A method for calculating damping coefficient of large-scale shore-based crane structure under earthquake excitation

Abstract

The application discloses a large-scale quay crane structure seismic excitation damping coefficient calculation method, and belongs to the technical field of port large-scale track structure earthquake resistance; the method comprises the following steps: constructing a finite element simulation model of the quay crane structure; establishing a Rayleigh damping equation based on the finite element simulation model; extracting the first-order natural frequency of structure vibration under X direction excitation through modal analysis, and extracting the main frequency of the seismic wave through spectrum analysis on the input seismic wave; determining the damping ratio ξ of the finite element simulation model; determining two basic frequencies of the Rayleigh damping equation according to the first-order natural frequency and the main frequency of the seismic wave, wherein the first basic frequency is ω1, the second basic frequency is ω2, and n is an odd number greater than 1; and calculating the damping coefficient c according to the damping ratio and the two basic frequencies; the application considers the dynamic characteristics of the quay crane structure and the spectrum characteristics of the seismic wave, improves the accuracy of the damping coefficient calculation, and makes the seismic response simulation result more reliable.

Description

Technical Field

[0001] This invention relates to the field of seismic resistance technology for large port rail structures, specifically a method for calculating the damping coefficient of a large quay crane structure under seismic excitation. Background Technology

[0002] As a key loading and unloading equipment in ports, the seismic performance of quay cranes (shore container cranes) is of paramount importance. Due to the large size of quay crane structures, it is impossible to conduct on-site earthquake tests. Usually, a combination of finite element simulation and scaled-down model tests is used for research. In the structural seismic dynamics simulation analysis, the setting of damping parameters is one of the key difficulties. A reasonable damping coefficient directly determines the accuracy of the simulation results.

[0003] Currently, Rayleigh damping is the most commonly used damping model in engineering, and its core lies in determining the damping coefficient. and The calculation of these two coefficients essentially depends on the reasonable selection of two fundamental frequencies. In the existing technology, the method for calculating the damping coefficient of quay bridge structures mainly draws on the mature experience in the field of civil engineering, and usually selects the first two natural frequencies of the structure as the fundamental frequencies of Rayleigh damping. However, quay bridge structures and conventional civil structures have significant differences in structural form, mass distribution, stiffness characteristics, etc. Directly applying the damping coefficient calculation method of civil structures to quay bridge seismic simulation analysis will inevitably lead to large calculation errors.

[0004] Therefore, given the unique characteristics of quay bridge structures, there is an urgent need for a method specifically designed for calculating the damping coefficient of large quay bridge structures under seismic excitation, in order to improve the accuracy of seismic response simulation. Summary of the Invention

[0005] To address the inaccurate calculation of damping coefficients for quay bridge structures under seismic excitation mentioned in the background section, this invention provides a method for calculating the damping coefficients of large quay bridge structures under seismic excitation.

[0006] The above-mentioned objective of this application is achieved through the following technical solution:

[0007] A method for calculating the damping coefficient of a large quay bridge structure under seismic excitation includes the following steps:

[0008] Construct a finite element simulation model of the quay crane structure;

[0009] Based on the aforementioned finite element simulation model, the Rayleigh damping equation is established;

[0010] The first natural frequency of structural vibration under X-direction excitation was extracted by modal analysis. The input seismic waves were subjected to spectral analysis to extract their dominant frequency. ;

[0011] Determine the damping ratio ξ of the finite element simulation model;

[0012] According to the first natural frequency and seismic wave dominant frequency Determine the two fundamental frequencies of the Rayleigh damping equation;

[0013] The damping coefficient of the quay bridge was calculated based on the damping ratio and the two fundamental frequencies. and .

[0014] By adopting the above scheme, the dynamic characteristics of the structure itself (first-order natural frequency) will be... Characteristics of external excitation (dominant frequency of seismic waves) The fundamental frequency of Rayleigh damping is determined by combining the two methods. Compared with the traditional method of selecting only the first two natural frequencies of the structure, this method fully considers the energy distribution characteristics of the seismic input, so that the calculated damping coefficient can better reflect the actual energy consumption of the structure under seismic action, thereby improving the accuracy of seismic response simulation of quay bridge structures.

[0015] In a preferred embodiment, this application can be further configured such that the Rayleigh damping equation is:

[0016]

[0017] in, and Both are damping coefficients, and ξ is the damping ratio. and All of these are fundamental frequencies.

[0018] By adopting the above scheme, the specific mathematical form of the Rayleigh damping equation was clarified, and the damping coefficient ( , ) and damping ratio (ξ) and fundamental frequency ( , The equation establishes a quantitative relationship between the mass and stiffness proportionality coefficients. This equation forms the theoretical basis for subsequent calculations of the damping coefficient, providing a reliable calculation basis for back-deriving the mass proportionality coefficient and stiffness proportionality coefficient from a selected specific frequency point, thus ensuring the operability of the method.

[0019] In a preferred embodiment, this application can be further configured such that the two fundamental frequencies are:

[0020] The first natural frequency of structural vibration under X-direction excitation as well as n is greater than odd numbers, among which This is the dominant frequency of the seismic wave.

[0021] By adopting the above scheme, an odd-numbered harmonic factor n is introduced to determine the second fundamental frequency. By setting n to be greater than The smallest odd number, which not only ensures Effectively covers or is close to the dominant frequency where seismic wave energy is most concentrated. It also utilizes the characteristic that odd-numbered multiples of frequency correspond to the main bending modes of the structure; this selection method makes it possible to... to Within the frequency range, the damping ratio of the structure can be controlled within a reasonable range, avoiding overestimation or underestimation of the structural damping.

[0022] In a preferred embodiment, the damping ratio can be further configured to be 0.05.

[0023] By adopting the above scheme, the damping ratio ξ is set to 0.05. This value strictly follows the relevant standards such as the "General Code for Seismic Design of Cranes" and the engineering experience of vibration energy dissipation of steel structures in the elastic stage, ensuring the standardization and universality of the basic parameters in the calculation of the damping coefficient, so that the calculation results are comparable and have reference value in different projects.

[0024] In a preferred embodiment, this application can be further configured such that the finite element structural model is a model with a scale of 1:20 to the original model of the quay bridge.

[0025] By adopting the above scheme, a 1:20 scaled finite element model is used. This scale matches the common scaled shaking table model test, which not only greatly reduces the scale of simulation calculation and improves the computational efficiency, but also facilitates direct comparison and verification of simulation results with subsequent physical model test data, thereby enhancing the credibility and practicality of the simulation analysis method.

[0026] In a preferred embodiment, this application can be further configured such that: the fundamental frequency of structural vibration under X-direction excitation is obtained using modal analysis. Specifically, it includes:

[0027] Modal analysis was performed on the finite element simulation model to extract the natural frequencies corresponding to each mode shape;

[0028] The mode shape with the largest participation coefficient under X-direction excitation is selected, and its natural frequency is determined as the fundamental frequency. .

[0029] By adopting the above scheme, the "mode participation factor" was introduced as a screening criterion in modal analysis. Since the lowest-order frequency of a complex structure may not correspond to the main vibration direction, the frequency corresponding to the mode shape with the largest participation factor in the X-direction (the main direction of earthquake damage) was selected as the mode shape. This ensures that the selected frequency has a clear physical meaning and accurately represents the most important vibration mode of the structure under seismic excitation, avoiding calculation deviations caused by selecting the wrong vibration mode.

[0030] In a preferred embodiment, this application can be further configured such that: the extraction of the dominant frequency of the seismic wave through spectral analysis of the input seismic wave is performed. Specifically, it includes:

[0031] Acquire the acceleration time history signal of the input seismic wave;

[0032] The acceleration time history signal is subjected to Fourier transform to obtain the spectral distribution of the seismic wave;

[0033] The frequency corresponding to the peak amplitude in the spectral distribution is determined as the dominant frequency of the seismic wave. .

[0034] By employing the above scheme, Fourier transform is used to perform spectral analysis on the acceleration time history signal of the input seismic wave, accurately identifying the dominant frequency corresponding to the peak energy of the seismic wave. The frequency domain characteristics of external loads are transformed from qualitative "spectral characteristics" to quantitative "dominant frequency parameters," providing key technical support for the subsequent accurate incorporation of seismic motion characteristics into damping coefficient calculations.

[0035] The second objective of this invention is achieved through the following technical solution:

[0036] A device for calculating the damping coefficient of a large quay bridge structure under seismic excitation includes:

[0037] The model building module is used to build finite element simulation models of quay crane structures.

[0038] The damping equation construction module is used to establish the Rayleigh damping equation based on the finite element simulation model.

[0039] The frequency extraction module is used to obtain the fundamental frequency of structural vibration under X-direction excitation using modal analysis methods. The dominant frequency of the seismic wave was extracted by performing spectral analysis on the input seismic wave. ;

[0040] The control frequency determination module is used to determine the frequency based on the base frequency. and seismic wave dominant frequency Determine the two control frequencies of the Rayleigh damping equation;

[0041] The damping coefficient calculation module is used to calculate the damping coefficient of the quay bridge based on the damping ratio and two control frequencies. and .

[0042] By adopting the above technical solution, and through the collaborative work of the model building module, damping equation building module, frequency extraction module, control frequency determination module, and damping coefficient solution module, the entire process from model establishment to coefficient solution is automated, reducing the complexity of manual calculation and facilitating engineers to quickly and accurately obtain damping parameters suitable for seismic analysis of large quay bridges.

[0043] The above-mentioned objective three of this application is achieved through the following technical solution:

[0044] A device for calculating the damping coefficient of a large quay bridge structure under seismic excitation includes: a processor and a memory;

[0045] The memory stores a computer-readable program that can be executed by the processor;

[0046] When the processor executes the computer-readable program, it implements the steps in the method for calculating the damping coefficient of a large quay bridge structure under seismic excitation as described in any one of claims 1-7.

[0047] The fourth objective of this application is achieved through the following technical solution:

[0048] A computer-readable storage medium storing one or more programs that can be executed by one or more processors to implement the steps in the method for calculating the damping coefficient of a large quay bridge structure under seismic excitation as described in any one of claims 1-7.

[0049] In summary, this application includes at least one of the following beneficial technical effects:

[0050] 1. Abandoning the conventional method in the field of civil engineering that only selects the first two natural frequencies of a structure, this paper for the first time selects the first natural frequency of a structure under X-direction excitation (…). ) and the dominant frequency of seismic waves ( The fundamental frequency of Rayleigh damping is determined by combining the following: an odd harmonic factor (n greater than 1) is introduced. Determine the second fundamental frequency ( This allows the calculation of the damping coefficient to take into account both the dynamic characteristics of the structure itself and the spectral characteristics of the external seismic input, improving the consistency between the simulation results and the shaking table test data under large, medium and small earthquakes, with the error controllable within 10%.

[0051] 2. In view of the differences in mass distribution and stiffness characteristics between quay bridge structures and conventional civil structures, the mode frequency with the largest participation coefficient in the X direction (perpendicular to the direction of the trolley track) is selected as the fundamental frequency, and the main frequency of seismic waves is introduced as a constraint condition. This effectively avoids the phenomenon of "overdamping" or "underdamping" caused by directly applying the damping calculation method of civil structures.

[0052] 3. A 1:20 scaled finite element model matching the shaking table test was adopted, and spectrum analysis was performed based on measured seismic wave data. This allowed the damping coefficient obtained from the simulation calculation to be directly applied to the pre-analysis and post-correction of the model test, thus constructing a closed-loop R&D system of "simulation guiding test and test verifying simulation". This improved the reliability and economy of the seismic design of large quay bridge structures while reducing the number of physical tests. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating an embodiment of the method for calculating the damping coefficient of a large quay bridge structure under seismic excitation according to this application.

[0054] Figure 2 This is a schematic diagram of the finite element simulation model of a large quay bridge structure for calculating the damping coefficient under seismic excitation, as described in this application.

[0055] Figure 3 This is a schematic diagram of an embodiment of a damping coefficient calculation device for a large quay bridge structure under seismic excitation according to this application. Detailed Implementation

[0056] The following is in conjunction with the appendix Figure 1-3 This application will be described in further detail.

[0057] In one embodiment, such as Figure 1 As shown, this application discloses a method for calculating the damping coefficient of a large quay bridge structure under seismic excitation, which specifically includes the following steps:

[0058] S10: Construct a finite element simulation model of the quay crane structure.

[0059] In this embodiment, the quay crane (quayside container crane) is mainly composed of a trolley traveling mechanism, gantry structure, front and rear beams, tie rod system, machine room, traveling trolley and spreaders, etc. The gantry structure specifically includes sea-side and land-side gantry legs, columns, upper and lower crossbeams, gantry frame crossbeams and tie rods, etc. The finite element simulation model refers to the numerical calculation model of the quay crane structure established using the finite element method, which is used to simulate the dynamic response of the quay crane under actual seismic excitation.

[0060] Specifically, a 3D simulation model of the quay crane structure was established using Abaqus finite element software. The modeling process is as follows: The main components, such as the portal legs, columns, upper and lower crossbeams of the portal frame, and front and rear main beams, were modeled using beam elements. The specific cross-sectional dimensions of each component were edited in the software preprocessing and assigned to the corresponding elements. The trapezoidal frame struts, portal frame struts, and front and rear tie rods were modeled using rod elements. The machine room, trolley and spreader, and containers were simplified as concentrated masses and simulated by applying loads to specified nodes. The connections between the front and rear main beams of the quay crane, the connections between the upper crossbeam lugs and tie rods of the trapezoidal frame, and the connections between the lugs and tie rods of the front and rear main beams were simulated by releasing the rotational degrees of freedom at the corresponding nodes. The stiffeners, partitions, and other components arranged in the box girder were uniformly distributed as additional masses in the overall structure in the model. The quay crane trolley system model was replaced by equivalent beam elements of the same length and stiffness.

[0061] Furthermore, the finite element simulation model described in this embodiment is a model established at a 1:20 scale with the original quay crane model; using a scaled-down model can effectively reduce the scale of simulation calculations and improve computational efficiency while ensuring dynamic similarity.

[0062] S20: Based on the finite element simulation model, establish the Rayleigh damping equation.

[0063] In this embodiment, the Rayleigh damping equation is an expression describing the mathematical relationship between the damping coefficient and the frequency. It is a commonly used damping model in structural dynamics analysis. Damping is the characteristic of a system to gradually reduce the amplitude of vibration due to its own or external factors. When a certain amount of energy is input into the structure, it will cause vibration. If the external energy input stops, the structure will experience vibration decay until the vibration stops. Damping is a parameter that reflects the irreversible dissipation of energy during the vibration process of the system.

[0064] Specifically, the Rayleigh damping equation established in this embodiment is:

[0065] Where α and β are damping coefficients, ξ is the damping ratio, and ω1 and ω2 are the fundamental frequencies; this equation reflects the relationship between the damping ratio, frequency, and damping coefficients, and is the basis for subsequent solutions to the damping coefficients.

[0066] Although damping force is much smaller than inertial force and restoring force in numerical terms, damping is the most critical and difficult problem to solve in structural dynamics. The existence of damping prevents the amplitude of the system at resonance from being amplified indefinitely, and can also reduce the destructive effect of earthquakes on structures through seismic isolation and damping design, and dissipate the energy input by earthquakes by utilizing the internal damping of materials.

[0067] When using Rayleigh damping for dynamic analysis, only two mode shapes and their corresponding frequencies can be selected to solve the two algebraic equations to determine the coefficients α and β. Once the damping ratios and corresponding frequencies of the two mode shapes are selected, the damping ratios of other mode shapes can be calculated using their corresponding frequencies. Therefore, the calculation of coefficients α and β is essentially the selection of mode shapes. Selecting appropriate mode shapes and their corresponding frequencies will yield the most reasonable α and β.

[0068] S30: Extracting the first natural frequency of structural vibration under X-direction excitation through modal analysis. The input seismic waves were subjected to spectral analysis to extract their dominant frequency. .

[0069] In this embodiment, the first-order natural frequency refers to the lowest-order natural vibration frequency of the structure during free vibration, reflecting the most fundamental dynamic characteristics of the structure. The dominant frequency of the seismic wave refers to the frequency component where the seismic wave energy is most concentrated, usually corresponding to the frequency corresponding to the largest amplitude in the Fourier amplitude spectrum.

[0070] Specifically, modal analysis was performed on the finite element simulation model, and the natural frequencies corresponding to each mode shape were extracted using the Block Lanczos method. The extraction frequency range was set to 0-100Hz, and the number of mode shapes extracted was no less than 20. In the post-processing results, the mode shape with the largest participation coefficient under X-direction excitation was selected, and its corresponding natural frequency was taken as the first natural frequency ω1. Studies have shown that the main seismic component causing the failure of the quay bridge structure is in the X direction (perpendicular to the direction of the trolley track). Therefore, selecting the first natural frequency in the X direction as one of the fundamental frequencies can accurately reflect the main dynamic characteristics of the structure under seismic action.

[0071] Acceleration time history signals of the input seismic waves are acquired, with a sampling frequency of not less than 100Hz to ensure signal integrity. A Fast Fourier Transform is performed on the acceleration time history signals to obtain the spectral distribution curve of the seismic waves. The frequency corresponding to the maximum amplitude in the spectral distribution curve is identified as the dominant frequency of the seismic waves. This frequency represents the frequency component where earthquake energy is most concentrated and has a significant impact on structural response.

[0072] S40: Determine the damping ratio ξ of the finite element simulation model.

[0073] In this embodiment, the damping ratio refers to the ratio of actual damping to critical damping, which is a dimensionless parameter characterizing the vibration decay rate of a structure.

[0074] Specifically, since it is usually assumed that the damping ratios corresponding to lower-order vibration modes are the same when performing general seismic response characteristic analysis on the pontoon bridge structure, the damping ratio is selected as 0.05 according to relevant specifications and engineering experience.

[0075] S50: Based on the first natural frequency and seismic wave dominant frequency The two fundamental frequencies of the Rayleigh damping equation are determined.

[0076] In this embodiment, the fundamental frequency refers to the two characteristic frequencies used in the Rayleigh damping equation to solve for the damping coefficient. The appropriateness of their selection directly determines the accuracy of the damping coefficient. Studies have shown that under the combined action of bidirectional horizontal earthquakes, the peak acceleration at each measuring point is slightly higher than that under unidirectional horizontal earthquakes, but the curve trends are the same. This indicates that the Z-direction (vertical) earthquake component has a certain influence on the dynamic response of the main vibration direction of the structure, but the influence is very small and can be ignored. Therefore, in selecting the fundamental frequency in this embodiment, the main earthquake direction that causes structural damage—the X-direction—is mainly considered. This simplifies the calculation model, grasps the main contradiction, and ensures the calculation accuracy.

[0077] Specifically, the two fundamental frequencies are: the first fundamental frequency is the first natural frequency of structural vibration under X-direction excitation. The second fundamental frequency is where n is greater than odd numbers, The dominant frequency of the seismic wave is n; the selection principle for n is to take a value greater than 1. The smallest odd number, chosen in this way It not only covers the frequency components near the dominant frequency of seismic waves, but also ensures the correspondence with the main vibration modes through odd harmonics. Since odd harmonics usually correspond to the main bending vibration modes of the structure and contribute more to the seismic response of the structure, this selection method can more comprehensively reflect the dynamic characteristics of the structure under seismic loading.

[0078] S60: Calculate the damping coefficient of the quay crane based on the damping ratio and the two fundamental frequencies. and .

[0079] In this embodiment, the damping coefficient and These are two undetermined parameters in the Rayleigh damping model, corresponding to the mass proportional damping coefficient and the stiffness proportional damping coefficient, respectively.

[0080] Specifically, the two fundamental frequencies , Substituting the damping ratio ξ into the Rayleigh damping equation:

[0081] ξ = / (2 ) + ( ) / 2

[0082] ξ = / (2 ) + ( ) / 2

[0083] Solving the above system of equations simultaneously will yield the damping coefficient. and ;

[0084] and The value can also be calculated using the following formula:

[0085] .

[0086] Where, ξ m ω m These are the damping ratio of the m-th mode and its corresponding natural frequency, respectively; ξ n and ω n These are the damping ratio of the nth mode and the corresponding natural frequency, respectively.

[0087] After obtaining α and β, the damping ratios of other vibration modes can be solved using the following formula:

[0088]

[0089] When using Rayleigh damping for dynamic analysis, only the damping ratio and frequency of two vibration modes can be selected to solve the two algebraic equations in the formula to determine the coefficients. , Once the damping ratios and corresponding frequencies of two vibration modes are selected, the damping ratios of other vibration modes can be calculated using their corresponding frequencies; coefficients , The calculation essentially involves selecting the mode shape; choosing a suitable mode shape and its corresponding frequency yields the most reasonable result. , .

[0090] This calculation method takes into account both the frequency characteristics of the structure and the spectral characteristics of seismic motion, and avoids overestimating or underestimating the structure's performance. and Within a certain range, setting the calculated damping coefficient in finite element software can yield time history response results that are closer to the actual situation.

[0091] In one verification embodiment, a shaking table seismic simulation test was used to verify the damping coefficient calculation method of the present invention; the dynamic response data and simulation calculation results of key measuring points in the test show that:

[0092] When the peak acceleration is 0.22g (small earthquake), the simulation results are similar under different damping coefficients and are close to the experimental values.

[0093] When the peak acceleration is 0.4g (moderate earthquake), the simulation calculation results obtained by the damping coefficient method of this invention are the best match with the experimental values, and the error with the experimental values ​​is the smallest under two different types of quay bridges and various different seismic excitations.

[0094] When the peak acceleration is 0.62g (major earthquake), only the simulation calculation results obtained by the damping coefficient method of this invention have an error of less than 10% compared with the experimental values.

[0095] The above verification results show that the damping coefficient calculation method provided by the present invention has high accuracy and reliability under different earthquake intensities, and its advantages are more significant under large earthquakes.

[0096] In one embodiment, in step S20, the Rayleigh damping equation is:

[0097]

[0098] in, and Both are damping coefficients, and ξ is the damping ratio. and All of these are fundamental frequencies.

[0099] In this embodiment, the equation is a damping model commonly used in time history analysis of structural dynamics; the damping matrix is ​​constructed by a linear combination of the mass matrix and the stiffness matrix, where the coefficients... and This is the ultimate goal of this method; the equation establishes the functional relationship between the damping ratio ξ and the frequency ω, which will be used in subsequent steps by selecting a specific frequency point ( , The damping ratio (ξ) is used to inversely deduce the coefficient. and Provides a theoretical basis.

[0100] In one embodiment, in step S50, the two fundamental frequencies are respectively:

[0101] The first natural frequency of structural vibration under X-direction excitation as well as n is greater than odd numbers, among which This is the dominant frequency of the seismic wave.

[0102] In this embodiment, the dominant frequency of the seismic wave is... Introduced to the second fundamental frequency In the selection. By introducing a value greater than An odd multiple of the factor n, such that = n· Able to "cover" or "approach" the dominant frequency where seismic wave energy is concentrated ; in the and Determined damping coefficient and This ensures that the damping ratio of the structure is controlled within a reasonable range (close to the preset 0.05) in the frequency band near the dominant frequency of seismic waves, thus simulating the seismic response more realistically.

[0103] In one embodiment, the damping ratio is 0.05.

[0104] In this embodiment, the value of the damping ratio ξ is usually determined based on specifications or experimental experience. For steel structure quay bridges, when performing seismic response analysis, according to relevant standards such as the "General Code for Seismic Design of Cranes" and a large amount of engineering practice experience, the damping ratio of the low-order vibration mode is usually taken as 0.05 (5%). This is a recognized typical value that can represent the vibration energy dissipation capacity of steel structures in the elastic stage. This method adopts this value to ensure the universality and comparability of the calculation results.

[0105] In one embodiment, such as Figure 2 As shown, the finite element structural model is a model with a scale of 1:20 to the original model of the quay crane.

[0106] In this embodiment, establishing a 1:20 scaled model is a conventional practice for shaking table testing. On the one hand, the original-size quay bridge is too large to be directly tested on a shaking table. On the other hand, under the conditions of geometric similarity, mass similarity, and dynamic similarity (such as frequency similarity), the dynamic response of the scaled model can be converted back to the original structure through the similarity ratio. Using the scaled model for simulation can significantly reduce the complexity of modeling and the consumption of computing resources, and can also be easily verified with the results of subsequent scaled model shaking table tests, making the simulation method more convincing.

[0107] In one embodiment, in step S30, the fundamental frequency of the structural vibration under X-direction excitation is obtained using modal analysis. ,include:

[0108] Modal analysis was performed on the finite element simulation model to extract the natural frequencies corresponding to each mode shape;

[0109] The mode shape with the largest participation coefficient under X-direction excitation is selected, and its natural frequency is determined as the fundamental frequency. .

[0110] In this embodiment, modal analysis is a standard method for obtaining the natural frequencies and mode shapes of a structure; the participation factor measures the degree to which a certain mode shape is excited under excitation in a specific direction (such as the X direction); for complex structures such as quay cranes, the mode shape corresponding to its first natural frequency may not be the main vibration mode in the X direction (for example, it may be oscillation or torsion in the Y direction), so simply selecting the mathematically "first" frequency is inaccurate. By calculating the participation factor of each mode shape in the X direction and selecting the one with the largest participation factor, the selected mode shape is ensured to be effective. It is indeed the frequency corresponding to the most important vibration mode of the structure when the seismic motion is input in the X direction, and its physical meaning is clearer.

[0111] In one embodiment, in step S30, that is, extracting the dominant frequency of the seismic wave by performing spectral analysis on the input seismic wave. Specifically, it includes:

[0112] Acquire the acceleration time history signal of the input seismic wave;

[0113] The acceleration time history signal is subjected to Fourier transform to obtain the spectral distribution of the seismic wave;

[0114] The frequency corresponding to the peak amplitude in the spectral distribution is determined as the dominant frequency of the seismic wave. .

[0115] In this embodiment, seismic waves are a complex stochastic process containing multiple frequency components; the dominant frequency represents the frequency band where seismic wave energy is most concentrated and most likely to induce structural resonance; by converting the time-domain acceleration signal into a frequency-domain spectrum using Fourier transform, the distribution of energy at different frequencies can be visually observed; the frequency corresponding to the highest amplitude point (i.e., energy peak) in the spectrum is the dominant frequency of the seismic wave. Incorporating external excitation characteristics into the calculation of the damping coefficient is the key difference between this method and traditional methods.

[0116] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0117] In one embodiment, a device for calculating the damping coefficient of a large quay bridge structure under seismic excitation is provided. This device corresponds one-to-one with the method for calculating the damping coefficient of a large quay bridge structure under seismic excitation described in the above embodiment. Figure 3 As shown, the damping coefficient calculation device for a large quay bridge structure under seismic excitation includes:

[0118] The model building module is used to build finite element simulation models of quay crane structures.

[0119] The damping equation construction module is used to establish the Rayleigh damping equation based on the finite element simulation model.

[0120] The frequency extraction module is used to obtain the fundamental frequency of structural vibration under X-direction excitation using modal analysis methods. The dominant frequency of the seismic wave was extracted by performing spectral analysis on the input seismic wave. ;

[0121] The control frequency determination module is used to determine the frequency based on the base frequency. and seismic wave dominant frequency Determine the two control frequencies of the Rayleigh damping equation;

[0122] The damping coefficient calculation module is used to calculate the damping coefficient of the quay bridge based on the damping ratio and two control frequencies. and .

[0123] Specific limitations regarding the device for calculating the damping coefficient of a large quay bridge structure under seismic excitation can be found in the above-described method for calculating the damping coefficient of a large quay bridge structure under seismic excitation, and will not be repeated here. Each module in the aforementioned device for calculating the damping coefficient of a large quay bridge structure under seismic excitation can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0124] In one embodiment, a device for calculating the damping coefficient of a large quay bridge structure under seismic excitation is provided, comprising: a processor and a memory; the memory stores a computer-readable program that can be executed by the processor; when the processor executes the computer-readable program, it implements the steps in the method for calculating the damping coefficient of a large quay bridge structure under seismic excitation as described in the above embodiment.

[0125] In one embodiment, a computer-readable storage medium is provided that stores one or more programs that can be executed by one or more processors to perform the steps in the method for calculating the damping coefficient of a large quay bridge structure under seismic excitation as described in the above embodiments.

[0126] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A method for calculating the damping coefficient of a large quay bridge structure under seismic excitation, characterized in that, Includes the following steps: Construct a finite element simulation model of the quay crane structure; Based on the aforementioned finite element simulation model, the Rayleigh damping equation is established; The first natural frequency of structural vibration under X-direction excitation was extracted by modal analysis. The input seismic waves were subjected to spectral analysis to extract their dominant frequency. ; Determine the damping ratio ξ of the finite element simulation model; According to the first natural frequency and seismic wave dominant frequency Determine the two fundamental frequencies of the Rayleigh damping equation; The damping coefficient of the quay bridge was calculated based on the damping ratio and the two fundamental frequencies. and .

2. The method for calculating the damping coefficient of a large quay bridge structure under seismic excitation according to claim 1, characterized in that, The Rayleigh damping equation is as follows: in, and Both are damping coefficients, and ξ is the damping ratio. and All of these are fundamental frequencies.

3. The method for calculating the damping coefficient of a large quay bridge structure under seismic excitation according to claim 2, characterized in that, The two fundamental frequencies are as follows: The first natural frequency of structural vibration under X-direction excitation as well as n is greater than odd numbers, among which This is the dominant frequency of the seismic wave.

4. The method for calculating the damping coefficient of a large quay bridge structure under seismic excitation according to claim 3, characterized in that, The damping ratio is 0.

05.

5. The method for calculating the damping coefficient of a large quay bridge structure under seismic excitation according to claim 1, characterized in that, The finite element structural model is a model with a scale of 1:20 compared to the original model of the quay bridge.

6. The method for calculating the damping coefficient of a large quay bridge structure under seismic excitation according to claim 1, characterized in that, The fundamental frequency of structural vibration under X-direction excitation is obtained using modal analysis. Specifically, it includes: Modal analysis was performed on the finite element simulation model to extract the natural frequencies corresponding to each mode shape; The mode shape with the largest participation coefficient under X-direction excitation is selected, and its natural frequency is determined as the fundamental frequency. .

7. The method for calculating the damping coefficient of a large quay bridge structure under seismic excitation according to claim 1, characterized in that, The method involves extracting the dominant frequency of the input seismic wave through spectral analysis. Specifically, it includes: Acquire the acceleration time history signal of the input seismic wave; The acceleration time history signal is subjected to Fourier transform to obtain the spectral distribution of the seismic wave; The frequency corresponding to the peak amplitude in the spectral distribution is determined as the dominant frequency of the seismic wave. .

8. A device for calculating the damping coefficient of a large quay bridge structure under seismic excitation, characterized in that, include: The model building module is used to build finite element simulation models of quay crane structures. The damping equation construction module is used to establish the Rayleigh damping equation based on the finite element simulation model. The frequency extraction module is used to obtain the fundamental frequency of structural vibration under X-direction excitation using modal analysis methods. The dominant frequency of the seismic wave was extracted by performing spectral analysis on the input seismic wave. ; The control frequency determination module is used to determine the frequency based on the base frequency. and seismic wave dominant frequency Determine the two control frequencies of the Rayleigh damping equation; The damping coefficient calculation module is used to calculate the damping coefficient of the quay bridge based on the damping ratio and two control frequencies. and .

9. A device for calculating the damping coefficient of a large quay bridge structure under seismic excitation, characterized in that, include: Processor and memory; The memory stores a computer-readable program that can be executed by the processor; When the processor executes the computer-readable program, it implements the steps in the method for calculating the damping coefficient of a large quay bridge structure under seismic excitation as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores one or more programs, which can be executed by one or more processors to implement the steps in the method for calculating the damping coefficient of a large quay bridge structure under seismic excitation as described in any one of claims 1-7.

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