Composite cross arm pole tower wind vibration response calculation method and device, storage medium and computer equipment

Abstract

The application discloses a composite cross arm pole tower wind vibration response calculation method and device, a storage medium and a computer device. The method comprises the following steps: establishing a tower-line coupling system finite element model of a target power transmission line; generating a random wind field time history acting on the tower-line coupling system finite element model; based on the random wind field time history, performing transient dynamics analysis on the tower-line coupling system finite element model, solving the dynamic response of the tower-line coupling system in the time domain, and taking the aerodynamic coupling effect between the wind and the tower-line coupling system into account in the analysis process; extracting time history data of key response indexes from the dynamic response; performing time domain statistical analysis on the time history data to obtain time domain analysis results, and performing frequency domain analysis on the time history data based on a power spectral density function to obtain frequency domain analysis results; and evaluating the wind vibration response characteristics of the composite cross arm pole tower according to the time domain analysis results and the frequency domain analysis results.

Description

Technical Field

[0001] This application relates to the field of wind-resistant design and structural dynamic analysis technology for transmission lines, and in particular to a method and device for calculating the wind vibration response of composite crossarm towers, a storage medium, and a computer device. Background Technology

[0002] High-voltage transmission lines are vital lifeline projects, and their structural safety directly affects the stable operation of the power system. Wind load is the main driving force causing damage and failure of transmission tower structures. Traditional angle steel transmission towers, due to their large wind-blocking area, severe wind-induced vibration response, and high requirements for the width of the transmission line corridor, exhibit significant structural defects under strong winds. In recent years, composite materials (such as glass fiber reinforced polymer GFRP) have been gradually applied to the lightweight transformation and performance improvement of transmission tower crossarms due to their advantages of being lightweight, high-strength, insulating, and corrosion-resistant, aiming to replace traditional angle steel crossarms and improve the wind resistance of the lines.

[0003] However, existing research on composite material crossarms mostly focuses on static load-bearing capacity and electrical insulation properties. There is a lack of systematic research on the dynamic response characteristics of the modified transmission tower structure under random pulsating wind loads, especially a refined evaluation method considering the coupling effect between the tower and the transmission line. Existing wind-induced vibration analysis methods either calculate the tower and conductor separately, failing to accurately reflect the dynamic characteristics of the tower-line coupled system (where tower vibration and conductor sway interact); or they use equivalent static methods, which struggle to accurately capture the structural resonance response and time-varying characteristics under high-frequency excitation by pulsating wind, leading to discrepancies between the evaluation results and actual engineering conditions.

[0004] Nevertheless, composite crossarms, due to their inherent properties such as lightweight, high strength, and insulation, have demonstrated significant advantages in reducing tower weight, shortening wind load transmission paths, and narrowing transmission line corridors. Existing static tests and preliminary analyses indicate that composite crossarms can effectively reduce conductor wind deflection and improve tower stiffness, offering potential for improving the wind resistance of transmission towers. However, due to the lack of dynamic response calculation methods that comprehensively consider stochastic wind fields and tower-line coupling effects, the quantitative improvement effect of composite crossarm retrofitting on the overall wind resistance of transmission towers has not yet been scientifically evaluated. Summary of the Invention

[0005] In view of this, this application provides a method and device for calculating the wind vibration response of composite crossarm towers, a storage medium, and a computer device. First, by using tower-line coupled modeling and stochastic wind field simulation, it overcomes the shortcomings of traditional methods that calculate the tower and line separately or use equivalent static wind to fail to reflect time-varying characteristics, making the evaluation results closer to engineering reality. Second, by using time-domain and frequency-domain dual-perspective analysis, it can identify hidden risks such as resonance, providing a precise basis for structural optimization. Third, because a complete calculation process has been established, the composite crossarm modified tower can be directly compared with the traditional angle steel tower under the same load conditions, quantitatively providing data such as conductor wind deflection reduction, tower top displacement change, crosswind shear force increment, and member axial force increase, thereby scientifically judging the wind resistance benefits (such as compression of the line corridor) and new risks (such as increased crosswind base reaction force) brought about by the modification.

[0006] According to one aspect of this application, a method for calculating the wind-induced vibration response of a composite crossarm tower is provided, comprising: A finite element model of the tower-line coupling system of the target transmission line is established, wherein the finite element model of the tower-line coupling system includes a tower model, a composite crossarm model, and a conductor model connected to the tower. A time history of a stochastic wind field is generated on the finite element model of the tower-line coupled system, wherein the stochastic wind field includes an average wind component and a fluctuating wind component, and the coherence of the fluctuating wind speed at different points in space is considered. Based on the time history of the random wind field, a transient dynamic analysis is performed on the finite element model of the tower-line coupled system to solve the dynamic response of the tower-line coupled system in the time domain, and the aerodynamic coupling effect between the wind and the tower-line coupled system is taken into account during the analysis. Time history data of key response indicators are extracted from the dynamic response, wherein the key response indicators include at least one of conductor displacement, conductor tension, tower displacement, base shear force, and member axial force. Time-domain statistical analysis is performed on the time-history data to obtain time-domain analysis results, and frequency-domain analysis based on the power spectral density function is performed on the time-history data to obtain frequency-domain analysis results. Based on the time-domain analysis results and the frequency-domain analysis results, the wind vibration response characteristics of the composite crossarm tower are evaluated.

[0007] According to another aspect of this application, a calculation device for the wind vibration response of a composite crossarm tower is provided, comprising: The model building module is used to build a finite element model of the tower-line coupling system of the target transmission line, wherein the finite element model of the tower-line coupling system includes a tower model, a composite crossarm model, and a conductor model connected to the tower. The wind field time history generation module is used to generate the time history of the random wind field acting on the finite element model of the tower-line coupled system. The random wind field includes the average wind component and the fluctuating wind component, and considers the coherence of the fluctuating wind speed at different points in space. The solution module is used to perform transient dynamic analysis on the finite element model of the tower-line coupled system based on the time history of the random wind field, solve the dynamic response of the tower-line coupled system in the time domain, and take into account the aerodynamic coupling effect between the wind and the tower-line coupled system during the analysis process. The time history data extraction module is used to extract time history data of key response indicators from the dynamic response, wherein the key response indicators include at least one of conductor displacement, conductor tension, tower displacement, base shear force, and member axial force. The wind-induced vibration response evaluation module is used to perform time-domain statistical analysis on the time history data to obtain time-domain analysis results, and to perform frequency-domain analysis on the time history data based on the power spectral density function to obtain frequency-domain analysis results. Based on the time-domain analysis results and the frequency-domain analysis results, the wind-induced vibration response characteristics of the composite crossarm tower are evaluated.

[0008] According to another aspect of this application, a storage medium is provided that stores a computer program thereon, which, when executed by a processor, implements the above-described method for calculating the wind vibration response of a composite crossarm tower.

[0009] According to another aspect of this application, a computer device is provided, including a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, wherein the processor executes the program to implement the above-described method for calculating the wind vibration response of a composite crossarm tower.

[0010] By utilizing the aforementioned technical solutions, this application provides a method and apparatus for calculating the wind vibration response of composite crossarm towers, a storage medium, and computer equipment. Firstly, through tower-line coupled modeling and stochastic wind field simulation, it overcomes the shortcomings of traditional methods that calculate towers and lines separately or use equivalent static wind to fail to reflect time-varying characteristics, making the evaluation results closer to engineering reality. Secondly, through dual-perspective analysis in the time and frequency domains, it can identify hidden risks such as resonance, providing a precise basis for structural optimization. Thirdly, due to the establishment of a complete calculation process, it can directly compare composite crossarm modified towers with traditional angle steel towers under identical load conditions, quantitatively providing data such as conductor wind deflection reduction, tower top displacement change, crosswind shear force increment, and member axial force increase, thereby scientifically judging the wind resistance benefits (such as compressed line corridors) and new risks (such as increased crosswind base reaction force) brought about by the modification.

[0011] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0012] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 A flowchart illustrating a method for calculating the wind vibration response of a composite crossarm tower according to an embodiment of this application is shown. Figure 2 A schematic diagram of a finite element model of a prototype tower provided in an embodiment of this application is shown; Figure 3 A schematic diagram of a finite element model of a modified tower provided in an embodiment of this application is shown; Figure 4 A schematic diagram of a tower-line coupled system finite element model corresponding to a prototype tower provided in an embodiment of this application is shown; Figure 5 A schematic diagram of a tower-line coupled system finite element model corresponding to a modified tower provided in an embodiment of this application is shown; Figure 6 This paper presents a comparison chart of the PSD function of a simulated fluctuating wind speed time history target according to an embodiment of this application. Figure 7 This paper presents a comparison diagram of the coherence function curves of simulated wind speed time histories at two points and the target coherence function curve, provided in an embodiment of this application. Figure 8 This paper presents a time-domain diagram of the X-direction response of a conductor mid-span displacement according to an embodiment of this application. Figure 9 This paper presents a time-domain diagram of the Z-direction response of a conductor mid-span displacement according to an embodiment of this application. Figure 10 A schematic diagram of the X-direction power spectrum of a conductor displacement provided in an embodiment of this application is shown; Figure 11 A schematic diagram of the Z-axis power spectrum of a conductor displacement provided in an embodiment of this application is shown; Figure 12 This paper illustrates a time-domain diagram of the conductor tension response provided in an embodiment of this application. Figure 13 A schematic diagram of a conductor tension power spectral density curve provided in an embodiment of this application is shown; Figure 14This paper presents a time-domain diagram of the X-direction response of a tower top displacement according to an embodiment of this application. Figure 15 This paper presents a time-domain diagram of the Z-axis response of a tower top displacement according to an embodiment of this application. Figure 16 This application provides an embodiment of a power spectral density curve of the tower top displacement in the X direction. Figure 17 This application provides an embodiment of a power spectral density curve of the tower top displacement in the Z direction. Figure 18 This paper illustrates a time-domain diagram of the X-direction shear force response provided in an embodiment of this application. Figure 19 This paper illustrates a time-domain diagram of the Z-direction shear force response provided in an embodiment of this application. Figure 20 An X-axis base shear power spectral density curve provided in an embodiment of this application is shown; Figure 21 This application provides an embodiment of a Z-axis base shear power spectral density curve. Figure 22 This application illustrates a maximum axial force in an X-direction member according to an embodiment of the present application; Figure 23 This application illustrates a maximum axial force in a Z-direction member according to an embodiment of the present application; Figure 24 This paper shows a schematic diagram of the structure of a composite crossarm tower wind vibration response calculation device provided in an embodiment of this application; Figure 25 A schematic diagram of the device structure of a computer device provided in an embodiment of this application is shown. Detailed Implementation

[0013] The present application will be described in detail below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in the embodiments of the present application can be combined with each other.

[0014] This embodiment provides a method for calculating the wind vibration response of a composite crossarm tower, such as... Figure 1 As shown, the method includes: Step 101: Establish a finite element model of the tower-line coupling system of the target transmission line, wherein the finite element model of the tower-line coupling system includes a tower model, a composite crossarm model, and a conductor model connected to the tower.

[0015] Step 102: Generate the time history of the stochastic wind field acting on the finite element model of the tower-line coupled system, wherein the stochastic wind field includes the mean wind component and the fluctuating wind component, and considers the coherence of the fluctuating wind speed at different points in space.

[0016] Step 103: Based on the time history of the random wind field, perform transient dynamic analysis on the finite element model of the tower-line coupled system, solve the dynamic response of the tower-line coupled system in the time domain, and take into account the aerodynamic coupling effect between the wind and the tower-line coupled system during the analysis.

[0017] Step 104: Extract time history data of key response indicators from the dynamic response, wherein the key response indicators include at least one of conductor displacement, conductor tension, tower displacement, base shear force, and member axial force.

[0018] Step 105: Perform time-domain statistical analysis on the time history data to obtain time-domain analysis results, and perform frequency-domain analysis on the time history data based on the power spectral density function to obtain frequency-domain analysis results. Based on the time-domain analysis results and the frequency-domain analysis results, evaluate the wind vibration response characteristics of the composite crossarm tower.

[0019] This application provides a method for calculating the wind-induced vibration response of a composite crossarm tower. First, a finite element model of the tower-line coupled system is established. The core of this step is to construct a digital model in a computer that accurately reflects the interaction between the transmission tower and the transmission line. A "finite element model" discretizes the actual structure into numerous tiny elements (such as pole elements, beam elements, and cable elements), each with distinct mechanical properties (mass, stiffness, damping, etc.). The mechanical behavior of the overall structure is then reconstructed through the connections between these elements. Traditional methods often model and calculate the tower and conductor separately, neglecting the interaction between conductor sway and tower vibration. This solution, however, models the tower, composite crossarm, and conductor as a unified system. The conductor is rigidly connected to the composite crossarm via hardware (eliminating the pendulum effect of traditional insulator strings), allowing the force and displacement generated by conductor vibration to be directly transmitted to the tower, thus laying the foundation for subsequent accurate analysis of the dynamic coupling between the tower and the conductor.

[0020] Real wind load is not a constant wind force, but a process that fluctuates randomly over time, containing a relatively stable average wind component and a high-frequency pulsating wind component. In this embodiment, based on meteorological conditions and ground roughness, an exponential law model is used to calculate the average wind speed at different heights (the higher the location, the greater the wind speed). Then, stochastic process theory (such as the harmonic superposition method) is used to generate the pulsating wind speed time history, and a spatial coherence function is introduced to describe the degree of synchronization of wind speed changes between different spatial points. For example, the wind speed at the top and bottom of a tower is not completely independent; the closer they are, the higher the correlation, and the farther they are, the lower the correlation. Finally, the average wind and the pulsating wind are superimposed to obtain a sequence of instantaneous wind speeds that continuously change over time at each simulated point, thus forming a stochastic wind field that conforms to the statistical characteristics of natural wind in both time and space.

[0021] With the time history of the stochastic wind field, the dynamic response of the structure under these wind loads can be calculated. Transient dynamic analysis involves solving the equations of motion of the structure time-by-time to obtain the displacement, velocity, acceleration, and other responses of the tower and conductor at each moment. The key here is to "incorporate the aerodynamic coupling effect": wind drives the structure to move, and the structure's motion, in turn, changes the wind load acting on it. For example, when the conductor swings in the wind, its own velocity changes the relative wind speed, thus affecting air resistance. In this embodiment, quasi-steady theory is used for the conductor, and an aerodynamic damping term related to the conductor's vibration velocity is introduced into the dynamic equation, so that the load calculation at each time step can be corrected in real time according to the current structural velocity; for the tower, the shape coefficient is determined based on the windbreak coefficient to calculate the wind load. This truly reflects the two-way interaction between wind and structure, avoiding the fragmented treatment of "wind is wind, structure is structure" in traditional methods.

[0022] After calculation, a massive amount of time history data is obtained (displacement, velocity, internal force, etc. at each node and at each moment). This application's embodiments select several categories of indicators most valuable for engineering evaluation: conductor mid-span displacement (reflecting whether the conductor will swing excessively and touch surrounding objects), conductor tension (determining whether the conductor will break or slack), tower top displacement (reflecting whether the overall stiffness of the tower is sufficient), base shear force (the horizontal force on the tower base, determining the foundation design strength), and member axial force (the tensile and compressive forces on each component, used to identify weak members), etc. The complete time history of these indicators is extracted (e.g., 20 data points per second from 0 to 120 seconds) to provide raw material for subsequent statistical analysis.

[0023] The extracted time history data includes both amplitude information and frequency information that changes over time. This application employs two parallel analysis paths: first, time-domain statistical analysis, which directly calculates the average, standard deviation, and extreme values ​​of the data. It also allows for the identification of the specific location of the maximum tension / compression force across the entire tower through envelope analysis of the axial force time history of the members, and the quantification of wind deflection amplitude through extreme values ​​or root mean square values ​​of conductor displacement to assess the compression effect of the line corridor; second, frequency-domain analysis, which involves performing Fourier transform on the time history data to obtain the power spectral density curve, identifying the main frequency components of the response, and then comparing them with the dominant frequency of pulsating wind (the frequency where wind energy is most concentrated, typically 0.1~0.2Hz) and the natural frequency of the structure itself. By combining time-domain statistics ("how strong is the vibration") and frequency-domain characteristics ("which frequency dominates the vibration"), a comprehensive assessment of the safety and dynamic characteristics of the composite crossarm tower under random wind conditions can be achieved.

[0024] By applying the technical solution of this embodiment, firstly, through tower-line coupled modeling and stochastic wind field simulation, the shortcomings of traditional methods that calculate the tower and line separately or use equivalent static wind to fail to reflect time-varying characteristics are overcome, making the evaluation results closer to the actual engineering situation; secondly, through dual-perspective analysis in the time domain and frequency domain, hidden risks such as resonance can be identified, providing a precise basis for structural optimization; thirdly, since a complete calculation process has been established, the composite crossarm modified tower and the traditional angle steel tower can be directly compared under the same load conditions, quantitatively providing data such as conductor wind deflection reduction, tower top displacement change, crosswind shear force increment, and member axial force increase, thereby scientifically judging the wind resistance benefits (such as compression of the line corridor) and new risks (such as increased crosswind base reaction force) brought about by the modification.

[0025] Optionally, in this embodiment, step 101 includes: for each conductor in the target transmission line, determining the initial alignment and initial tension of the conductor based on parabolic theory, wherein when the conductor sag-to-span ratio is less than 1 / 8, the initial alignment is described using a parabolic formula; discretizing the conductor using cable elements that can only withstand tension, and assigning the initial alignment and initial tension to the cable elements to obtain the corresponding conductor model; discretizing the tower and composite crossarm corresponding to the conductor using beam elements that can withstand bending moment, shear force, and axial force to obtain the corresponding tower model and composite crossarm model; and rigidly connecting the conductor model to the composite crossarm model through fittings to directly transmit the force and displacement generated by the conductor vibration to the composite crossarm.

[0026] In this embodiment, when establishing the finite element model of the target transmission line, the natural shape of the conductor under its own weight and initial tension can be determined first. This embodiment can use parabolic theory to describe the initial shape of the conductor. This is because when the height difference between the suspension points at both ends of the conductor is small and the sag-to-span ratio (the height difference between the lowest point of the conductor and the suspension point divided by the span) is less than 1 / 8, the shape of the conductor under its own weight can be very accurately approximated as a parabola without using the more complex catenary formula, thus significantly reducing the computational load while ensuring accuracy. Simultaneously, the initial tension of the conductor (i.e., the preload applied during installation) is given according to design specifications or actual operating conditions. This tension determines the initial slack of the conductor and its subsequent stiffness characteristics under wind load. Through this step, an initial geometric configuration and stress state conforming to the real physical state are established for each conductor, providing a correct starting point for subsequent dynamic analysis.

[0027] Once the initial alignment and initial tension of the conductor are determined, it can be transformed into a computer-calculate finite element model. For the conductor, cable elements (such as Link10 elements) capable only of withstanding tension are used for discretization. These elements cannot withstand compression or bending moment; they can only transmit tension along the axial direction, perfectly simulating the physical characteristics of a real conductor—flexible and only capable of being stretched, not compressed. When creating the cable elements, the initial alignment determined in the first step is used as the geometric coordinates of the elements, and the initial tension is assigned as the initial stress or strain of the elements, thus giving the conductor model a correct initial equilibrium state. For towers and composite crossarms, beam elements (such as Beam188 elements) capable of simultaneously withstanding bending moment, shear force, and axial force are used for discretization. This is because towers and crossarms are rigid components that must withstand not only tension and compression but also bending and shear forces. By using these two types of elements in combination, the flexible large deformation behavior of the conductor can be accurately simulated, and the rigid stress characteristics of the tower can be precisely characterized.

[0028] In traditional angle steel towers, the conductor is suspended below the crossarm by long strings of insulators, with the ends of the insulator strings hinged, allowing them to swing freely like a pendulum. This results in significant lateral swaying (wind deflection) of the conductor under wind load. However, in the composite crossarm modification scheme of this application, since the composite material itself possesses insulating properties, the independent insulator strings can be eliminated, and the conductor can be directly and rigidly connected to the composite crossarm via hardware (such as clamps or connecting plates). Here, the rigid connection means that there is no relative rotational freedom between the conductor and the composite crossarm; the force and displacement generated by the conductor vibration can be directly transmitted to the composite crossarm without buffering. This connection method, on the one hand, enhances the constraint on conductor swaying, which helps reduce the amplitude of wind deflection and compress the width of the line corridor; on the other hand, it also changes the force transmission path between the tower and the line, making the conductor vibration act more directly on the tower body. This is the physical root cause of the increased crosswind shear force found in subsequent analysis.

[0029] Compared to the traditional separate modeling of "tower + insulator string + conductor," the modeling method of this application has three significant advantages: First, it accurately sets the initial alignment and tension through parabolic theory, and through the reasonable division of labor between cable elements and beam elements, the model's static and dynamic characteristics closely match those of the real structure. Second, when the sag-span ratio is small, it uses a parabolic approximation instead of a catenary, avoiding complex nonlinear iterative solutions. Simultaneously, the use of cable and beam elements controls the computational scale while ensuring accuracy. Third, it explicitly uses "rigid connection" as a modeling feature, directly reflecting the mechanical mechanism after removing the insulator string, laying a solid model foundation for subsequent comparative analysis of the wind-induced vibration response differences between traditional and modified towers. This modeling method is not only applicable to composite crossarm towers but can also be extended to the dynamic analysis of other cable-beam composite structures.

[0030] In this embodiment of the application, step 102 may optionally include: calculating the average wind speed at different heights using an exponential law model to form a profile distribution of the average wind component along the height; describing the frequency domain energy distribution of the fluctuating wind using a fluctuating wind speed power spectral density function, and quantifying the correlation of fluctuating wind speeds between different spatial points using a spatial coherence function model to generate a fluctuating wind speed time history that meets the coherence requirement; superimposing the average wind speed at the same height with the fluctuating wind speed time history to obtain the instantaneous wind speed time history at the height; and using the instantaneous wind speed time history at each height as the time history of the stochastic wind field acting on the finite element model of the tower-line coupled system.

[0031] In this embodiment, in natural wind, the wind speed increases with altitude, a phenomenon that can be described by a mathematical model. This embodiment employs an exponential law model. This model allows for the assignment of a corresponding average wind speed to each node at different heights in the tower-line coupled system. For example, the wind speed at the top of the tower will be significantly greater than at the bottom, and wind speed differences will also exist along the conductor due to elevation variations. This creates a profile distribution where the average wind component continuously varies along the height, forming the basis for generating a complete wind field.

[0032] In addition to a stable average wind, real wind also contains a fluctuating component of random fluctuations. This application first selects a standard fluctuating wind speed power spectral density function (such as the Davenport spectrum) to describe the frequency domain energy distribution of the fluctuating wind, that is, to tell the computer how strong the wind energy is at different frequencies (low-frequency strong winds have long wavelengths and high energy, while high-frequency weak winds have short wavelengths and low energy). However, simply knowing the frequency domain characteristics of each point is insufficient, because wind speeds at different locations in space are not independent: the wind speed changes at the top and bottom of the tower exhibit a certain degree of synchronicity; the closer the distance, the higher the synchronicity, and the farther the distance, the lower the synchronicity. This spatial correlation can be quantified using a spatial coherence function model (such as the Davenport coherence function), whose inputs are the horizontal and vertical distances between two points and the wind frequency, and whose output is a coherence coefficient between 0 and 1. Based on the target power spectrum and the coherence function, using numerical techniques such as the harmonic superposition method, a set of fluctuating wind speed time histories that satisfy both their respective frequency domain energy distributions and their spatial coherence can be generated.

[0033] For any node at a specific height in a tower-line coupled system, the actual wind speed it experiences changes continuously over time. In this embodiment, the average wind speed (a constant) calculated in the first step at that height is directly added to the fluctuating wind speed time history (a curve that fluctuates over time) generated in the second step, yielding the instantaneous wind speed time history at that node. The average wind determines the basic level of wind speed, while the fluctuating wind superimposes the fluctuations around this basic level. Since the average wind is treated differently at different heights, and the fluctuating wind ensures the correlation between nodes through a coherence function, the superimposed instantaneous wind speed time history has both a correct mean profile and correct fluctuation characteristics, thus truly reflecting the randomness of natural wind.

[0034] Subsequently, the instantaneous wind speed time histories at each height node obtained in the previous step are used as the complete stochastic wind field time histories acting on the entire tower-line coupled system finite element model. This wind field is a time-varying spatial vector field; at any given moment, different heights and locations have their own wind speed values, which maintain the correct spatial correlation. As time progresses, the entire stochastic wind field time histories continuously evolve according to the simulated wind speed time histories. Subsequent transient dynamic analyses will use this wind field as the input load to calculate the dynamic response of the structure moment by moment.

[0035] Compared to traditional equivalent static wind or simple random wind assumptions, the wind field generation method of this application has three significant advantages: First, it simultaneously considers the profile distribution of the mean wind, the frequency domain energy distribution of the fluctuating wind, and the coherence of spatial points. All three dimensions are indispensable, making the simulated wind field highly consistent with the real atmospheric boundary layer wind field in terms of statistical characteristics. Second, since it generates independent and related wind speed time histories for each node, it can be directly loaded into various parts of the finite element model. It is especially suitable for structural systems with large height, long span, and significant spatial distribution, such as transmission towers, providing a real and reliable load input for subsequent accurate evaluation of the dynamic response of the tower-line coupled system under random wind.

[0036] Optionally, in this embodiment, step 103 includes: for conductor nodes, calculating the wind load of the conductor node based on the random wind field time history using quasi-steady theory, and introducing an aerodynamic damping term related to the conductor vibration velocity into the conductor dynamic equation to account for the aerodynamic coupling effect between the wind and the conductor, thereby obtaining the wind load time history of the conductor node; for tower nodes and composite crossarm nodes, determining the wind load shape coefficient based on the wind-blocking coefficient of the structural components, and calculating the wind load based on the random wind field time history and the wind load shape coefficient, thereby obtaining the wind load time history of the tower node and the composite crossarm node; using the wind load time history of the conductor node and the wind load time history of the tower node and the composite crossarm node together as excitation, and using the transient dynamics solution method to solve the time history of the finite element model of the tower-line coupled system, thereby obtaining the dynamic response of the tower-line coupled system in the time domain.

[0037] In this embodiment, for flexible structures like conductors, the force exerted by wind on the conductor cannot be simply calculated using a fixed wind speed because the vibration of the conductor itself changes its relative velocity with the air. This embodiment employs a quasi-steady theory, which assumes that at any given instant, the wind resistance on the conductor is proportional to the square of the instantaneous relative wind speed and is related to the conductor diameter and air density. The relative wind speed refers to the incoming wind speed (average wind plus fluctuating wind) minus the conductor's own vibration velocity. When the conductor oscillates with the wind, its vibration velocity can change the magnitude of the relative wind speed, thus affecting the wind load. Mathematically, this effect is represented by an additional term proportional to the velocity, namely, an aerodynamic damping term. In practice, the conductor vibration velocity is directly introduced into the wind load expression of the conductor's dynamic equation, allowing the wind load to be updated in real-time at each time step based on the current conductor velocity. The wind load time history of the conductor nodes calculated in this way includes the modulating effect of conductor vibration on the load, truly reflecting the two-way coupling between the wind and the conductor.

[0038] Unlike conductors, towers and composite crossarms are rigid structures. Their vibration velocity has a much smaller impact on relative wind speed than conductors, thus aerodynamic coupling can be ignored, but the structural shape can still accurately reflect the influence of wind load. This application's embodiments introduce a wind load shape coefficient to characterize this effect. The shape coefficient depends on the tower's windbreak coefficient, which is the ratio of the projected area of ​​the windward component to its outline area, reflecting the tower's density: the denser the filling, the more severe the leeward side is blocked by the windward side, and the smaller the overall shape coefficient. According to design specifications, the shape coefficient can be calculated using the formula... =1.3(1+ ) Calculate, where The shape coefficient is obtained by referring to a table based on the wind damming coefficient and tower depth ratio. After determining the shape coefficient, the instantaneous wind speed in the random wind field time history is substituted into the standard wind load formula. , A This represents the windward area of ​​the node. air density, V The wind speed is determined based on the time history of the random wind field. This allows us to obtain the wind load time history for each node of the tower and composite crossarm. This method conforms to power industry design specifications while ensuring computational efficiency.

[0039] Having obtained the wind load time histories for the conductor nodes and the tower and composite crossarm nodes, the next step is to apply them as external excitations to the entire tower-line coupled system finite element model to solve for the dynamic response of the system at each time step. The core of transient dynamic analysis is to solve the equations of motion of the structure step by step. Since the conductor will undergo large displacements under wind, this embodiment considers geometric nonlinearity (i.e., stiffness changes with deformation) during the solution process and uses a direct integration method (such as the Newmark method) to advance in the time domain. The final results obtained are the displacement, velocity, acceleration, and internal forces of the tower-line coupled system at each time step from the initial state, which constitute the complete time-domain dynamic response required for subsequent analysis.

[0040] In this embodiment, firstly, aerodynamic damping is incorporated into the flexible conductor to capture the coupling effect, and a standardized shape coefficient method is used for the rigid tower, ensuring both accuracy and controlling computational costs. Secondly, the wind loads of the conductor and tower are applied to the same model and solved synchronously, avoiding errors caused by traditional methods such as "calculating the tower first, then the conductor" or "equivalent static loads," and accurately capturing the mutual influence between conductor sway and tower vibration. Thirdly, the quasi-steady theory, aerodynamic damping terms, and windbreak coefficient lookup tables are all derived from mature wind engineering theories and design specifications, with parameter values ​​following established procedures, facilitating implementation by engineers. This scheme obtains a complete time-domain response, including conductor mid-span displacement, tower top displacement, base shear force, and member axial force, providing a reliable data foundation for subsequent time-frequency domain evaluation and comparison of composite crossarm modification effects.

[0041] In this embodiment of the application, optionally, when the key response indicators include member axial force and conductor displacement, step 105, "performing time-domain statistical analysis on the time history data to obtain time-domain analysis results," includes: performing envelope analysis on the member axial force time history data of each member of the tower, traversing all time steps within the analysis period, extracting the maximum axial tension and maximum axial compression of each member, and recording the time points of occurrence of each extreme value and the corresponding member position number to obtain the axial force extreme value distribution of all tower members; calculating the extreme values ​​or root mean square values ​​of the conductor displacement time history data at the mid-span node of the conductor in both the downwind and crosswind directions, quantifying the conductor wind deflection amplitude based on the extreme values ​​or root mean square values ​​to determine the compression effect of the composite crossarm on the width of the line corridor; and using the axial force extreme value distribution of all tower members and the compression effect of the composite crossarm on the width of the line corridor as the time-domain analysis results.

[0042] In this embodiment, after the transient dynamics analysis is completed, each member of the tower can generate an axial force curve that varies with time. A positive axial force indicates tension, and a negative axial force indicates compression. This embodiment performs envelope analysis on these curves. Envelope analysis involves traversing every time step within the entire analysis period to find the maximum tensile and maximum compressive force values ​​(i.e., the maximum and minimum values ​​of the axial force time history) for each member throughout the entire time history, and recording the specific time points at which these extreme values ​​occur and the corresponding member numbers. Since a transmission tower has hundreds or even thousands of members, the result of this operation is an "extreme value distribution table," clearly indicating which member at which location on the entire tower bears the greatest tensile force and which member at which location bears the greatest compressive force. The essence of this step is to extract the most engineering-significant information from massive amounts of time-domain data: the weakest link in the structure and the time when it occurs.

[0043] The mid-span of the conductor is the location with the largest swing amplitude and a key control point for determining whether wind-induced discharge or collision with surrounding objects will occur. This application extracts displacement time-history data for the mid-span node in two directions: the along-wind direction (i.e., the main direction of wind flow, usually X-axis) and the cross-wind direction (perpendicular to the direction of wind flow, usually Z-axis). For the time-history curves in these two directions, extreme values ​​(including the maximum positive and negative displacements, taking the larger of their absolute values) or root mean square (RMS) values ​​can be calculated. Extreme values ​​directly provide the maximum swing amplitude, used to determine whether the safety limit is exceeded; the RMS value reflects the average energy level of displacement fluctuations, more stably characterizing the severity of wind deflection. By comparing the displacement statistics of traditional angle steel towers and composite crossarm modified towers in the above two directions, the suppression effect of the composite crossarm on conductor wind deflection can be quantitatively determined, and the compression of the line corridor width can be calculated.

[0044] The first two steps of calculation yielded two important time-domain analysis results: the extreme distribution of axial force across all tower members, and the extreme or root-mean-square values ​​of the conductor's mid-span displacement in the along-wind and cross-wind directions, reflecting the corridor width compression effect. These two results, as the core outputs of the time-domain analysis, are passed on to the subsequent evaluation stage. The extreme axial force distribution can be used to identify whether the tower body needs local reinforcement after modification and the specific location of such reinforcement; the corridor compression effect indicates the required clearance distance between adjacent lines or between the line and surrounding obstacles, while ensuring electrical safety distances.

[0045] In this embodiment, firstly, by performing envelope analysis on each member, the most unfavorable member and its extreme stress value can be accurately located, rather than simply knowing the overall response (such as tower top displacement), thus providing clear engineering guidance for structural reinforcement; secondly, the displacement statistics in two directions at the mid-span of the conductor are specifically extracted, directly serving the core objective of the transformation—reducing the width of the line corridor—ensuring that the evaluation results are closely aligned with engineering requirements; thirdly, the extreme value distribution table generated by the envelope analysis provides directly comparable values, facilitating a point-by-point comparison between the transformed tower and the traditional angle steel tower under the same wind load, providing a solid quantitative basis for subsequent wind-resistant optimization design recommendations.

[0046] In this embodiment of the application, optionally, step 105, "performing frequency domain analysis on the time history data based on the power spectral density function to obtain frequency domain analysis results," includes: for each key response index, performing a Fourier transform on the time history data of the key response index, calculating the power spectral density function based on the Fourier transform result, and obtaining the corresponding power spectral density curve; identifying the peak frequency and energy distribution characteristics in the power spectral density curve, and comparing the peak frequency with the dominant frequency of the pulsating wind load and the natural frequency of the tower-line coupled system; obtaining a forced vibration judgment result based on the closeness between the peak frequency and the dominant frequency, and obtaining a resonance judgment result based on the closeness between the peak frequency and the natural frequency; and using the energy distribution characteristics of the power spectral density curve, the peak frequency, the forced vibration judgment result, and the resonance judgment result as the frequency domain analysis results.

[0047] In this embodiment, the time history data for each key response indicator describes the curve of the corresponding key response indicator (such as tower top displacement, conductor tension) over time. However, it is difficult to determine the frequencies at which the structure vibrates strongly based solely on this curve. To understand the vibration energy distribution from a frequency domain perspective, this embodiment first performs a Fourier transform on the time history data of each key response indicator. The Fourier transform decomposes a time-varying curve into a superposition of countless sine waves with different frequencies and amplitudes. The transformed data yields a spectrum, which provides the amplitude and phase of each frequency component. However, the spectrum does not directly express energy; in engineering, the power spectral density function is more commonly used: by squaring the amplitude of the spectrum and performing appropriate normalization, the power spectral density function can be obtained. Plotting this function with frequency as the abscissa and power spectral density value as the ordinate yields the power spectral density curve. The higher the peak value of this curve, the stronger the energy of that frequency component, and the more significant the vibration of the structure near that frequency.

[0048] Two key pieces of information can be gleaned from the power spectral density curve: first, at which frequencies the curve exhibits peaks (i.e., peak frequencies); and second, the energy distribution characteristics across different frequency bands (e.g., whether energy is concentrated in the low-frequency band or whether there are also significant peaks in the high-frequency band). Next, the peak frequencies are compared with two reference frequencies: the first reference is the dominant frequency of the pulsating wind load, i.e., the frequency at which the wind load itself has the most concentrated energy, typically around 0.1–0.2 Hz, determined by the natural characteristics of atmospheric turbulence; the second reference is the natural frequency of the tower-line coupled system, i.e., the inherent vibration frequencies of the structure itself, such as the first-order bending frequency (typically 1–2 Hz) and second-order bending frequency of the tower, which can be obtained in advance through modal analysis. By comparing the response peak frequency with these two references, the cause of the vibration can be preliminarily determined.

[0049] After comparison, two conclusions were drawn based on the proximity of the peak frequency to the reference frequency: First, if a peak frequency is very close to the dominant frequency of the pulsating wind load, it indicates that the structure is under forced vibration, which is normal, but it is necessary to confirm whether the amplitude is within a safe range. Second, if a peak frequency is very close to a certain natural frequency of the tower-line coupled system, it indicates that the energy of the wind load has just fallen into the structure's own resonance-sensitive frequency band. In this case, the structure resonates, and even if the wind load is not large, it may cause a violent vibration response, which is a risk point that requires special attention. In a specific embodiment, if the structure is dominated by forced vibration, the optimization direction can be to reduce the wind load or increase the damping.

[0050] After the above steps, four items are combined as the frequency domain analysis results: first, the energy distribution characteristics of the power spectral density curve (e.g., in which frequency band the main energy is concentrated, and whether there are multiple obvious peaks); second, the specific values ​​of one or more identified peak frequencies; third, the forced vibration judgment result based on comparison with the dominant frequency (e.g., "the response is mainly forced vibration" or "no obvious forced vibration characteristics"); and fourth, the resonance judgment result based on comparison with the natural frequency (e.g., "there is a risk of resonance" or "no risk of resonance"). Outputting these results can corroborate the time domain analysis results, jointly supporting a comprehensive evaluation of the wind-induced vibration response characteristics of composite crossarm towers.

[0051] In this application embodiment, firstly, frequency domain analysis can be used to determine whether the peak frequency coincides with the natural frequency of the structure. Even if the time domain amplitude has not exceeded the standard, potential fatigue damage or dynamic instability can be predicted in advance. Secondly, it can distinguish whether the structure is under forced vibration, thereby determining the optimization direction. Thirdly, it incorporates energy distribution characteristics into the evaluation to help engineers understand the dynamic behavior of the structure in different frequency bands. For example, whether the composite crossarm modification has changed some modal frequencies of the tower-line system, thereby leading to enhanced crosswind response.

[0052] Optionally, in this embodiment of the application, the method further includes: comparing and analyzing the time history data of various key response indicators of traditional angle steel towers and composite crossarm towers under the same wind load conditions to obtain comparative analysis results; quantifying the impact of composite crossarm modification on the reduction of conductor mid-span displacement, tower top displacement change, base shear redistribution, and member axial force increment based on the comparative analysis results; and outputting wind-resistant optimization design suggestions based on the quantified impact data, wherein the wind-resistant optimization design suggestions include at least one of the following: suggestions on the compression of the line corridor width, suggestions on the adjustment direction of tower stiffness, suggestions on the verification requirements of foundation bearing capacity, and suggestions on the strengthening position and degree of weak members.

[0053] In this embodiment, after completing all the above calculations (including modeling, wind field simulation, transient dynamics analysis, time-domain and frequency-domain analysis), a crucial comparative evaluation step is added. Specifically, for both traditional angle steel towers and towers modified with composite crossarms, under identical random wind load conditions (i.e., wind speed profile, pulsation characteristics, spatial coherence, and other parameters remain consistent), a complete set of time history data for key response indicators is calculated and extracted, including conductor mid-span displacement, tower top displacement, base shear force, and member axial force. These two sets of data are then compared item by item; for example, the conductor displacement time history of the modified tower and the traditional tower are plotted on the same graph to observe the differences in trend and magnitude. The results of the comparative analysis directly answer a core question: what quantitative changes occur in the dynamic response of the tower-conductor system after replacing the traditional angle steel crossarm with a composite material crossarm?

[0054] Based on the comparative analysis, the impact of the modification on four key indicators was further quantified: First, the reduction in conductor mid-span displacement: the percentage reduction in displacement in the downwind and crosswind directions compared to the traditional tower was calculated, directly reflecting the wind deflection suppression effect; Second, the change in tower top displacement: the tower top displacement usually decreases slightly after modification, and its rate of change can be calculated to assess the change in overall stiffness; Third, the redistribution of base shear force: the changes in base shear force in the downwind and crosswind directions were examined, especially the crosswind shear force, which may increase significantly due to the removal of insulator strings, and the increase can be quantitatively given; Fourth, the increase in axial force of members: the difference between the maximum axial tensile force and axial compressive force before and after modification, obtained through envelope analysis, was used to determine which members were subjected to increased stress. These quantitative results provide a scientific basis for engineering judgment.

[0055] With the aforementioned quantified impact data, this can be further transformed into design recommendations that can directly guide engineering practice. For example, if the conductor displacement decreases significantly, it can be suggested to compress the specific width of the line corridor (e.g., reduce it by 2-3 meters); if the tower top displacement decreases but there is still room for optimization, the direction of tower stiffness adjustment can be proposed (e.g., appropriately reducing the tower cross-section size to save materials, or conversely, increasing local stiffness); if a significant increase in crosswind base shear force is found, it should be clearly required that crosswind bearing capacity be checked during foundation design, and the traditional method of only checking the downwind direction should no longer be used; if the axial force increment of certain members exceeds the safety margin, the specific location of these weak members (through previously recorded member numbers) and the degree of reinforcement required (e.g., increasing the cross-section or replacing with higher strength steel) should be indicated.

[0056] This application not only calculates the response, but also provides how to improve the design based on the response results, thus upgrading this application from a pure analysis tool to a wind-resistant optimization design tool; it presents both the positive and negative effects of the modification with specific numerical values, avoiding the ambiguity of subjective judgment and providing a complete basis for decision-making.

[0057] Furthermore, as a refinement and extension of the specific implementation of the above embodiments, and to fully illustrate the specific implementation process of this embodiment, another method for calculating the wind vibration response of composite crossarm towers is provided. Taking a typical 500kV double-circuit transmission line as the object, the wind vibration response of a traditional angle steel tower (hereinafter referred to as the "prototype tower") and its composite material crossarm modification scheme (hereinafter referred to as the "modified tower") is calculated and compared. The design reference wind speed is 27m / s, and the ground roughness category is Class B.

[0058] (1) Establishing a finite element model: The prototype tower has a total height of 67.28m and a nominal height of 42.0m. The main structural material is Q345, and the diagonal bracing is Q235. The finite element model of the prototype tower is as follows: Figure 2 As shown. The modified tower replaces the upper, middle, and lower crossarms with double-column, double-diagonal GFRP composite crossarms, with an elastic modulus of 35 GPa and a density of 2100 kg / m³. The finite element model of the modified tower is shown below. Figure 3 As shown. The conductor spans two spans (450m + 286m), simulated using Link10 cable elements, with the initial shape determined based on parabolic theory (sag-to-span ratio 1 / 20). The prototype tower has a 5m long type I insulator string (hinged at both ends); the modified tower eliminates the insulators, and the conductor is directly rigidly connected to the composite crossarm. The tower body uses Beam188 beam elements, with fully constrained tower feet. The finite element model of the tower-line coupling system corresponding to the prototype tower is shown below. Figure 4 As shown, the finite element model of the tower-line coupled system corresponding to the modified tower is as follows: Figure 5 As shown in the figure. The remaining parameters are shown in Table 1.

[0059] Table 1. Tower body material parameters

[0060] (2) Random wind field simulation: First, wind profile: The average wind speed is described using an exponential law model:

[0061] Represents height z The average wind speed at that location; The reference height is conventionally taken as 10 m above the ground, and is usually taken from a height of 10 m. The surface roughness index, which reflects the roughness of the underlying surface, is set at 0.15 for this project, which is classified as Class B landform. z Represents the actual height; Represents reference height The average wind speed at that location.

[0062] Meanwhile, the Davenport spectrum (pulsating wind speed power spectral density function) is used to describe the downwind fluctuating wind speed power spectral density:

[0063] In the formula, , f Indicates the frequency of pulsating wind. L This represents the downwind integral scale of turbulence (usually taken as 1200m). This represents the power spectral density of fluctuating wind speed; This indicates frictional wind speed (or shear wind speed). This represents the average wind speed at a height of 10 meters.

[0064] By applying spatial correlation to pulsating winds, we can obtain the Davenport spatial coherence function:

[0065] In the formula, Represents the spatial coherence function; Indicates angular frequency; , These are the exponential decay coefficients, which are relevant for slender structures like transmission towers. Usually, 16 is chosen. Usually, 10 is taken; and They are respectively and The average wind speed at that location; )and Then ) represents the coordinates of two points in space, and the corresponding , .

[0066] Second, wind field simulation verification: The wind speed time histories at each mass point can be generated by numerical simulation from an n-dimensional random vector. , , ... If the time histories of the lateral wind speeds at the representative points in each segment are given, then the cross-spectral density matrix can be expressed as:

[0067]

[0068] Here, This represents the self-power spectral density at particle j; This represents the cross-power spectral density between particle j and particle k; Let be the power spectral density function of the fluctuating wind speed at particle j; Let be the power spectral density function of the fluctuating wind speed at particle point k; The degree of coherence of the time histories of fluctuating wind speeds at points j and k is described.

[0069] like Figure 6 As shown, a comparison chart of the PSD (power spectral density) functions of a simulated fluctuating wind speed time history target provided in an embodiment of this application is illustrated. Here, the Object PSD function is the target power spectral density function, the PSD function of simulated wind speed is the power spectral density function of the simulated wind speed, and the vertical axis represents the power spectral density function of wind speed. Figure 7 As shown, a comparison diagram of the coherence function curves of simulated wind speed time histories at two points and the target coherence function curve is presented in an embodiment of this application.

[0070] The simulated wind speed time history was generated based on the above method and compared with the theoretical time history. The verification results show that the simulated wind speed power spectrum and the target Davenport spectrum, as well as the simulated coherence function and the target coherence function, are in high agreement. The simulated wind speed time history is consistent with the target random characteristics in both the frequency domain energy distribution and spatial correlation dimensions, which can provide a reliable wind load input for the subsequent wind vibration response analysis of the tower-line coupled system.

[0071] Third, wind load simulation: To simplify the model and improve numerical computation efficiency, a single conductor was uniformly divided into 30 elements for wind speed simulation. Since the wind speed fluctuation amplitude at each node within each element is small, an equivalent wind load can be applied to the same element.

[0072] Considering large geometric deformation, the dynamic equations of the conductor under its own weight and wind load are as follows:

[0073] in, X It is the displacement vector of the conductor node. It is the corresponding velocity vector. Here, M is the corresponding acceleration vector, M is the mass matrix, and C is the mechanical damping matrix. It is a nonlinear restoring force vector. It is the vector of pulsating wind force and aerodynamic damping force. It is the static effect of mean wind and gravity. Therefore, when the time interval is less than the structure's dominant period, the structure velocity at a certain moment can be approximated as the sum of the mean wind speed and the fluctuating wind speed at that moment. It can be represented as:

[0074]

[0075]

[0076] In the formula, For the nth unit Total load at any given time; air density; According to the "Design Code for 110~750kV Overhead Transmission Lines (GB50545-2010)", the conductor resistance coefficient should be 1.2 for conductors with a diameter less than 17mm or when icing occurs, and 1.1 for conductors with a diameter greater than or equal to 17mm. The diameter of the conductor; V The average wind speed vector; The length of the line unit; for The vector wind speed of the conductor element at any given time; and They are respectively The vertical conductor direction and vertical vibration velocity component of the nth element at time n. Considering The structural vibration velocity at a given time is an unknown quantity, when the time step is... When the size is sufficiently small, an approximation can be introduced, that is, it is assumed that... and .

[0077] For the towers, the wind field time history simulation follows the treatment method of the current Chinese industry standard "Technical Specification for Design of 110-500kV Overhead Transmission Lines" (DL / T 5092-1999), limiting the aerodynamic effects of the tower-line system under strong winds to along-wind buffeting, and using quasi-steady theory for calculation. Based on the method for calculating the buffeting wind load of slender structures proposed by Dyrbye and Hansen (1996), the wind load F(t) acting on the entire structure can be derived from the wind load per unit length, and its expression is:

[0078] In the formula, air density, The node coordinates are respectively The average wind speed and fluctuating wind speed at the location. The vibration velocity of the structure; This represents the windward area of ​​the node. The wind load shape coefficient of the structure.

[0079] Wind load shape coefficient for transmission tower structure Based on the relevant processing methods in the "Technical Specification for Design of 110-500kV Overhead Transmission Lines (DL / T5092-1999)," the calculation formula is as follows:

[0080] Where η is the windbreak coefficient, the value of which can be determined according to the filling rate of the structural components. Its relationship with the filling rate is shown in the table below, and the intermediate value is determined by interpolation.

[0081] Table 2. Load Reduction Coefficient on the Leeward Side of the Tower

[0082]

[0083] Note: 1: A – Outline area of ​​the tower; As – Calculated projected area of ​​the windward component; a – Width of the windward side of the tower; b – Distance between the windward and leeward sides of the tower; 2: Intermediate values ​​can be calculated using linear interpolation.

[0084] In the calculations of this section, the aerodynamic coupling between the structure and the line is not considered for the time being, and the direction of the wind force on the transmission tower is determined. Therefore, formula (11) can be simplified to a scalar form as follows:

[0085] (3) Transient dynamic analysis: The wind speed time history is converted into nodal wind loads. Aerodynamic damping effects are considered in the conductor wind load, and the quasi-steady theory is adopted, with a drag coefficient of 1.1. The tower wind load is calculated using a simplified formula (12), and the shape coefficient is calculated as follows:μ s =1.31+ η Values, η The damping coefficient is determined based on the segmented windbreak coefficient. Large deformation is enabled in ANSYS, and a complete transient solution is used with a time step of 0.05s and a total duration of 120s. The damping ratio is set to 0.1%.

[0086] (4) Extraction and analysis of dynamic response: After the calculations are completed, the key responses of the two tower types under tower-line coupled operating conditions are extracted.

[0087] First, conductor mid-span displacement: In tower-line coupled systems, transmission lines, as typical wind-sensitive flexible components, have mid-span displacement and tension as important indicators of line safety. Based on transient dynamic analysis results, the response differences between prototype tower conductors (O-TCS) and composite tower conductors (M-TCS) are compared. Figure 8 , Figure 9 As shown, time-domain diagrams of the X-axis and Z-axis responses of a conductor mid-span displacement provided in an embodiment of this application are illustrated.

[0088] Under tower-line coupled conditions, the average X-direction displacement of the conductor suspended by the composite crossarm tower was 4.39m, while that of the prototype tower was 5.81m, a reduction of approximately 24.4%. This is because the composite crossarm combines load-bearing and insulation functions, allowing direct connection to hardware and eliminating the need for traditional insulator strings. This avoids the pendulum-like amplification effect of insulator strings under wind loads, strengthens the constraint at the conductor ends, and reduces the swing amplitude. Therefore, the composite crossarm modification can effectively reduce conductor wind deflection, thereby shortening the corridor width.

[0089] Further Fourier transform of the mid-span displacement time history yields the power spectral density curve. For example... Figure 10 , Figure 11 As shown, the X-axis and Z-axis power spectra of a conductor displacement provided in an embodiment of this application are illustrated.

[0090] The peak power spectrum of the conductor displacement mainly appears in the 0.1~0.2Hz frequency band, which is consistent with the dominant frequency of the pulsating wind load, indicating that the frequency domain characteristics of the conductor displacement response are dominated by the pulsating wind.

[0091] Second, conductor tension: The time history response of conductor tension is also given. Figure 12 A time-domain diagram of the tension response of a conductor provided in an embodiment of this application is shown.

[0092] Under tower-line coupled operating conditions, the average tension values ​​before and after the modification were 212.76 kN and 205.00 kN, respectively. Overall, the tension levels of the two tower types are similar, but the average tension value of the conductor in the composite crossarm tower is reduced by about 5% to 8% compared to the original tower, with smaller fluctuations and more stable stress.

[0093] The power spectral density curve was further obtained: Figure 13 An embodiment of this application provides a conductor tension power spectral density curve.

[0094] The power spectrum trend of conductor tension is similar to that of conductor displacement.

[0095] Third, tower top displacement: Tower top displacement is a direct reflection of the overall structural stiffness of the tower under wind load. Figure 14 , Figure 15 The diagram shows the time-domain response diagrams of the tower top displacement in the X and Z directions provided in an embodiment of this application.

[0096] As shown in the figure, the average displacement at the top of the modified tower is lower than that of the original tower, with a reduction of approximately 5.9%. The main reason is that after the composite crossarm modification, the conductor suspension point was moved inward, reducing the additional bending moment of the conductor on the tower body. At the same time, the end constraints were strengthened, changing the interaction mode between the tower and the conductor.

[0097] The power spectrum can be obtained in the same way. Figure 16 , Figure 17 The diagram shows the X-axis and Z-axis power spectral density curves of the tower top displacement provided in an embodiment of this application.

[0098] The figure shows that the power spectrum in both directions exhibits its first peak in the 0.1–0.2 Hz frequency band, corresponding to the energy concentration range of the pulsating wind load itself. Simultaneously, a smaller peak appears in the power spectrum near 1.4 Hz, which is basically consistent with the first-order natural frequency of the single tower, indicating that the structure has undergone a resonant response.

[0099] Fourth, base shear force: Base shear force is a key indicator reflecting the stress state at the bottom of the transmission tower. Figure 18 , Figure 19 The illustration shows a time-domain diagram of shear force response in the X and Z directions provided in an embodiment of this application.

[0100] The time history diagram shows that X is the principal direction of the base shear force. Under the tower-line coupled condition, the base shear force in the X direction of the prototype tower and the composite tower increases to -274.4kN and -295.3kN respectively, with little overall difference.

[0101] It is noteworthy that the average crosswind base shear force of the composite crossarm tower under coupled operating conditions reached -47.4 kN, significantly higher than the -15.6 kN of the prototype tower. This is because the insulator strings were eliminated, allowing crosswind vibration of the conductor to be transmitted more directly to the tower body through rigid connections. Therefore, although the foundation design of the composite crossarm tower still focuses on X-axis control, the crosswind base reaction force should no longer be simply ignored, especially under operating conditions where crosswind vibration of the conductor is significant, and should be specifically checked.

[0102] Figure 20 , Figure 21The illustration shows the X-axis and Z-axis base shear power spectral density curves provided in an embodiment of this application.

[0103] In the power spectrum, the composite crossarm tower has a higher peak shear force in the Z direction and more concentrated energy because it eliminates the buffering effect of the insulator string, making the force transmission path more rigid.

[0104] Fifth, axial force of members: The maximum axial tensile (compressive) force of members reflects the stress level of the most unfavorable component of the tower. Figure 22 , Figure 23 This illustration shows the maximum axial force of a member in the X and Z directions provided in an embodiment of this application.

[0105] The average maximum axial tensile force of the modified tower (493.62 kN) under operating conditions is approximately 11.3% higher than that of the original tower (443.37 kN). This may be because the removal of the insulators increases the rigidity of the force transmission path between the conductor and the tower, allowing conductor vibrations to be transmitted more directly to the tower. When coupled operation is the control condition, the modified tower should have a greater safety margin.

[0106] Conclusion: This embodiment successfully quantifies the impact of composite crossarm modification on the wind-induced vibration response of 500kV transmission towers, proving that the method can effectively evaluate the wind resistance benefits (conductor wind deflection suppression, corridor compression) and new risks (increased crosswind shear force, increased internal forces of members) brought about by the modification, and provides a complete technical solution for the wind resistance optimization design and safety assessment of composite crossarm towers.

[0107] Furthermore, as Figure 1 In terms of specific implementation, this application provides a device for calculating the wind vibration response of a composite crossarm tower, such as... Figure 24 As shown, the device includes: The model building module is used to build a finite element model of the tower-line coupling system of the target transmission line, wherein the finite element model of the tower-line coupling system includes a tower model, a composite crossarm model, and a conductor model connected to the tower. The wind field time history generation module is used to generate the time history of the random wind field acting on the finite element model of the tower-line coupled system. The random wind field includes the average wind component and the fluctuating wind component, and considers the coherence of the fluctuating wind speed at different points in space. The solution module is used to perform transient dynamic analysis on the finite element model of the tower-line coupled system based on the time history of the random wind field, solve the dynamic response of the tower-line coupled system in the time domain, and take into account the aerodynamic coupling effect between the wind and the tower-line coupled system during the analysis process. The time history data extraction module is used to extract time history data of key response indicators from the dynamic response, wherein the key response indicators include at least one of conductor displacement, conductor tension, tower displacement, base shear force, and member axial force. The wind-induced vibration response evaluation module is used to perform time-domain statistical analysis on the time history data to obtain time-domain analysis results, and to perform frequency-domain analysis on the time history data based on the power spectral density function to obtain frequency-domain analysis results. Based on the time-domain analysis results and the frequency-domain analysis results, the wind-induced vibration response characteristics of the composite crossarm tower are evaluated.

[0108] Optionally, the model building module is used for: For each conductor in the target transmission line, the initial shape and initial tension of the conductor are determined based on parabolic theory. When the sag-to-span ratio of the conductor is less than 1 / 8, the initial shape is described by a parabolic formula. The conductor is discretized using cable elements that can only withstand tension, and the initial alignment and initial tension are assigned to the cable elements to obtain the corresponding conductor model. The towers and composite crossarms corresponding to the conductor are discretized using beam elements that can withstand bending moment, shear force and axial force to obtain the corresponding tower models and composite crossarm models. The conductor model is rigidly connected to the composite crossarm model via fittings to directly transmit the force and displacement generated by the vibration of the conductor to the composite crossarm.

[0109] Optionally, the wind field time history generation module is used for: An exponential law model is used to calculate the average wind speed at different heights to form a profile distribution of the average wind component along the height. The frequency domain energy distribution of pulsating wind is described by the power spectral density function of pulsating wind, and the correlation between pulsating wind speeds at different spatial points is quantified by the spatial coherence function model in order to generate pulsating wind speed time histories that meet the coherence requirements. The instantaneous wind speed time history at the same height is obtained by superimposing the average wind speed and the fluctuating wind speed time history at the same height. The instantaneous wind speed time history at each altitude is taken as the time history of the stochastic wind field acting on the finite element model of the tower-line coupled system.

[0110] Optionally, the solution module is used for: For the conductor node, based on the random wind field time history, the wind load of the conductor node is calculated using the quasi-steady theory, and an aerodynamic damping term related to the conductor vibration velocity is introduced into the conductor dynamic equation to account for the aerodynamic coupling effect between the wind and the conductor, so as to obtain the wind load time history of the conductor node. For tower nodes and composite crossarm nodes, the wind load shape coefficient is determined based on the wind resistance coefficient of the structural components, and the wind load is calculated based on the random wind field time history and the wind load shape coefficient to obtain the wind load time history of tower nodes and composite crossarm nodes. The wind load time histories of the conductor nodes, tower nodes, and composite crossarm nodes are used together as excitations. The transient dynamic solution method is adopted to solve the time history of the finite element model of the tower-line coupled system, so as to obtain the dynamic response of the tower-line coupled system in the time domain.

[0111] Optionally, when the key response indicators include member axial force and conductor displacement, the wind-induced vibration response evaluation module is used to: Envelope analysis was performed on the time history data of axial force of each member of the tower. All time steps within the analysis period were traversed to extract the maximum axial tension and maximum axial compressive force of each member. The time points of occurrence of each extreme value and the corresponding member position number were recorded to obtain the distribution of extreme axial force values ​​of all members of the tower. Calculate the extreme values ​​or root mean square values ​​of the conductor displacement time history data at the mid-span node in both the downwind and crosswind directions, and quantify the conductor wind deflection amplitude based on the extreme values ​​or root mean square values ​​to determine the compression effect of the composite crossarm on the width of the line corridor. The extreme distribution of axial force of the entire tower members and the compression effect of the composite crossarm on the width of the line corridor are used as the time-domain analysis results.

[0112] Optionally, the wind-induced vibration response evaluation module is further used for: For each key response index, a Fourier transform is performed on the time history data of the key response index, and the power spectral density function is calculated based on the Fourier transform result to obtain the corresponding power spectral density curve. Identify the peak frequency and energy distribution characteristics in the power spectral density curve, and compare the peak frequency with the dominant frequency of the pulsating wind load and the natural frequency of the tower-line coupled system; Based on the degree of proximity between the peak frequency and the dominant frequency, a forced vibration judgment result is obtained, and based on the degree of proximity between the peak frequency and the natural frequency, a resonance judgment result is obtained. The energy distribution characteristics of the power spectral density curve, the peak frequency, the forced vibration judgment result, and the resonance judgment result are used as the frequency domain analysis results.

[0113] Optionally, the apparatus further includes a comparison module; the comparison module is configured to: The time history data of key response indicators of traditional angle steel towers and composite crossarm towers under the same wind load conditions were compared and analyzed to obtain the comparative analysis results. Based on the comparative analysis results, the effects of the composite crossarm modification on the reduction of conductor mid-span displacement, tower top displacement change, base shear redistribution, and member axial force increment were quantified. Based on the quantified impact data, wind-resistant optimization design suggestions are output, which include at least one of the following: suggestions on the compression amount of the line corridor width, suggestions on the adjustment direction of tower stiffness, suggestions on the verification requirements of foundation bearing capacity, and suggestions on the reinforcement location and degree of weak members.

[0114] It should be noted that other corresponding descriptions of the functional units involved in the composite crossarm tower wind vibration response calculation device provided in this application embodiment can be found in the following references. Figures 1 to 23 The corresponding descriptions in the method will not be repeated here.

[0115] This application also provides a computer device, which may specifically be a personal computer, a server, a network device, etc. Figure 25 As shown, the computer device includes a bus, a processor, memory, and a communication interface, and may also include an input / output interface and a display device. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database stores location information. The network interface allows communication with external terminals via a network connection. When the computer program is executed by the processor, it implements the steps in the various method embodiments.

[0116] Those skilled in the art will understand that Figure 25 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0117] In one embodiment, a computer-readable storage medium is provided, which may be non-volatile or volatile, having stored thereon a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0118] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0119] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0120] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0121] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0122] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for calculating the wind-induced vibration response of a composite crossarm tower, characterized in that, include: A finite element model of the tower-line coupling system of the target transmission line is established, wherein the finite element model of the tower-line coupling system includes a tower model, a composite crossarm model, and a conductor model connected to the tower. A time history of a stochastic wind field is generated on the finite element model of the tower-line coupled system, wherein the stochastic wind field includes an average wind component and a fluctuating wind component, and the coherence of the fluctuating wind speed at different points in space is considered. Based on the time history of the random wind field, a transient dynamic analysis is performed on the finite element model of the tower-line coupled system to solve the dynamic response of the tower-line coupled system in the time domain, and the aerodynamic coupling effect between the wind and the tower-line coupled system is taken into account during the analysis. Time history data of key response indicators are extracted from the dynamic response, wherein the key response indicators include at least one of conductor displacement, conductor tension, tower displacement, base shear force, and member axial force. Time-domain statistical analysis is performed on the time-history data to obtain time-domain analysis results, and frequency-domain analysis based on the power spectral density function is performed on the time-history data to obtain frequency-domain analysis results. Based on the time-domain analysis results and the frequency-domain analysis results, the wind vibration response characteristics of the composite crossarm tower are evaluated.

2. The method according to claim 1, characterized in that, The establishment of the finite element model of the tower-line coupled system of the target transmission line includes: For each conductor in the target transmission line, the initial shape and initial tension of the conductor are determined based on parabolic theory. When the sag-to-span ratio of the conductor is less than 1 / 8, the initial shape is described by a parabolic formula. The conductor is discretized using cable elements that can only withstand tension, and the initial alignment and initial tension are assigned to the cable elements to obtain the corresponding conductor model. The towers and composite crossarms corresponding to the conductor are discretized using beam elements that can withstand bending moment, shear force and axial force to obtain the corresponding tower models and composite crossarm models. The conductor model is rigidly connected to the composite crossarm model via fittings to directly transmit the force and displacement generated by the vibration of the conductor to the composite crossarm.

3. The method according to claim 1, characterized in that, The generation of the stochastic wind field time history acting on the finite element model of the tower-line coupled system includes: An exponential law model is used to calculate the average wind speed at different heights to form a profile distribution of the average wind component along the height. The frequency domain energy distribution of pulsating wind is described by the power spectral density function of pulsating wind, and the correlation between pulsating wind speeds at different spatial points is quantified by the spatial coherence function model in order to generate pulsating wind speed time histories that meet the coherence requirements. The instantaneous wind speed time history at the same height is obtained by superimposing the average wind speed and the fluctuating wind speed time history at the same height. The instantaneous wind speed time history at each altitude is taken as the stochastic wind field time history acting on the finite element model of the tower-line coupled system.

4. The method according to claim 1, characterized in that, The transient dynamic analysis of the tower-line coupled system finite element model based on the stochastic wind field time history is performed to solve the dynamic response of the tower-line coupled system in the time domain, and the aerodynamic coupling effect between the wind and the tower-line coupled system is taken into account during the analysis, including: For the conductor node, based on the random wind field time history, the wind load of the conductor node is calculated using the quasi-steady theory, and an aerodynamic damping term related to the conductor vibration velocity is introduced into the conductor dynamic equation to account for the aerodynamic coupling effect between the wind and the conductor, so as to obtain the wind load time history of the conductor node. For tower nodes and composite crossarm nodes, the wind load shape coefficient is determined based on the wind resistance coefficient of the structural components, and the wind load is calculated based on the random wind field time history and the wind load shape coefficient to obtain the wind load time history of tower nodes and composite crossarm nodes. The wind load time histories of the conductor nodes, tower nodes, and composite crossarm nodes are used together as excitations. The transient dynamic solution method is adopted to solve the time history of the finite element model of the tower-line coupled system, so as to obtain the dynamic response of the tower-line coupled system in the time domain.

5. The method according to claim 1, characterized in that, When the key response indicators include member axial force and conductor displacement, the time-domain statistical analysis of the time history data to obtain time-domain analysis results includes: Envelope analysis was performed on the time history data of axial force of each member of the tower. All time steps within the analysis period were traversed to extract the maximum axial tension and maximum axial compressive force of each member. The time points of occurrence of each extreme value and the corresponding member position number were recorded to obtain the distribution of extreme axial force values ​​of all members of the tower. Calculate the extreme values ​​or root mean square values ​​of the conductor displacement time history data at the mid-span node in both the downwind and crosswind directions, and quantify the conductor wind deflection amplitude based on the extreme values ​​or root mean square values ​​to determine the compression effect of the composite crossarm on the width of the line corridor. The extreme distribution of axial force of the entire tower members and the compression effect of the composite crossarm on the width of the line corridor are used as the time-domain analysis results.

6. The method according to claim 1, characterized in that, The frequency domain analysis of the time history data based on the power spectral density function, to obtain the frequency domain analysis results, includes: For each key response index, a Fourier transform is performed on the time history data of the key response index, and the power spectral density function is calculated based on the Fourier transform result to obtain the corresponding power spectral density curve. Identify the peak frequency and energy distribution characteristics in the power spectral density curve, and compare the peak frequency with the dominant frequency of the pulsating wind load and the natural frequency of the tower-line coupled system; Based on the proximity of the peak frequency to the dominant frequency, a forced vibration judgment result is obtained; and based on the proximity of the peak frequency to the natural frequency, a resonance judgment result is obtained. The energy distribution characteristics of the power spectral density curve, the peak frequency, the forced vibration judgment result, and the resonance judgment result are used as the frequency domain analysis results.

7. The method according to claim 1, characterized in that, The method further includes: The time history data of key response indicators of traditional angle steel towers and composite crossarm towers under the same wind load conditions were compared and analyzed to obtain the comparative analysis results. Based on the comparative analysis results, the effects of the composite crossarm modification on the reduction of conductor mid-span displacement, tower top displacement change, base shear redistribution, and member axial force increment were quantified. Based on the quantified impact data, wind-resistant optimization design suggestions are output, which include at least one of the following: suggestions on the compression amount of the line corridor width, suggestions on the adjustment direction of tower stiffness, suggestions on the verification requirements of foundation bearing capacity, and suggestions on the reinforcement location and degree of weak members.

8. A calculation device for the wind-induced vibration response of a composite crossarm tower, characterized in that, include: The model building module is used to build a finite element model of the tower-line coupling system of the target transmission line, wherein the finite element model of the tower-line coupling system includes a tower model, a composite crossarm model, and a conductor model connected to the tower. The wind field time history generation module is used to generate the time history of the random wind field acting on the finite element model of the tower-line coupled system. The random wind field includes the average wind component and the fluctuating wind component, and considers the coherence of the fluctuating wind speed at different points in space. The solution module is used to perform transient dynamic analysis on the finite element model of the tower-line coupled system based on the time history of the random wind field, solve the dynamic response of the tower-line coupled system in the time domain, and take into account the aerodynamic coupling effect between the wind and the tower-line coupled system during the analysis process. The time history data extraction module is used to extract time history data of key response indicators from the dynamic response, wherein the key response indicators include at least one of conductor displacement, conductor tension, tower displacement, base shear force, and member axial force. The wind-induced vibration response evaluation module is used to perform time-domain statistical analysis on the time history data to obtain time-domain analysis results, and to perform frequency-domain analysis on the time history data based on the power spectral density function to obtain frequency-domain analysis results. Based on the time-domain analysis results and the frequency-domain analysis results, the wind-induced vibration response characteristics of the composite crossarm tower are evaluated.

9. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

10. A computer device, comprising a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 7.

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