Railway beam bridge damping system based on metal damper coordination and design method

Abstract

The invention relates to the technical field of earthquake resistance of bridge engineering, and particularly discloses a railway beam bridge damping system based on metal damper coordination and a design method.The railway beam bridge damping system adopts direct displacement design based on equivalent linearization and comprises the steps that firstly, shock insulation displacement and an initial equivalent damping ratio are set as design parameters; the design displacement target is achieved within the reasonable range of the two parameters, accurate calculation can be conducted according to specific structural requirements, blind accumulation only based on the number of existing dampers in previous design is avoided, and design pertinence and scientificity are effectively improved. On the premise that different metal dampers are combined, the independent design of the equivalent damping ratio and the equivalent rigidity is achieved, the flexibility of the damping design is improved, the damping design of a common railway beam bridge is optimized, and the cost of the damping device is reduced.

Description

Vibration Reduction System and Design Method for Railway Beam Bridges Based on Metal Dampers Technical Field

[0001] This invention relates to the field of seismic resistance technology in bridge engineering, and in particular to a seismic reduction system and design method for railway beam bridges based on the coordination of metal dampers. Background Technology

[0002] In railways located in high-intensity seismic zones, ordinary beam bridges often employ metal damping devices for vibration reduction. These metal dampers typically utilize mild steel with a low yield point, with the most representative examples being tenon-type and curved steel damping bearings. The performance of metal dampers is primarily determined by the properties of the metal material and the damper's deformation characteristics. Extensive experimental results show that for metal dampers with the same deformation characteristics, those using high-yield-point metal materials have a lower equivalent damping ratio, while those using low-yield-point metal materials have a higher equivalent damping ratio. A key characteristic of metal dampers is their high equivalent damping ratio and excellent energy dissipation capacity; however, their equivalent stiffness and equivalent damping ratio are highly coupled.

[0003] The general process for seismic damping design of ordinary railway beam bridges is as follows: First, the type of damper needs to be selected. After determining the tonnage (yield force) and seismic displacement of the damper, the damping effect is checked by increasing or decreasing the number or tonnage of individual dampers. If the damping ratio exceeds the limit, one approach is to ignore the excess damping ratio, resulting in a waste of metal dampers. Another approach is to use nonlinear time history analysis to recalculate the damping design, which increases the complexity and uncertainty of the calculations. If the displacement check fails, the number of dampers is increased to adjust the design, rather than more effectively controlling it by increasing the additional stiffness of the dampers. In other words, existing damping designs assume the coupling between the additional stiffness of metal dampers and the equivalent damping ratio. When the additional stiffness is insufficient, it can only be inefficiently superimposed, wasting the benefits of additional damping during the superposition process. In essence, current damping designs only check the number of dampers and cannot specifically design parameters such as the equivalent damping ratio and additional stiffness of metal dampers according to the damping requirements. Summary of the Invention

[0004] To address the problems encountered in the vibration reduction design of ordinary railway beam bridges using metal dampers, such as unreasonable additional stiffness and additional damping design, and coupling of damper yield force, additional stiffness and additional damping, this invention provides a vibration reduction system and design method for railway beam bridges based on the coordination of metal dampers.

[0005] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0006] In a first aspect, the present invention provides a design method for a railway beam bridge vibration reduction system based on coordinated metal dampers. The metal dampers include a first damper and a second damper. The method includes: setting the isolation displacement and initial equivalent damping ratio of the target bridge; performing structural requirements calculations for the target bridge to obtain the equivalent stiffness of the dampers on each pier / abutment; combining the first and second dampers on each pier / abutment according to the equivalent stiffness of the dampers to obtain the metal damper combination on each pier / abutment, thus completing the design; wherein the requirements calculation includes: calculating a damping adjustment coefficient based on the initial equivalent damping ratio; obtaining the total equivalent stiffness of the target bridge based on the damping adjustment coefficient and the isolation displacement; and calculating the equivalent stiffness of the dampers on each pier / abutment based on the total equivalent stiffness. The equivalent stiffness of the dampers on the pier / platform; the combined design includes: constructing a combination sequence of the first damper and the second damper based on the damper control quantity and the equivalent stiffness of the damper on each pier / platform, and calculating the equivalent damping ratio corresponding to each row of the combination sequence to generate an equivalent damping ratio sequence; selecting the value in the equivalent damping ratio sequence whose difference from the initial equivalent damping ratio is less than a preset threshold, and determining whether convergence iteration is satisfied; if yes, then obtaining the metal damper combination based on the combination sequence corresponding to the value whose difference from the initial equivalent damping ratio is less than the preset threshold; if no, then taking the value whose difference from the initial equivalent damping ratio is less than the preset threshold as the initial equivalent damping ratio, and re-performing the requirement calculation and combined design until a metal damper combination that satisfies convergence iteration is obtained.

[0007] According to one specific implementation, in the above design method, the damping ratio of the first damper is smaller than that of the second damper, and the yield point of the first damper is higher than that of the second damper.

[0008] According to a specific implementation, in the above design method, the first damper and the second damper adopt a damping tenon, and the damper control quantity includes the total number of dampers and the number of intervals; constructing the combination sequence includes: based on the total number of dampers, increasing the number of the first dampers according to the number of intervals, and decreasing the number of the second dampers, to complete the construction.

[0009] According to a specific implementation, in the above design method, after obtaining the metal damper combination that satisfies convergence iteration, the number of the first damper and the second damper in the metal damper combination is rounded down, and then it is determined again whether the rounded metal damper combination satisfies convergence iteration.

[0010] According to a specific implementation, in the above design method, the first damper and the second damper are arc-shaped dampers, and the damper control quantity includes the total thickness of the damper and the interval thickness; constructing the combined sequence includes: increasing the first damper according to the interval thickness based on the total thickness of the damper, and decreasing the second damper, to complete the construction.

[0011] According to a specific implementation, the above design method further includes: filtering the values ​​in the combination sequence based on a first filtering condition, and performing the combination design on the filtered combination sequence; if none of the values ​​in the combination sequence meet the first filtering condition, then resetting the initial equivalent damping ratio, and re-performing the requirement calculation and combination design.

[0012] According to a specific implementation, in the above design method, the first screening condition includes: when the horizontal displacement of the first damper and the second damper increases from 50% of the seismic isolation displacement to the seismic isolation displacement, the increase in the restoring force of the target bridge is not less than 2.5% of the weight of the superstructure it bears.

[0013] According to a specific implementation, the above design method further includes filtering the values ​​in the equivalent damping ratio series based on the second screening condition, and performing the combined design on the filtered equivalent damping ratio series; if none of the values ​​in the equivalent damping ratio series meet the second screening condition, the seismic isolation displacement is reset, and the requirement calculation and combined design are performed again.

[0014] According to a specific implementation, in the above design method, the second screening condition includes: the value in the equivalent damping ratio series is less than a preset threshold.

[0015] Secondly, a vibration reduction system for railway beam bridges based on coordinated metal dampers includes: multiple metal dampers installed between the piers and the beam; the metal dampers include a first damper and a second damper; wherein the ratio of the number of the first damper and the second damper is determined by the design method described in any of the above-mentioned embodiments.

[0016] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention proposes a vibration reduction system and design method for railway beam bridges based on coordinated metal dampers. It adopts direct displacement design based on equivalent linearization, first setting the isolation displacement and initial equivalent damping ratio as design parameters. This ensures that the design displacement target is achieved within a reasonable range of these two parameters, enabling precise calculations based on specific structural requirements. This avoids the blind accumulation of existing damper quantities used in previous designs, effectively improving the design's relevance and scientific rigor. Furthermore, this invention achieves a reasonable combination of the first and second dampers through comprehensive analysis of the equivalent stiffness of the dampers on each pier / abutment. This helps to fully utilize the characteristics of different types of dampers, thereby improving the overall vibration reduction effect. Simultaneously, the convergence iterative mechanism employed in this invention continuously adjusts the initial equivalent damping ratio to achieve a metal damper combination that meets design requirements. The dynamic optimization method effectively solves the problem of initial design not meeting requirements, ensuring effective improvement in the design process. This invention, by combining different metal dampers, achieves independent design of equivalent damping ratio and equivalent stiffness, improves the flexibility of vibration reduction design, optimizes the vibration reduction design of ordinary railway beam bridges, and reduces the cost of vibration reduction devices. Attached Figure Description

[0017] Figure 1 is a schematic diagram of the change of the adjustment coefficient provided in the embodiment of the present invention; Figure 2 is a schematic diagram of the change of the damping period provided in the embodiment of the present invention; Figure 3 is a flowchart of a design method for a railway beam bridge damping system based on metal damper coordination provided in the embodiment of the present invention; Figure 4 is a schematic diagram of the combination sequence and the corresponding equivalent damping ratio sequence provided in the embodiment of the present invention; Figure 5 is a flowchart of the design method provided in the embodiment of the present invention; Figure 6 is a constitutive schematic diagram of the first damper provided in the embodiment of the present invention; Figure 7 is a constitutive schematic diagram of the second damper provided in the embodiment of the present invention; Figure 8 is a schematic diagram of the A-type damper combination provided in the embodiment of the present invention; Figure 9 is a schematic diagram of the B-type damper combination provided in the embodiment of the present invention. Detailed Implementation

[0018] The present invention will be further described in detail below with reference to experimental examples and specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0019] The terms "first," "second," etc., used in the specification, embodiments, claims, and drawings of this invention are for distinguishing purposes only and should not be construed as indicating or implying relative importance or order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as including a series of steps or units. A method, system, product, or apparatus is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products, or apparatuses.

[0020] Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner for ease of understanding.

[0021] The term "damping adjustment coefficient" in this embodiment of the invention can be selected according to the corresponding damping adjustment coefficient formula based on applicable industry standards (such as railway seismic design code, highway bridge seismic design code, or AASHTO code). This invention is not limited to a specific code, and can be implemented as long as it conforms to the iterative design process of this invention.

[0022] Currently, scholars both domestically and internationally have conducted extensive research on dampers and vibration reduction design. The main research findings focus on improving one or more key vibration reduction parameters, such as energy dissipation capacity, deformation capacity, and additional stiffness, by employing special structural forms or novel material types. While these newly developed dampers are ingeniously designed, they generally suffer from high costs and a lack of practical verification, failing to directly address the problems of currently widely used metal dampers in vibration reduction design. Another area of ​​research focuses on combined vibration reduction designs using different types of dampers, such as superimposing velocity-type dampers with metal dampers. This type of research is not applicable to ordinary railway beam bridges but is more suitable for large bridges where investment is not critical. In terms of design methodology, this combined vibration reduction design of different types of dampers mainly emphasizes seismic segmentation design and fortification, without addressing the rational design of the equivalent stiffness and equivalent damping ratio of each damping device.

[0023] For ordinary railway bridges, the amount of metal dampers used along the line is very large. Considering cost and design difficulty, only a few fixed tonnage (yield load) metal damper models can be used for vibration reduction design (refer to QCR 709-2019 "Railway Bridge Vibration Damping Tenon and Tenon-Shaped Anti-Falling Beam Devices" and other soft steel damper specifications). It is impossible to achieve a one-bridge-one-pier-one-design approach. However, as mentioned earlier, in vibration reduction design, the additional damping and additional stiffness of the vibration reduction device should be reasonably adjusted. Excessive additional damping and insufficient additional stiffness will both lead to unreasonable vibration reduction design, which will result in a surge in cost and design difficulties. The high coupling between the equivalent stiffness and equivalent damping ratio of metal dampers is a particularly prominent problem in actual engineering.

[0024] In seismic design, excessively high damping ratios should be avoided. The *Code for Seismic Design of Highway Bridges* (JTG / T2231-01-2020) and the *Code for Seismic Design of Urban Bridges* (CJJ166-2011) stipulate that for bridge structures using seismic isolation and damping design, if the structural damping ratio exceeds 30% (the original damping ratio for concrete bridges is 5%, corresponding to an additional damping ratio of 25%), nonlinear time-history analysis must be used for verification. The *Technical Specification for Energy Dissipation and Vibration Reduction in Buildings* (JGJ297-2013) stipulates that when the effective damping ratio added to the structure by energy dissipation components exceeds 25%, it should be calculated as 25%. However, current railway seismic design codes do not have specific requirements for seismic design, and in actual design, highway and building codes are often strictly followed. For seismic-damping structures, different vibration modes have different damping ratios. When the additional damping ratio is too large (≥25%), the choice of vibration mode order and combination method has a significant impact on the calculation results, leading to complex calculations and insufficient consistency. Another important factor is that the damping benefit decreases continuously with the increase of the damping ratio. Referring to the formula for the response spectrum reduction factor 1 / BL in the American AASTHO standard, and comparing it with the formulas for the damping adjustment factor η2 in the "Code for Seismic Design of Highway Bridges" (JTG / T2231-01-2020) and the "Code for Seismic Design of Urban Bridges" (CJJ166-2011), the change in the adjustment factor is shown in Figure 1. As the equivalent damping ratio increases, the decrease in the damping adjustment factor corresponding to the direct reduction response spectrum value tends to level off.

[0025] Similarly, in seismic isolation and damping design, the design of additional stiffness and additional damping ratio present similar problems, as shown in Figure 2. As the additional stiffness increases, the displacement requirement of the structure decreases, but the resistance requirement of the substructure increases. Insufficient additional stiffness directly leads to excessive displacement requirements for the damping device, increasing structural instability and making the design of the damping device difficult. Therefore, the "Code for Seismic Design of Highway Bridges" (JTG / T 2231-01-2020) and the "Code for Seismic Design of Urban Bridges" (CJJ166-2011) stipulate that when the horizontal displacement of the seismic isolation device increases from 50% of the design displacement to the design displacement, its restoring force increment should not be less than 2.5% of the weight of the superstructure it supports.

[0026] Existing research cannot solve the problems encountered in the vibration reduction design of ordinary railway beam bridges using metal dampers, such as unreasonable additional stiffness and additional damping design, and coupling of damper yield force, additional stiffness, and additional damping. In order to solve these practical engineering problems, this invention proposes a vibration reduction system and design method for railway beam bridges based on the coordination of metal dampers, while ensuring the use of standard metal dampers.

[0027] Specifically, in the proposed design method for a railway beam bridge vibration reduction system based on coordinated metal dampers, the metal dampers include a first damper and a second damper. The damping ratio of the first damper is smaller than that of the second damper, and the yield point of the first damper is higher than that of the second damper. Specifically, in this embodiment, the first and second dampers are selected from two types of metal dampers with different mechanical properties: one with a high yield point and low damping ratio (low-alloy steel), and the other with a low yield point and high equivalent damping ratio (mild steel). These are superimposed or combined as needed to decouple the additional stiffness and the additional damping ratio. For the vibration reduction design of ordinary railway beam bridges, an equivalent single-degree-of-freedom displacement-based direct design is adopted to optimize the design process. Direct design is performed using additional stiffness and additional damping ratio as variables to avoid unreasonable vibration reduction design caused by excessively high additional damping ratios or excessively low additional stiffness.

[0028] In seismic isolation design, this invention employs the equivalent single-degree-of-freedom method for calculation. The equivalent single-degree-of-freedom method can be referenced from relevant domestic and international standards or existing research. In a preferred embodiment of this invention, considering that railway simply supported beam bridges typically have pier heights within 25m, and that the seismic isolation design objective requires the piers to remain elastic, the lateral stiffness of the pier / abutment is then... Much greater than the equivalent stiffness of the pier-beam connection after vibration reduction (i.e., stiffness ratio) (Tends to 0). Therefore, in order to simplify the calculation process and focus on the optimization of damper combination parameters, this embodiment of the invention simplifies the lower structure to a rigid base as the initial calculation condition, and directly designs the damping device using the first-order vibration mode (isolation vibration mode) after damping.

[0029] Specifically, please refer to Figure 3, which shows a flowchart of a design method for a railway beam bridge vibration reduction system based on metal damper coordination provided by an embodiment of the present invention. The design method includes: Step 1: Set the seismic isolation displacement and initial equivalent damping ratio of the target bridge, perform structural requirement calculations for the target bridge, and obtain the equivalent stiffness of the damper on each pier / abutment.

[0030] Specifically, according to conventional practice, based on the seismic design displacement D of the damping bearing... s The selected seismic isolation displacement D is 0.8 times the initial equivalent damping ratio ξ. eq-n Select according to the limit of 0.25. The calculation formula is: (1) Where n is the number of iterations, Let be the equivalent damping ratio of the damper on the i-th pier / abutment. Let k be the equivalent damping ratio of the i-th pier / abutment. Since the lateral stiffness of the pier / abutment is much greater than the equivalent stiffness of the pier-beam connection after vibration reduction, k... eff，i / k p，i Approaching 0, it can be simplified to: (2) Where N is the total number of piers and platforms. k p,i Let k be the lateral stiffness of pier / abutment number i. eff,i Let d be the equivalent stiffness of the damper on the i-th pier / platform. iso,i The deformation of the damper on the i-th pier / platform.

[0031] In one possible implementation, the demand calculation includes: step 101: calculating the damping adjustment coefficient based on the initial equivalent damping ratio; specifically, the damping adjustment coefficient... This is the reduction factor of the response spectrum, used to reflect the reduction effect of the damping ratio on seismic action. The damping adjustment factor η2 is calculated according to the following formula: (3) Among them, is the equivalent damping ratio at the nth iteration.

[0032] Step 102: Obtain the total equivalent stiffness of the target bridge based on the damping adjustment coefficient and the seismic isolation displacement; specifically, using the normal elastic spectrum S A Based on the pseudo-acceleration spectrum, and according to the definition of structural dynamics, it is transformed into a displacement spectrum S. D The calculation formula is: (4) Let the spectral value S D Equal to the isolation displacement D of the equivalent single-degree-of-freedom structure, T is obtained by solving. eq-nThe equivalent damping ratio ξ of the nth iteration is the equivalent damping ratio corresponding to the equivalent period iteration (n=0). eq-n Given the initial values, solve for the total equivalent stiffness K of the equivalent single-degree-of-freedom system. eff-n The calculation formula is: (5) (6) Among them, W eq / g represents the participating mass, W eq The equivalent weight of the equivalent single-degree-of-freedom system (usually the total weight of the superstructure). For the gravitational acceleration (9.8 m / s²), only the mass contribution of the beam can be considered at this stage.

[0033] Step 103: Calculate the equivalent stiffness of the damper on each pier / platform based on the total equivalent stiffness.

[0034] Specifically, the equivalent total stiffness K eq-n The equivalent stiffness k of the dampers on all piers / platforms of the beam eff,i The composition is as shown in the following formula: (7) In the calculation, the equivalent stiffness keff,i of the damper of the i-th pier / abutment can be distributed according to the sum of the static vertical bearing capacity of the supports of the pier / abutment obtained from the static design if the pier heights of the simply supported beam bridges are similar. If the difference in pier height is too large (the difference in stiffness dp,i between adjacent piers / abutments exceeds 20%), the following formula shall be used for calculation: (8) Wherein, d iso,i d represents the deformation of the pier-beam connection corresponding to pier / abutment number i. p,i The deformation of pier / platform number i.

[0035] In one possible implementation, the shear force at the top of the i-th pier / abutment is calculated, and the strength is checked according to the specifications. If the strength does not meet the design requirements, the appropriate option can be chosen based on the actual line design standards: either increase the design strength of the i-th pier / abutment through special design, or relax the overall target seismic isolation displacement D.

[0036] The calculations here are mainly related to the existing static design; the vibration reduction design will not be discussed further.

[0037] (9) Step 2: Based on the equivalent stiffness of the damper, design the combination of the first and second dampers on each pier / platform to obtain the metal damper combination on each pier / platform, and complete the design.

[0038] Taking the most commonly used bilinear model as an example, according to the definition of the bilinear model, the equivalent stiffness can be obtained as: (10) The area of ​​the hysteresis loop is: (11) The equivalent damping ratio is defined as: (12) Maximum strain energy E SIt can be defined as: (13) Where Qd is the characteristic strength, kd is the post-buckling stiffness, Wd is the hysteresis loop area, and dy is the yield displacement.

[0039] Specifically, the combined design includes: Step 201: Constructing a combination sequence of the first damper and the second damper based on the damper control quantity and the equivalent stiffness of the damper on each pier / platform, and calculating the equivalent damping ratio corresponding to each row of the combination sequence to generate an equivalent damping ratio sequence.

[0040] In one possible implementation, the first damper and the second damper are made of damping tenons, and the damper control quantity includes the total number of dampers and the number of intervals; constructing the combination sequence includes: based on the total number of dampers, increasing the number of the first dampers according to the number of intervals, and decreasing the number of the second dampers, to complete the construction.

[0041] Specifically, the total number of damping tenons required for the i-th pier / abutment is n. i The number of the first dampers is n i,A The number of damping tenons in the second damper is n. i,B Then we have: (14) The equivalent stiffness of the damping device of the i-th pier / abutment is: (15) Combining equations 14 and 15, from n i,A =0, increase n in increments. i,A In one possible implementation, the value of n is increased in increments of 0.5, up to n. i,B =0, obtain {n i,A}、{n i,B}、{n i The numerical matrices correspond one-to-one, and the calculated values ​​are not rounded down.

[0042] In another possible implementation, the first damper and the second damper are arc-shaped dampers, and the damper control parameters include the total thickness of the damper and the interval thickness; constructing the combined sequence includes: increasing the first damper according to the interval thickness based on the total thickness of the damper, and decreasing the second damper, to complete the construction.

[0043] Specifically, let the total thickness of the arc-shaped steel damper required for the i-th pier / abutment be n. i The thickness of the first damper is n i,A The thickness of the second damper is n i,B Then we have: (16) Combining equations 16 and 15, from n i,A =0, increase n in increments. i,AIn one possible implementation, the value is increased in increments of 0.5 cm, up to n. i,B =0, obtain {Σn i,A}、{Σn i,B}、{Σn i A numerical matrix with one-to-one correspondence.

[0044] In the simultaneous equations 14 and 15 and 16 and 15, there are three unknowns and two equations. In this embodiment, the calculation is performed using programming or a table.

[0045] Furthermore, substituting the obtained matrix of quantities, we calculate the equivalent damping ratio sequence on the i-th pier / abutment, which, according to the definition, yields: (17) Substituting each term into the equation, we get: (18) Among them, The characteristic strength of the first damper, The characteristic strength of the second damper is calculated. ξ is obtained. eff,i and ξ eq (i.e., Σξ) eff,i The corresponding column {ξ} of the scalar matrix eq As shown in Figure 4.

[0046] Step 202: Select the value in the equivalent damping ratio sequence whose difference from the initial equivalent damping ratio is less than a preset threshold, and determine whether convergence iteration is satisfied.

[0047] Specifically, in obtaining {ξ eq In the sequence, select the initial equivalent damping ratio ξ. eq-n The difference is less than a preset threshold value. In this embodiment of the invention, the preset threshold can be set according to actual needs, preferably ±0.1, as ξ. eq-(n+1) Then make a judgment.

[0048] The iterative convergence requirement is: (19) Step 203: If so, then the metal damper combination is obtained based on the combination sequence corresponding to the value whose difference with the initial equivalent damping ratio is less than a preset threshold.

[0049] In one possible implementation, the design ends directly for schemes using curved steel dampers, while for schemes using damping tenons, the design process in this iteration (n) needs to be further refined. i,A n i,B After rounding the numerical parameters, it is determined again whether the rounded metal damper combination satisfies the convergence iteration.

[0050] For the damping tenon scheme, in the initial iteration calculation, in order to find the optimal combination solution, it is allowed to... and Non-integer combination calculations are performed with a step interval of 0.5. These non-integer intermediate variables are only used for theoretical optimization. After the iteration converges to obtain the theoretically optimal combination ratio, the number of dampers is rounded up using the rounding step described in step 204 to obtain an integer number of damper combination schemes that are feasible in engineering. The rounded scheme is then subjected to a second convergence verification.

[0051] For the curved steel damper scheme, since the mechanical properties of the curved steel damper have a continuous functional relationship with the steel plate thickness, the interval thickness... The thickness can be set according to the actual rolled steel plate specifications or processing precision. In this invention, it is preferably 0.5cm or 1.0cm to construct a discrete series of thickness combinations.

[0052] Step 204: If not, take the value where the difference between the initial equivalent damping ratio and the initial equivalent damping ratio is less than a preset threshold as the initial equivalent damping ratio, and recalculate the requirements and design the combination until a metal damper combination that satisfies convergence iteration is obtained.

[0053] In one possible implementation, the method further includes: filtering the values ​​in the combined sequence based on a first filtering condition, and performing the combined design on the filtered combined sequence; if none of the values ​​in the combined sequence meet the first filtering condition, then resetting the initial equivalent damping ratio, and re-performing the requirement calculation and combined design.

[0054] The first screening condition includes: when the horizontal displacement of the first damper and the second damper increases from 50% of the seismic isolation displacement to the seismic isolation displacement, the increase in the restoring force of the target bridge is not less than 2.5% of the weight of the superstructure it bears. The calculation formula is: (20) In one possible implementation, the method further includes: filtering the values ​​in the equivalent damping ratio series based on the second screening condition, and performing the combined design on the filtered equivalent damping ratio series; if none of the values ​​in the equivalent damping ratio series meet the second screening condition, then the seismic isolation displacement is reset, and the requirement calculation and combined design are performed again.

[0055] In one possible implementation, the second screening condition in the above design method includes: the value in the equivalent damping ratio series is less than a preset threshold.

[0056] For example, in this embodiment of the invention, the preset threshold is preferably 0.3. This preferred value is based on the limit specified in highway / building codes.

[0057] Based on the above technical solution, this invention adopts a direct displacement design based on equivalent linearization. First, it sets the isolation displacement and initial equivalent damping ratio as design parameters, ensuring that the design displacement target is achieved within a reasonable range of these two parameters. This allows for precise calculation based on specific structural requirements, avoiding the blind accumulation of existing dampers as in previous designs, effectively improving the design's relevance and scientific rigor. Furthermore, this invention achieves a reasonable combination of the first and second dampers by comprehensively analyzing the equivalent stiffness of the dampers on each pier / abutment. This helps to fully utilize the characteristics of different types of dampers, thereby improving the overall vibration reduction effect. Simultaneously, the convergence iterative mechanism employed in this invention continuously adjusts the initial equivalent damping ratio to achieve a metal damper combination that meets design requirements. The dynamic optimization method effectively solves the problem of initial design not meeting requirements, ensuring effective improvement in the design process. This invention, under the premise of using different combinations of metal dampers, achieves independent design of equivalent damping ratio and equivalent stiffness, improving the flexibility of vibration reduction design, optimizing the vibration reduction design of ordinary railway beam bridges, and reducing the cost of vibration reduction devices.

[0058] Further, please refer to Figure 5, which shows a schematic diagram of the design method provided in an embodiment of the present invention. In this embodiment of the present invention, the constitutive schematic diagram of the first damper is shown in Figure 6, and the constitutive schematic diagram of the second damper is shown in Figure 7.

[0059] On the other hand, embodiments of the present invention provide a vibration reduction system for railway beam bridges based on coordinated metal dampers, comprising: a plurality of metal dampers installed between the piers and the beam; the metal dampers include a first damper and a second damper; wherein the ratio of the number of the first damper and the second damper is determined by any of the design methods described above.

[0060] Furthermore, taking the first damper as a type A damper and the second damper as a type B damper as an example, please refer to Figure 8, which shows a schematic diagram of the type A damper combination provided in the embodiment of the present invention, and please refer to Figure 9, which shows a schematic diagram of the type B damper combination provided in the embodiment of the present invention.

[0061] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for a vibration reduction system of a railway beam bridge based on metal damper coordination, characterized in that, The metal damper includes a first damper and a second damper. The method includes: setting the seismic isolation displacement and initial equivalent damping ratio of the target bridge, performing structural requirements calculations for the target bridge, and obtaining the equivalent stiffness of the damper on each pier / abutment; combining the first and second dampers on each pier / abutment according to the equivalent stiffness of the dampers to obtain the metal damper combination on each pier / abutment, thus completing the design; wherein, the requirements calculation includes: calculating the damping adjustment coefficient based on the initial equivalent damping ratio; obtaining the total equivalent stiffness of the target bridge based on the damping adjustment coefficient and the seismic isolation displacement; calculating the equivalent stiffness of the damper on each pier / abutment based on the total equivalent stiffness; the combination design includes: Based on the damper control values ​​and equivalent stiffness of each pier / platform, a combination sequence of the first and second dampers is constructed, and the equivalent damping ratio corresponding to each row of the combination sequence is calculated to generate an equivalent damping ratio sequence. Values ​​in the equivalent damping ratio sequence whose difference from the initial equivalent damping ratio is less than a preset threshold are selected, and it is determined whether convergence iteration is satisfied. If yes, a metal damper combination is obtained based on the combination sequence corresponding to the value whose difference from the initial equivalent damping ratio is less than the preset threshold. If no, the value whose difference from the initial equivalent damping ratio is less than the preset threshold is used as the initial equivalent damping ratio, and the requirement calculation and combination design are repeated until a metal damper combination that satisfies convergence iteration is obtained.

2. The design method for a railway beam bridge vibration reduction system based on metal damper coordination according to claim 1, characterized in that, The damping ratio of the first damper is smaller than that of the second damper, and the yield point of the first damper is higher than that of the second damper.

3. The design method for a railway beam bridge vibration reduction system based on metal damper coordination according to claim 2, characterized in that, The first damper and the second damper are equipped with shock-absorbing tenons. The damper control quantity includes the total number of dampers and the number of intervals. Constructing the combination sequence includes: based on the total number of dampers, increasing the number of the first dampers and decreasing the number of the second dampers according to the number of intervals, thereby completing the construction.

4. The design method for a railway beam bridge vibration reduction system based on metal damper coordination according to claim 3, characterized in that, After obtaining the metal damper combination that satisfies convergence iteration, the number of the first damper and the second damper in the metal damper combination is rounded down, and then it is determined again whether the rounded metal damper combination satisfies convergence iteration.

5. The design method for a railway beam bridge vibration reduction system based on metal damper coordination according to claim 2, characterized in that, The first damper and the second damper are arc-shaped dampers, and the damper control parameters include the total thickness of the damper and the spacing thickness. Constructing the combined sequence includes: increasing the first damper according to the interval thickness based on the total thickness of the damper, and decreasing the second damper, to complete the construction.

6. The design method for a railway beam bridge vibration reduction system based on metal damper coordination according to claim 1, characterized in that, The method further includes: filtering the values ​​in the combined sequence based on the first filtering condition, and performing the combined design on the filtered combined sequence; if none of the values ​​in the combined sequence meet the first filtering condition, then resetting the initial equivalent damping ratio, and re-performing the requirement calculation and combined design.

7. The design method for a railway beam bridge vibration reduction system based on metal damper coordination according to claim 6, characterized in that, The first screening condition includes: when the horizontal displacement of the first damper and the second damper increases from 50% of the seismic isolation displacement to the seismic isolation displacement, the increase in the restoring force of the target bridge is not less than 2.5% of the weight of the superstructure it bears.

8. The design method for a railway beam bridge vibration reduction system based on metal damper coordination according to claim 6, characterized in that, The method further includes filtering the values ​​in the equivalent damping ratio series based on the second filtering condition, and performing the combined design on the filtered equivalent damping ratio series; if none of the values ​​in the equivalent damping ratio series meet the second filtering condition, the seismic isolation displacement is reset, and the requirement calculation and combined design are performed again.

9. The design method for a railway beam bridge vibration reduction system based on metal damper coordination according to claim 8, characterized in that, The second screening condition includes: the value in the equivalent damping ratio series is less than a preset threshold.

10. A vibration reduction system for railway beam bridges based on metal damper coordination, characterized in that, include: Multiple metal dampers are installed between the bridge piers and the beam; the metal dampers include a first damper and a second damper; wherein the ratio of the number of the first damper and the second damper is determined by the design method described in any one of claims 1 to 9.

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