the quantitative evaluation of vibration reduction effect.

[0029] Based on the above embodiments, in this embodiment, a simple harmonic load with the same modal frequency is applied at the peak position of the main beam vibration mode displacement to determine the damping parameters of the first speed range, specifically including steps 1021 to 1023. In the process of determining the damping parameters of the medium and low speed range in this application, the target value of the vertical bending mode damping ratio is first set according to the actual engineering requirements of bridge wind vibration control. This target value is based on the limit requirements of vertical vibration amplitude in bridge design specifications to ensure that under typical wind speed, it can effectively suppress multimodal vertical vibrations such as vortex-induced vibration and buffeting, and avoid structural fatigue or driving comfort problems caused by excessive vibration amplitude. In the constructed refined spatial finite element model of the suspension bridge, the constitutive relationship of the longitudinal damper is parameterized by introducing longitudinal viscous damper elements. The damping coefficient C1 and velocity index α1 are used as core design variables to describe the nonlinear relationship between the longitudinal damping force and the longitudinal motion velocity at the beam end. This parameterized model can accurately reflect the dynamic response characteristics of the longitudinal damper under wind vibration conditions.

[0030] Based on bridge engineering experience, the initial damping coefficient C10 and initial velocity index α10 were set with reference to the typical parameter range of similar bridges, avoiding the blind selection of parameters. The time-domain decay method was used to process the structural displacement time history data to calculate the additional damping ratio of the vertical bending mode under different parameter combinations. This method can directly quantify the energy dissipation efficiency of the longitudinal damper. Subsequently, the influence of changes in C1 and α1 on the damping ratio was evaluated through parameter sensitivity analysis. Finally, the optimal combination that maximizes the target vertical modal damping ratio was determined within a reasonable parameter range using an optimization search algorithm. This ensures that the longitudinal damper achieves efficient dissipation of vertical vibration energy within the typical wind vibration velocity range, providing a reliable parameter basis for subsequent longitudinal damper installation and vibration reduction effect verification.

[0031] Specifically: Step 1021: Apply a simple harmonic load with the same frequency as the mode at the peak position of the main beam's vibration mode displacement, and obtain the structural displacement time history data; Step 1021 requires applying a simple harmonic load P=Fsin(ωnt) at the peak position of the main beam's mode displacement, which is consistent with the target mode frequency. ωn is the natural frequency of the nth vertical bending mode of the structure, and F is the amplitude of the excitation load. After continuous excitation for a certain period of time, the structure's vibration state stabilizes and enters the steady-state vibration stage. After several cycles of steady-state vibration, the excitation is stopped (F=0), and the structure's vibration decays.

[0032] This operation is based on the principle of vibration energy distribution: the peak displacement region of the vertical bending mode of the bridge (such as the mid-span position of the symmetrical vertical bending mode or both sides of the bridge deck of the antisymmetric vertical bending mode) is the location where the vibration energy is most concentrated. Applying a simple harmonic load that matches the natural frequency of the mode at this location can directly excite the resonance response of the mode, avoid the distortion of mode identification caused by the load position deviation, and thus obtain displacement time history data that reflects the true dynamic characteristics of the structure.

[0033] Step 1022: Calculate the additional damping ratio of the vertical bending mode using the structural displacement time history data, and determine the optimal damping coefficient.

[0034] The calculation of the vertical bending mode additional damping ratio and determination of the optimal damping coefficient using the structural displacement time history data specifically includes: First, based on the structural displacement time history data, the additional damping ratio of the vertical bending mode corresponding to multiple different damping coefficients is calculated, and the relationship curve between the additional damping ratio of the vertical bending mode and the damping coefficient is determined; then, the damping coefficient corresponding to the maximum additional damping ratio of the vertical bending mode is determined from the relationship curve; finally, this damping coefficient is taken as the optimal damping coefficient.

[0035] In the calculation of the additional damping ratio of the vertical bending mode, based on the structural displacement time history data, a continuous wave peak sequence of the free vibration decay segment is first selected, where m represents the interval between adjacent wave peaks, and Ak is the vibration response value of the k-th wave peak in the vibration decay segment; using the formula: ; The logarithmic decay rate δn of the nth vertical bending mode is calculated. This formula originates from the physical characteristic of exponential amplitude decay in vibration theory, and can accurately reflect the dissipation rate of vibration energy during free decay. Then, the formula is used: The logarithmic decay rate is converted into a damping ratio, where ξn represents the damping ratio of the nth vertical bending mode. This value directly characterizes the additional energy dissipation efficiency of the damper for vertical vibrations; a larger value indicates a stronger ability to dissipate vibration energy.

[0036] With the initial velocity index α10 fixed, the range of damping coefficient C1 is systematically adjusted, and the corresponding additional damping ratio ξn for each C1 value is repeatedly calculated to obtain multiple sets of corresponding data for C1 and ξn. Using these multiple sets of analytical data, C1-ξn relationship curves for multiple target vertical bending modes are plotted. Based on the target requirements for additional damping ratios for multiple target vertical bending modes, the C1 value that satisfies the vibration control requirements of multiple vertical bending modes is selected as the optimal damping coefficient. At this point, the longitudinal damper has the optimal energy dissipation efficiency for multiple target vertical vibration modes, effectively suppressing the amplitude increase of multi-mode vertical vibrations such as vortex-induced vibration and buffeting. This parameter determination method avoids trial and error, ensuring that the damper accurately matches the control requirements of bridge vertical vibration under wind-induced vibration conditions, providing a reliable basis for the subsequent quantitative evaluation of vibration reduction effects.

[0037] Step 1023: Under the condition that the optimal damping coefficient remains unchanged, change the velocity index of the longitudinal damper to determine the optimal velocity index; Under the condition that the optimal damping coefficient remains unchanged, the velocity index of the longitudinal damper is changed to determine the optimal velocity index. Specifically, this includes: first, changing the velocity index of the longitudinal damper while keeping the optimal damping coefficient unchanged; then, based on the structural displacement time history data, calculating the additional damping ratio of the vertical bending mode corresponding to different velocity indices, and determining the relationship curve between the additional damping ratio of the vertical bending mode and the velocity index; after completing the analysis of multiple target vertical bending modes, plotting the α1-ξn relationship curves of multiple target vertical bending modes; and, based on the condition that the additional damping ratio of multiple vertical bending modes is not lower than the target value, determining the velocity index corresponding to the maximum or near the peak value of the additional damping ratio of multiple target vertical bending modes from the relationship curves; finally, taking this velocity index as the optimal velocity index.

[0038] After determining the optimal damping coefficient C1, the velocity index α1 of the longitudinal damper is systematically adjusted to further optimize the vibration control effect in the low-to-medium speed range. The velocity index α1 is the core parameter of the nonlinear relationship between damping force and velocity, and its value directly determines the dynamic response characteristics of the damper in the typical wind vibration speed range. Under the condition that C1 remains unchanged, multiple sets of parameter tests are conducted within the commonly used engineering range with α1 as the variable. Finite element analysis is repeatedly performed for each α1 value to obtain the structural displacement time history data at the peak displacement of the main beam mode. Based on this data, the additional damping ratio ξn of the vertical bending mode is calculated using the time-domain decay method. By plotting the relationship curve between α1 and ξn, the curve usually shows a single-peak shape of rising first and then falling. The α1 value corresponding to the peak point is the optimal velocity index of the current vertical bending mode. The same analysis is repeated for multiple target vertical bending modes. On the basis of ensuring that the additional damping ratio of multiple vertical bending modes is not lower than the target value, the velocity index corresponding to the point where the additional damping ratio of multiple target vertical bending modes reaches the maximum or near the peak (not lower than 80% of the peak value) is selected as the optimal velocity index. This optimization process avoids the problem of delayed or excessive damping force response caused by velocity index mismatch, ensuring that the longitudinal damper can accurately adapt to changes in vibration velocity during multimodal vertical vibration of the bridge (such as symmetrical vertical bending and anti-symmetrical vertical bending), thus providing a reliable parameter basis for the subsequent quantitative evaluation of vibration reduction effect.

[0039] Step 1024: Use the optimal damping coefficient and optimal velocity index as the damping parameters for the first speed segment so that the vertical bending mode damping ratio reaches the target value.

[0040] After completing the systematic optimization of the damping parameters in the low-to-medium speed range, the optimal damping coefficient C1 and the optimal velocity index α1 are used as the damping parameters for the first speed range. These parameters ensure that C1 and α1 are automatically activated when the longitudinal motion velocity at the beam end is within the typical low-to-medium speed range of wind-induced vibration. This allows the longitudinal adaptive viscous damper to dynamically adjust the damping force response characteristics according to the actual velocity of the bridge's vertical vibration: when the vibration velocity is low (such as in the initial stage of vortex-induced vibration), the optimized value of C1 enhances the damping force's sensitivity to velocity, improving initial energy dissipation efficiency; when the velocity enters the medium speed range, the optimal value of α1 ensures a continuous and stable output of damping force, avoiding over-damping or under-damping. Through this parameter configuration, the additional damping ratio of the vertical bending mode is increased to the design target value, directly achieving synchronous suppression of multimodal vertical vibrations of the suspension bridge (such as typical modes like the first-order symmetrical vertical bend and the first-order anti-symmetrical vertical bend). This process requires no additional specialized equipment. By precisely matching the damper parameters, it can efficiently dissipate vertical vibration energy under wind-induced vibration conditions, ensuring that the bridge maintains vibration amplitude within safe limits under typical wind speeds. This provides a quantifiable parameter basis for subsequent verification of vibration reduction effects.

[0041] Based on the above embodiments, in this embodiment, a seismic wave that meets the site conditions of the bridge site is selected as the input excitation. The parameters of the second velocity segment are determined through nonlinear time history analysis. Specifically, this includes: first, selecting a seismic wave that meets the site conditions of the bridge site as the input excitation and performing nonlinear time history analysis; then, using the results of the nonlinear time history analysis, determining the damping coefficient and velocity index that satisfy the constraints of the maximum relative displacement between the tower and the beam, the internal force of the structure, and the output force of the damper; and finally, using the damping coefficient and velocity index as the parameters of the second velocity segment.

[0042] Specifically, in determining the parameters for the high-speed section, the core objective is to control the maximum relative displacement between the tower and the beam and the internal forces of the structure under seismic loading. Multiple seismic waves conforming to the site characteristics are selected as input excitations. Through nonlinear time-history analysis, the dynamic response of the bridge under seismic loading is simulated, focusing on quantifying the maximum relative displacement between the tower and the beam, the internal forces in key structural components, and the actual output of the longitudinal adaptive damper under high-speed vibration. The constitutive parameters C2 (damping coefficient) and α2 (velocity index) of the longitudinal damper in the high-speed section are set as design variables and systematically adjusted within commonly used engineering ranges. Response indices for each combination are calculated through parameter scanning analysis. For example, increasing C2 can improve the damping force to suppress displacement, but may exacerbate the internal forces of the structure; adjusting α2 optimizes the adaptability of the damping force to velocity, allowing the longitudinal damper to more accurately match the energy dissipation requirements under high-speed vibration. Finally, the optimal parameter combination that simultaneously satisfies three constraints is selected: the relative displacement between the tower and the beam does not exceed the safety threshold, the internal forces of the structure do not exceed the design limits, and the damper output is within the elastic range.

[0043] Based on the above embodiments, in this embodiment, in step 104, the first speed segment parameter and the second speed segment parameter are integrated into the longitudinal damper, and the first speed segment parameter (C1, α1) and the second speed segment parameter (C2, α2) are integrated into the variable parameter constitutive model of the same longitudinal damper.

[0044] The system sets the first speed range parameter to be used when the relative velocity between the two ends of the longitudinal damper is within the first threshold range, and the second speed range parameter to be used when the relative velocity between the two ends of the longitudinal damper is within the second threshold range.

[0045] This setting enables seamless switching control between wind-induced vibration and seismic conditions. Based on real-time detection of the longitudinal motion velocity at the beam end, the damping characteristics are dynamically adjusted: when the velocity is in the low-to-medium speed range, that is, when the relative motion velocity between the two ends of the longitudinal damper is v∈[Vmin, Vmax], the first speed segment parameter (C1, α1) is automatically activated, making the damping force nonlinear with the velocity (such as the optimized value of α1 enhancing the low-speed segment response), efficiently dissipating vertical vibration energy; when the velocity exceeds the threshold Vmax and enters the high-speed range, it seamlessly switches to the second speed segment parameter (C2, α2), by increasing the damping coefficient C2 and adjusting the velocity exponent α2, providing a continuous and stable high damping force to suppress the displacement between the tower and the beam and the internal forces of the structure. This integrated mechanism avoids the complexity of installing additional tuned mass dampers for vertical vibration in traditional solutions, ensuring that the longitudinal damper meets the requirements of wind-induced multimodal control and seismic resistance in a single device. Its parameter switching logic is entirely based on the physical characteristics of vibration velocity, requiring no external intervention and is directly implemented through the internal algorithm of the longitudinal damper, providing a simple and reliable engineering solution for vibration control of suspension bridges under all working conditions.

[0046] After integrating the variable-parameter constitutive model of the longitudinal adaptive damper, the bridge was systematically verified by re-performing wind-induced vibration analysis and nonlinear seismic time history analysis to validate the effectiveness of the integrated parameters under actual working conditions. By comparing and analyzing the vibration response data before and after integration, it was ensured that the bridge simultaneously meets the requirements for vertical vibration suppression and seismic control under all working conditions, providing a reliable technical verification basis for engineering applications.

[0047] Based on the above embodiments, in this embodiment, the method further includes: using a steady-state excitation test method to obtain the additional damping ratio contribution of the longitudinal damper to the vertical bending mode of the bridge target.

[0048] The method employed is a steady-state excitation test to obtain the additional damping ratio contribution of the longitudinal damper to the target vertical bending mode of the bridge. Specifically, this involves: first, applying harmonic excitation at the resonant frequency of the target vertical bending mode to obtain the uncontrolled inherent damping ratio; then, installing the longitudinal damper on the bridge to obtain the controlled damping ratio; and finally, calculating the additional damping ratio increment and damping effect improvement rate based on the uncontrolled inherent damping ratio and the controlled damping ratio to obtain the additional damping ratio contribution of the longitudinal damper to the target vertical bending mode of the bridge.

[0049] The application also requires a vibration reduction effect assessment. In this assessment, a steady-state excitation test method is used as the core verification tool. By controlling the excitation conditions and response measurements, the additional damping ratio contribution of the longitudinal adaptive viscous damper to the target vertical bending mode of the suspension bridge is directly quantified, ensuring the objectivity and reliability of the assessment results.

[0050] In practice, an uncontrolled state test is first conducted before the dampers are installed: a vertical acceleration sensor array is deployed in the peak displacement region of the key vibration modes of the bridge main girder. This arrangement strictly matches the vibration mode characteristics of the target mode, ensuring that the sensors can capture the modal vibration energy distribution. One or more vertical harmonic excitations are applied to the bridge deck using one or more exciters, and a systematic frequency scan is performed to locate the resonant frequency fn1 of the target mode. Steady-state excitation is maintained at the resonant frequency, exciting the bridge structure to gradually enter and remain stable in a high signal-to-noise ratio steady-state resonance state under the target mode. After the structural vibration stabilizes for several cycles, the excitation is stopped, and the vibration response time history of the free decay segment is recorded. To eliminate random test errors, at least three independent tests are performed for each excitation condition, and the average value is used to calculate the inherent damping ratio ξn1 of the uncontrolled state. This process is based on the principle of logarithmic decay, extracting a continuous wave peak sequence from the decay curve, and calculating the inherent damping ratio ξn1 of the target mode in the uncontrolled state with high precision.

[0051] Subsequently, after installing the longitudinal adaptive viscous damper between the tower and the beam, the sensor arrangement, exciter position, and excitation force were kept consistent with those before installation. The frequency scan was then performed again. (Because the damper increases the system damping, the measured resonant frequency fn2 of the vertical bending mode may change slightly at this time. Steady-state excitation and free decay records were repeated at the new resonant frequency fn2. At least three tests were performed, and the damping ratio ξn2 after installation was calculated using the same data processing method.)

[0052] Finally, the damping ratio increment was calculated. ξn=ξn2-ξn1 and the lifting rate ηn=( The method ξn / ξn1)×100% directly quantifies the additional damping contribution of the damper to the vertical bending mode. This method avoids the measurement distortion of the damping ratio caused by multi-mode coupling in traditional modal analysis, ensuring clear and unambiguous test results. At the same time, through the comprehensive ηn analysis of multi-mode (such as symmetrical vertical bending and anti-symmetrical vertical bending), the synergistic suppression effect of the damper on vertical multi-mode vibration under wind conditions is comprehensively evaluated.

[0053] This application, through the innovative application of a longitudinal adaptive viscous damper, achieves for the first time cross-dimensional synchronous control of longitudinal vibration and vertical multimodal vibration of a suspension bridge, changing the traditional design paradigm of requiring independent devices (such as longitudinal dampers and vertical tuned mass dampers) for vibrations in different directions in bridge vibration control. Its core mechanism stems from the dynamic coupling characteristics of the bridge structure: under wind loads, vertical multimodal vibrations of the suspension bridge (such as vortex-induced vibration and buffeting) naturally induce longitudinal displacement components at the beam ends. The longitudinal adaptive viscous damper dynamically adjusts the damping force response characteristics by monitoring the longitudinal velocity at the beam ends in real time, enabling the damper to suppress longitudinal displacement while simultaneously dissipating vertical vibration energy. This design avoids the complexity of adding additional tuned mass dampers (TMDs) for vertical vibration in traditional schemes, directly reducing the number of damper installation points, connecting components, and supporting control systems in the bridge structure. This significantly simplifies the overall structural system, reduces material and installation costs during bridge construction, and reduces the frequency of inspections, replacement difficulty, and calibration complexity caused by multiple devices during later maintenance.

[0054] This application addresses the industry pain points of long-span suspension bridges, which have long relied on two independent devices (such as longitudinal dampers and vertical tuned mass dampers) for vertical and longitudinal vibration control, resulting in complex systems, high construction costs, and difficult maintenance. It proposes a "dual-purpose" vibration reduction technology based on a longitudinal adaptive viscous damper, achieving cross-dimensional vibration control through the bridge structure dynamics coupling mechanism. Only a longitudinal adaptive damper needs to be installed between the tower and the beam to effectively control the longitudinal displacement at the beam ends and significantly suppress the vertical multimodal vibration of the main beam simultaneously, eliminating the need for additional specialized devices such as tuned mass dampers for vertical vibration control.

[0055] Furthermore, the steady-state excitation modal damping ratio evaluation method proposed in this application obtains vibration response data under uncontrolled conditions and after damper installation by applying a simple harmonic excitation with a matching frequency at the peak displacement position of the target vertical bending mode of the bridge (such as the mid-span region of the symmetrical vertical bending mode or both sides of the bridge deck of the antisymmetric vertical bending mode). The damping ratio increment Δξn and the lift rate ηn are directly calculated using the time-domain decay method. This effectively avoids the measurement distortion problems caused by multimodal coupling, environmental noise interference, or parameter calibration deviation in traditional modal analysis, ensuring that the test results are objective and repeatable. It provides direct quantitative support for the reliability of the technology in engineering practice, avoids the uncertainty of relying on experience judgment or indirect verification, and thus enhances the credibility and engineering applicability of the design.

[0056] Secondly, embodiments of this application provide a bridge multimodal vibration control system, comprising: a first module, a second module, a third module, and a fourth module. The first module is used to: establish a spatial finite element model of the suspension bridge and identify the key vertical bending modes of the bridge, as well as the frequencies and mode shapes of the key vertical bending modes, through modal analysis. The second module is used to: determine the peak displacement position of the main beam mode shape based on the mode shape, and apply a harmonic load consistent with the frequency of the mode shape at the peak displacement position of the main beam mode shape to determine the first velocity segment damping parameters. The third module is used to: select seismic waves that meet the site conditions of the bridge as input excitation and determine the second velocity segment parameters through nonlinear time history analysis. The fourth module is used to: integrate the first velocity segment parameters and the second velocity segment parameters into the longitudinal damper, and switch the operating parameters of the longitudinal damper between the first velocity segment damping parameters and the second velocity segment parameters based on the relative velocity at both ends of the longitudinal damper.

[0057] By establishing a spatial finite element model of the suspension bridge and identifying key vertical bending modes and their frequency modes, the damper parameters are optimized based on actual vibration characteristics rather than empirical formulas, thus ensuring a precise match between the damper and the bridge's vibration characteristics. Applying a harmonic load consistent with the target mode frequency at the peak displacement position of the main beam mode shape achieves efficient energy transfer at the mode shape peak, ensuring that the calculated additional damping ratio accurately reflects the damper's control capability over the target mode. The separate design of the first and second velocity parameters allows the damper to be specifically optimized for wind-induced vibration (medium-to-low speed vibration) and earthquake vibration (high-speed vibration), avoiding the inaccurate control effect caused by parameter mixing in traditional schemes. Integrating the first and second velocity parameters into the longitudinal damper and automatically switching them by relative velocity allows a single damper to adapt to the vibration characteristics of both working conditions simultaneously, eliminating the need for separate dedicated devices for vibrations in different directions. This significantly simplifies the structural system while ensuring control effectiveness, reducing construction costs and maintenance complexity.

[0058] The functions of each module in the above-mentioned bridge multimodal vibration control system correspond to the steps in the above-mentioned bridge multimodal vibration control method embodiment, and their functions and implementation processes will not be described in detail here.

[0059] Thirdly, embodiments of this application provide a bridge multimodal vibration control device, which can be a personal computer (PC), laptop computer, server, or other device with data processing capabilities.

[0060] In this embodiment of the application, the bridge multimodal vibration control device may include a processor, a memory, a communication interface, and a communication bus.

[0061] The communication bus can be of any type and is used to interconnect the processor, memory, and communication interface.

[0062] The communication interface includes input / output (I / O) interfaces, physical interfaces, and logical interfaces used for interconnecting components within the bridge multimodal vibration control equipment, as well as interfaces used for interconnecting the bridge multimodal vibration control equipment with other devices (such as other computing devices or user equipment). Physical interfaces can be Ethernet interfaces, fiber optic interfaces, ATM interfaces, etc.; user equipment can be displays, keyboards, etc.

[0063] Memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.

[0064] The processor can be a general-purpose processor, which can call the bridge multimodal vibration control program stored in the memory and execute the bridge multimodal vibration control method provided in the embodiments of this application. For example, the general-purpose processor can be a central processing unit (CPU). The method executed when the bridge multimodal vibration control program is called can be referred to the various embodiments of the bridge multimodal vibration control method of this application, and will not be repeated here.

[0065] Fourthly, embodiments of this application also provide a computer-readable storage medium.

[0066] The present application provides a computer-readable storage medium storing a bridge multimodal vibration control program, wherein when the bridge multimodal vibration control program is executed by a processor, it implements the steps of the bridge multimodal vibration control method described above.

[0067] The method implemented when the bridge multimodal vibration control program is executed can be referred to in the various embodiments of the bridge multimodal vibration control method of this application, and will not be repeated here.

[0068] It should be noted that the sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0069] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not indicate a sequence, nor do they limit "first," "second," and "third" to different types.

[0070] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0071] 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.

[0072] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0073] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to execute the methods described in the various embodiments of this application.

[0074] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for controlling multimodal vibration of a bridge, characterized in that, It includes: A spatial finite element model of the suspension bridge was established, and the key vertical bending modes of the bridge, as well as the frequencies and mode shapes of the key vertical bending modes, were identified through modal analysis. Based on the vibration mode, the peak position of the main beam vibration mode displacement is determined, and a simple harmonic load with the same frequency as the mode is applied at the peak position of the main beam vibration mode displacement to determine the damping parameters of the first velocity segment. Seismic waves that meet the site conditions of the bridge are selected as input excitation, and the parameters of the second velocity segment are determined through nonlinear time history analysis. The first speed segment parameter and the second speed segment parameter are integrated into the longitudinal damper, and the operating parameters of the longitudinal damper are switched between the first speed segment damping parameter and the second speed segment parameter based on the relative velocity at both ends of the longitudinal damper.

2. The bridge multimodal vibration control method as described in claim 1, characterized in that, A spatial finite element model of the suspension bridge was established, and key vertical bending modes of the bridge, as well as the frequencies and mode shapes of these key vertical bending modes, were identified through modal analysis. Specifically, this included: A spatial finite element model of a suspension bridge was established, and the dominant vertical vibration modes of the bridge were identified through modal analysis. The vertical bending modes within the wind-sensitive frequency band are identified as the key vertical bending modes; Determine the frequency and mode shape of each key vertical bending mode.

3. The bridge multimodal vibration control method as described in claim 1, characterized in that, Based on the relative velocity at both ends of the longitudinal damper, the operating parameters of the longitudinal damper are switched between the first-speed damping parameters and the second-speed damping parameters, specifically including: The first speed range parameter is used when the relative velocity between the two ends of the longitudinal damper is within the first threshold range. The second speed range parameter is used when the relative velocity between the two ends of the longitudinal damper is within the second threshold range.

4. The bridge multimodal vibration control method as described in claim 1, characterized in that, Applying a simple harmonic load with the same modal frequency at the peak position of the main beam's vibration mode displacement, and determining the damping parameters for the first velocity segment, specifically includes: A simple harmonic load with the same modal frequency is applied at the peak position of the main beam vibration mode displacement, and the time history data of the structural displacement are obtained. The additional damping ratio of the vertical bending mode is calculated using the structural displacement time history data, and the optimal damping coefficient is determined. Under the condition that the optimal damping coefficient remains unchanged, the speed index of the longitudinal damper is changed to determine the optimal speed index; The optimal damping coefficient and optimal velocity index are used as the damping parameters for the first velocity segment so that the damping ratio of the vertical bending mode reaches the target value.

5. The bridge multimodal vibration control method as described in claim 4, characterized in that, The additional damping ratio of the vertical bending mode is calculated using the structural displacement time history data, and the optimal damping coefficient is determined, specifically including: Based on the structural displacement time history data, the additional damping ratio of the vertical bending mode corresponding to multiple different damping coefficients is calculated, and the relationship curve between the additional damping ratio of the vertical bending mode and the damping coefficient is determined. Determine the damping coefficient corresponding to the maximum additional damping ratio of the vertical bending mode from the aforementioned relationship curve; This damping coefficient is taken as the optimal damping coefficient.

6. The bridge multimodal vibration control method as described in claim 4, characterized in that, Under the condition that the optimal damping coefficient remains unchanged, the velocity index of the longitudinal damper is changed to determine the optimal velocity index, specifically including: Under the condition that the optimal damping coefficient remains unchanged, the velocity index of the longitudinal damper is changed; Based on the structural displacement time history data, the additional damping ratio of the vertical bending mode corresponding to different velocity indices is calculated, and the relationship curve between the additional damping ratio of the vertical bending mode and the velocity index is determined. Determine the velocity index corresponding to the maximum additional damping ratio of the vertical bending mode from the aforementioned relationship curve; This speed index is taken as the optimal speed index.

7. The bridge multimodal vibration control method as described in claim 1, characterized in that, Seismic waves suitable for the bridge site conditions were selected as the input excitation. Nonlinear time history analysis was used to determine the parameters of the second velocity band, specifically including: Seismic waves that meet the site conditions of the bridge were selected as the input excitation for nonlinear time history analysis. Based on the nonlinear time history analysis results, the damping coefficient and velocity index that satisfy the constraints of maximum relative displacement between the tower and beam, internal forces of the structure, and output force of the damper are determined. The damping coefficient and speed index are used as parameters for the second speed range.

8. The bridge multimodal vibration control method as described in claim 1, characterized in that, The method further includes: The additional damping ratio contribution of the longitudinal damper to the vertical bending mode of the bridge target was obtained by using a steady-state excitation test method.

9. The bridge multimodal vibration control method as described in claim 8, characterized in that, The steady-state excitation test method was used to obtain the additional damping ratio contribution of the longitudinal damper to the vertical bending mode of the bridge target, specifically including: By applying harmonic excitation at the target vertical bending mode resonance frequency, the inherent damping ratio of the uncontrolled state is obtained. Install longitudinal dampers on the bridge to obtain the controlled state damping ratio; Based on the inherent damping ratio in the uncontrolled state and the damping ratio in the controlled state, the additional damping ratio increment and the damping effect improvement rate are calculated to obtain the additional damping ratio contribution of the longitudinal damper to the target vertical bending mode of the bridge.

10. A bridge multimodal vibration control system, characterized in that, It includes: The first module is used to: establish a spatial finite element model of the suspension bridge, and identify the key vertical bending modes of the bridge and the frequencies and mode shapes of the key vertical bending modes through modal analysis; The second module is used to: determine the peak position of the main beam mode displacement based on the mode shape, and apply a simple harmonic load with the same modal frequency at the peak position of the main beam mode displacement to determine the damping parameters of the first velocity segment; The third module is used to: select seismic waves that meet the site conditions of the bridge as input excitation, and determine the parameters of the second velocity segment through nonlinear time history analysis; The fourth module is used to: integrate the first speed segment parameters and the second speed segment parameters into the longitudinal damper, and switch the operating parameters of the longitudinal damper between the first speed segment damping parameters and the second speed segment parameters based on the relative speed at both ends of the longitudinal damper.

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