Flow-induced self-excited vibration may exhibit high-frequency numerical oscillations and chaotic-like responses in long-duration simulations due to strong nonlinearity and multimodal coupling. In this study, a two-node cable finite element model incorporating torsional degrees of freedom, nonlinear aerodynamic forces, and geometric nonlinearity is developed to evaluate the long-term computational performance of the Newmark average acceleration method and the Bathe composite integration scheme. Simulations are conducted for weakly nonlinear, transitional nonlinear, and near 1:1 internal resonance regimes. The results show that, as the degree of nonlinearity increases, the Newmark method produces more pronounced non-principal high-frequency components, a more scattered distribution of Poincar & eacute; points, and larger deviations from the expected principal-mode-dominated beating response. These observations indicate that, under the present model and discretization conditions, the chaotic-like response obtained by the Newmark method is strongly affected by non-principal high-frequency contamination. In contrast, the response computed by the Bathe method remains stably governed by the two dominant frequencies associated with the near-resonant beating mechanism. The results indicate that, for the long-duration nonlinear galloping problems considered in this study, appropriate algorithmic dissipation can reduce non-principal high-frequency disturbances and improve the interpretability of the numerical results.

Achieving an optimal balance among computational efficiency, robustness, and accuracy is a central challenge in simulating second-order nonlinear dynamical systems. While the existing parameterized two-sub-step composite integrator provides rigorous nonlinear stability and controllable dissipation, its fixed-step formulation limits efficiency in simulations with strongly varying dynamics. This paper presents a novel adaptive time integration method that augments the second-order base scheme with an explicit auxiliary stage for efficient error estimation. Its key innovation is a cost-free, direct error estimator, constructed by rigorously deriving the embedding coefficients via order conditions and analytically combining the implicit base stages with an extrapolated explicit stage to derive a local error estimate based on a third-order embedding without additional nonlinear iterations or matrix operations. Combined with a proportional-integral-derivative-like step-size controller, systematic numerical tests show that the proposed method achieves a significantly better computational cost-to-accuracy trade-off than highorder algebraically stable singly diagonally implicit Runge-Kutta methods. The algorithm demonstrates strong robustness in stiff and large-scale nonlinear problems while preserving the unconditional nonlinear stability and controllable dissipation of the base scheme. In summary, the proposed adaptive method offers an efficient, reliable, and self-starting tool for simulating largescale, long-duration, strongly nonlinear systems.

This paper presents an independently developed finite element analysis software built on the QT and VTK platforms. Its core innovation is the integration of the analytical solution from catenary theory with nonlinear finite element methods. The software accurately predicts the initial configuration and tension distribution of conductors based on catenary theory, utilizing these results as high-precision initial values for static equilibrium iterations. This approach overcomes the convergence difficulties commonly encountered in traditional commercial software when analyzing such flexible cable structures. Using this software, we systematically investigated the nonlinear effects of asymmetric span arrangements on the mean value and standard deviation of wind deflection angles, and subsequently established a practical wind deflection calculation model that accounts for span asymmetry. The study reveals that higher wind speeds lead to larger wind deflection angles, with static wind deflection angles approximating the mean values under pulsating wind conditions. When one span length is fixed, the wind deflection angle first increases and then decreases as the adjacent span length increases. Symmetrical span arrangements were found to amplify the fluctuation range of the wind deflection angles. The research further developed polynomial regression models to systematically analyze the influence of wind speed and span length on dynamic amplification factors and elucidate their interactions and nonlinear relationships. Finally, based on symbolic regression and least squares methods, three expressions for the dynamic amplification factor in terms of span length and wind speed were derived. These formulas all demonstrate certain engineering applicability for predicting the dynamic amplification factor.

The vortex-induced vibration characteristics of transmission conductors under wind fields constitute a critical factor influencing structural safety. This study establishes a three-dimensional fluid-structure interaction numerical model based on the large eddy simulation method, systematically investigating the two-degree-of-freedom vibration characteristics of transmission conductors in pulsating wind fields. The vibration process evolves through four distinct stages: initial small-amplitude steady state, frequency-locked large-amplitude state, transitional modulation phase, and ultimately nonlinear chaotic stage under high wind speeds. The research reveals that within specific parameter ranges of reduced wind speed (4 < U-r < 5) and transverse displacement amplitude ratio (0.7 < A(y) < 1) identified as the transition zone of vortex wake modes, the wake flow exhibits unique unsteady characteristics. This transition in vortex shedding patterns triggers significant fluid-structure interaction effects, resulting in substantial enhancement of alongwind displacement. Analysis of aerodynamic work shows that drag force performs predominantly positive work during lock-in and nonlinear stages, sustaining streamwise motion, while lift force does negative work at crosswind peaks, limiting lateral excursions. These findings clarify the multi-stage evolution of vortex-induced vibration, elucidate the wake-driven mechanism of high-amplitude vibration, and quantify the complementary roles of shear-layer instability and phase-dependent lift/drag work in governing conductor dynamics.

The fracture speed of a high-grade gas pipeline subjected to high gas pressure is usually very high, such that the gas pressure near the crack-tip could not decompress rapidly. It is difficult for a high-grade pipeline to arrest crack propagation by itself; hence, an arrestor should be installed to prevent the pipeline from fracturing continuously. Because the optimization of the geometric size of the arrestor has not been well-recognized at present, it is of interest to study the dependence of crack arresting ability on arrestor size and obtain a satisfactory method to design the geometric size of the arrestor. Based on Hill's yield theory and a plastic strain-dependent damage evolution law, a transversely isotropic elastic-plastic damage model is established. The mechanical responses of X80 pipeline material under static and dynamic loadings were successfully simulated by the proposed constitutive law. Using the cohesive zone model, the high-speed dynamic fracture and crack arresting ability of the X80 gas pipeline were simulated. The dependences of crack arresting ability on the thickness and length of the arrestor were numerically investigated. The simulation results showed that the crack arresting performance increases significantly with the thickness of the arrestor. The satisfactory geometrical size of an arrestor is economically suggested.

The phenomenon of galloping in transmission lines has long been a topic of significant interest, and establishing an accurate galloping model is highly challenging. Consequently, the sparse identification of nonlinear dynamics (SINDy), Integral SINDy (ISINDy), and Weak SINDy (WSINDy) algorithms are employed to directly identify galloping models from data. A theoretical mechanical model is established for different degrees of freedom (DOFs), using the galloping of iced quad bundle conductors as an illustrative example. Simulated data obtained from the theoretical model are utilized to perform parameter identification of the galloping model using the three algorithms. For the 1-DOF and 2-DOF galloping models, the data is preprocessed using the Hodrick-Prescott (H-P) filter method, and then the parameter identification effects of the three algorithms are compared under different noise levels. The parameter identification effects of the three algorithms for the 3-DOF galloping model are analyzed using noise-free data, while also comparing their robustness across different data lengths. The research findings demonstrate that the WSINDy algorithm exhibits high accuracy and robustness in the parameter identification process of galloping models with varying DOF, surpassing the performance of the SINDy and ISINDy algorithms. The identification models play a crucial role in validating anti-galloping designs and formulating anti-galloping plans in engineering applications.

In cold climates, the damage to the transmission tower-line system is usually caused by ice shedding, broken conductors, and broken ground wires. To replicate the ice shedding and broken conductor scenarios more accurately and expeditiously within the transmission tower-line system, we have engineered a finite element computational program leveraging the co-rotational theory method, utilizing the C++ programming language. Additionally, we have orchestrated its visualization interface utilizing the QT and Visualization Toolkit (VTK) platforms. This program can accurately and rapidly simulate large displacement geometric nonlinear problems. An ice detachment criterion considering the combined acceleration is proposed. Compared with previous judgment criteria, the criterion proposed in this article can adapt to the previous prediction accuracy and is more efficient in calculation. A finite element method for disconnection simulation of “node failure” was proposed, and its accuracy and computational efficiency were verified by comparison with experiments. By analyzing the coupling effect of disconnection and deicing in the tower line system, it is concluded that ground wires often have a stronger deicing effect than conductors. Although broken conductor will cause large-scale ice shedding from the span, the impact on the most dangerous point of the tower will be very small, this providing a theoretical basis for ice-covered broken conductor in the tower-line system. The simulation method proposed in this article also provides a new research idea for the simulation of ice shedding and broken conductor of tower-line systems.

Ensuring the safe operation of transmission line engineering is an important means to achieve efficient energy transportation. However, with the frequent occurrence of extreme weather, transmission line operation faults caused by icing and ice-shedding often occur. In order to obtain the initial weightless configuration of the transmission line quickly and accurately, and realize the nonlinear simulation of the dynamic response of ice-covered conductor ice-shedding, the catenary theory is used to obtain the configuration of the conductor under gravity. The elastic deformation of the conductor under gravity is calculated based on the theory of linear elasticity, and then the original length of the conductor without gravity is obtained. Based on the original length, the corresponding finite element model is established, and the dynamic response of the ice-covered conductor under ice-shedding load is calculated by the implicit dynamic method. Combined with the example verification, the ice-shedding amplitude is in good agreement with the experimental results, which verifies the accuracy and practicability of this form-finding method and the simulation method of ice-covered and ice-shedding.

The galloping of iced conductors is a serious threat to the safe operation of power systems. Establishing an accurate galloping model of iced conductors has always been a difficult point in galloping research. Therefore, the sparse identification of nonlinear dynamics (SINDy) algorithm is used to identify the galloping model from noise measurement data. A theoretical model of galloping of iced quad bundle conductors is established. Meanwhile, the algorithm is used to identify the simulated data of the theoretical model. The parameter identification ability of the algorithm under noisy velocity measurement is analyzed. An excellent denoising method was selected for data preprocessing, and then the model identification effect of the algorithm after data preprocessing is studied. Besides, the accuracy of the prediction model based on this algorithm and the support vector regression (SVR) prediction model under different training data lengths are compared. The results show that the model identified by the SINDy algorithm in the noise measurement data after data preprocessing has high accuracy and robustness. Moreover, the amount of data used is small. The model identified by this algorithm plays an important role in the rapid investigation, prediction and early warning of galloping phenomena.

[Introduction] The galloping of transmission lines will lead to trip, worn hardware, broken insulator string, damaged tower-arm and other accidents. In serious cases, collapsed tower accidents may occur. Therefore, it is very meaningful to establish the galloping model of transmission lines and analyze its galloping. [Method] Classic and cutting-edge literature at home and abroad was systematically studied, and the research status about bending stiffness, aerodynamic coefficient, numerical simulation, and the analytic method of galloping equations was comprehensively summarized. The advantages and disadvantages of existing research was analyzed, and the development trend of transmission lines galloping topics was summarized here. [Result] The relevant results will have high reference value for the development of iced transmission lines galloping in China. [Conclusion] At this stage, the research of iced transmission lines galloping has made certain progress and conclusions, but there are still many challenges and problems to be solved.

The galloping of ice-covered transmission lines will cause conductor strand breakage and phase-to-phase flashover, even serious safety accidents such as tower toppling. In this paper, the nonlinear vibration system is studied mainly by the analytical method. Firstly, based on the Hamilton's principle, the governing equations for iced conductor galloping are derived, then through matlab, the law of amplitude change of each equation is simulated and shown as different images for analysis. The results show that the period of vibration in three directions is constant after stabilization, and the amplitude will eventually reach a stable maximum, and when the amplitude in one direction reaches the maximum, the other direction will also reach the maximum amplitude soon.

As an important part of transmission lines, preformed helical fitting plays an indispensable role in the safe and stable operation of electronic circuits. However, due to the poor service environment of transmission lines, preformed helical fitting can often slip, scatter, and detwist. This paper explores variations in the holding force of the preformed helical fitting under different geometric parameters. First, the geometric structure of preformed helical fitting is analyzed, and the secondary development is conducted using the ABAQUS finite element software. The script program is written in Python language to realize the parametric modeling. Based on the experimental results, the changing trend of the holding force is consistent, which confirms the correctness of the finite element model. In addition, the preformed helical fitting is studied under different values of molding aperture, pitch length, pitch number, and armor rod diameter, and changes in the holding force under different parameters are analyzed. The results show that the holding force of the preformed helical fitting increases with the decrease in the molding aperture and pitch length, and the molding aperture has a negative linear correlation with the overall holding force. The holding force increases linearly with the pitch number; so, reducing the pitch length can increase the holding force of preformed helical fitting. Moreover, the results indicate that the holding force increases with the armor rod diameter. The research results presented in this study have important guiding value for the design of performed helical fitting.

为了研究动态风对覆冰输电线非线性舞动特征的影响,在原有稳定风作用下覆冰输电线舞动控制方程中添加周期激励载荷,并建立了新的受迫-自激振动控制方程,该控制方程也适用于描述相邻档导线对舞动档导线运动特征的影响。运用多尺度法分别对弱激励和强激励下的受迫-自激振动求解,得到主共振和谐波共振的幅频响应函数,分析了|受迫-自激系统的主共振、超谐波和亚谐波共振。研究表明:弱激励下的主共振,当调谐参数大于0时,风速或激励幅值的增加会使得响应幅值出现跳跃、多值等不稳定的非线性动力学行为,并呈现硬弹簧特征;强激励下的自激系统，当激励频率接近固有频率的整数倍和分数倍时,更容易出现2次超谐波共振和1/2次亚谐波共振;当发生1/2次亚谐波共振时,随着激励幅值的增大,响应幅值也不断增大,共振峰值对应的调谐参数趋向于正轴方向,呈现硬弹簧特征,风速的增加会增强系统的非线性和硬弹簧特征。

With the increase of transmission line mileage and more frequent occurrence of extreme weather, the possibility of transmission line galloping is also increasing. The nonlinear dynamic equation of transmission line is established in this paper. This equation is combined with the modal superposition method. The theoretical analysis of the transmission line is carried out by the multi-scale method, and the analytical solution of the nonlinear vibration of the iced conductor is obtained. Finally, the multi-scale solution is carried out by applying the nonlinear aerodynamic load. The results show that the multi-scale method can effectively reflect the nonlinear vibration characteristics of conductor on time scale. According to the multi-scale theory, the approximate solution of nonlinear galloping of iced conductor can be obtained. This result has important application value for the prediction of transmission line galloping tension and galloping amplitude, which is helpful for the design of transmission line anti-galloping.

Because of their superior mechanical properties, preformed helical fittings are widely used in UHV transmission lines. However, they easily slip and become loose under extreme environments, so it is very important to study the fastening characteristics of preformed helical fittings. According to the stress characteristics of preformed helical fittings, a parametric finite element model including a core and preformed armor rods was established. Finally, the finite element model calculation was verified by comparing it with the test results. In this paper, the influences of the preformed armor rod diameter, pitch, length and forming aperture on the fastening characteristics were investigated. The numerical simulation results showed that the smaller the forming aperture of preformed armor rods, the larger the grip force. However, a small forming aperture is inconvenient to install, and too large of a grip force on the core easily leads to core damage. With the increase in the preformed armor rod length, the grip force increased gradually and linearly, and the increase slowed after the pitch number reached 9. The larger the pitch, the smaller the grip force of the preformed helical fittings. The fastening characteristics of preformed armor rods with slightly larger diameters were better and the fourth power of the diameter of the preformed armor rods has a linear relationship with the grip force.

A full multispan two-degree-of-freedom (2-DOF) iced covered transmission line model is presented. Taking multispan conductors as the research object, based on the Hamiltonian principle, a nonlinear galloping model of multispan conductors considering the influence of insulator strings is established, and its galloping equation is derived. Based on the theoretical formula, the modes and frequencies in-plane and out-of-plane of the multispan conductor plane were obtained. After the partial differential equation was transformed into an ordinary differential equation by the Galerkin discrete method, the multiple scale method was used to solve the dynamic response of the multispan conductors. Through numerical calculations, this study is the first to systematically analyze the effects of parameters such as span number, span length, and tension on the in-plane and out-of-plane motion characteristics of multi-span conductors from a theoretical perspective. The research results in this paper have certain reference value for preventing multispan conductor galloping and interphase flashover.

As the key connecting components between tower and conductors, electric power fittings play an important role in the provision of the safe operation of transmission lines. Taking 500kV transmission lines as the research object, electric power fittings failure in heavy icing areas is studied. The following three questions are considered: first, the influence of different ice-shedding methods on the tension of quad bundle conductors; second, the influence of the spans number, span length, height difference, and ice thickness on the conductor tension under the most dangerous ice-shedding mode; lastly, the mechanical characteristics of tension string and suspension string under ice-shedding condition in the stable wind. The results show that the von Mises stress of the parts that connect with the iced conductor in the tension string model is greater than those of the parts connected with the ice-shedding conductor. What is more, the shackle is the most vulnerable part of the whole model, which is prone to wear and damage, and the failure is most likely to occur at the upper shackle. The middle part in the rectangular hanging plate which is connected with the iced conductor is prone to damage, for its maximum stress has already exceeded the yield stress, with a danger degree inferior only to the shackle. In the suspension string model, the von Mises stress of each part is relatively small and does not reach the yield stress. Similarly, the shackle is most likely to be damaged in the overall model, while other parts maintain larger safety margins. The structure of the parts with smaller stress can be optimized according to the simulation results where design margins may be reduced and additional cost benefits realized.

预绞式金具作为输电线路的重要部件,可起到保护输电线路安全运行的作用.由于预绞式金具形成的内径小于导线直径,会产生预紧力作用.本文借助ABAQUS有限元软件采用等效降温法、ODB导入法和过盈接触法赋予耐张型预绞式金具一个预紧力,模拟单根耐张型预绞式金具缠绕在导线上的不同工况,基于数值仿真结果研究了不同预应力施加方式对耐张型预绞式金具紧固性能的影响.结果表明:应力最大值出现在耐张型预绞式金具施加荷载的端部;节距增加,过盈法中的精确过盈量逐步减小,降温法设置的降温数值减小;采用降温法时无论何种工况下耐张型预绞式金具的仿真握力值最大,能为预应力的模拟提供参考.

为了进一步提高预绞式金具的安全性,采用有限元方法分析了影响预绞式金具紧固特性的关键因素,得出预绞丝半径、节距、长度、摩擦系数和材料性质是预绞式金具设计中重要的参数.基于预绞丝的空间几何理论,编写Python程序实现了参数化建模,研究预绞丝设计参数对预绞丝与导线之间的接触应力和抗拔力的影响规律.结果表明:增大单根预绞丝的半径、增加预绞丝长度,其抗拔作用显著;减小单根预绞丝的节距,导线和预绞丝间接触较好,其抗拔效果明显;选用弹性模量较大的材料也能提高预绞丝抗拔性能.