移动载荷作用下输电线路的动力响应分析

doi:10.3969/j.issn.1004-132X.2025.09.025

摘要/Abstract

摘要：

针对巡检设备对输电线路振动激励大、振动机理不明确的问题，通过研究移动载荷对输电线的动力学特性，探究其动力响应及振动规律。提出了一种三维动态非线性柔索模型，并对巡检机器人进行了动力学建模；采用联合拉格朗日-里兹法对移动载荷输电线耦合系统的动力学方程进行离散，利用MATLAB进行数值仿真，分析了非线性效应对输电线路的影响；针对移动载荷速度和输电线路安装高差的典型工况进行了仿真计算。结果表明，在移动载荷作用下，输电线呈非线性大位移特性并具有端部效应，轴向力增量的非线性因子最高达1.677；增大移动荷载速度（0.5~2 m/s），横向位移、纵向位移和轴向力增量分别增大2.4%、3.9%和4.4%，端部效应振幅分别增大140%、138%和225%；增大安装高差（0~10 m），输电线下垂距离减小，纵向位移与轴向力增量分别减小7.3%和6.2%，端部效应振频最大降低50%。研究成果可为移动载荷作用下柔索结构的相关工程设计提供理论参考。

关键词: 动力响应分析, 输电线, 移动载荷, 非线性效应

Abstract:

Given the substantial vibrational excitation caused by inspection equipment on transmission lines and unclear vibration mechanism， the dynamic characteristics of power transmission lines under the influences of moving loads was investigated to explore their dynamic responses and vibration patterns. A three-dimensional dynamic nonlinear cable model was developed， and dynamics modeling of the inspection robots was conducted. Using the combined Lagrange-Ritz method， dynamics equations of the coupled systems of moving loads and power transmission lines were discretized. Numerical simulations were performed with MATLAB to analyze the impacts of nonlinear effects on the power transmission lines. Simulations were conducted for typical scenarios involving varying speeds of moving loads and different installation height differences of the power transmission lines. The results show that under the influences of moving loads， the power transmission lines exhibit significant nonlinear large-displacement characteristics and terminal effectiveness， with a maximum nonlinearity factor for axial force increments reaching 1.677. Increase the moving load speeds（0.5~2 m/s） results in increases of 2.4%， 3.9%， and 4.4% in lateral displacement， longitudinal displacement and axial force increments， respectively， with terminal effect amplitudes increasing by 140%， 138%， and 225%. Increasing the installation height difference （0~10 m） reduces the vertical sag distance of the transmission lines， with longitudinal displacement and axial force increments decreasing by 7.3% and 6.2% respectively， and a maximum reduction in terminal effect vibration frequency of 50%. These findings provide theoretical reference for the engineering designs of similar cable structures under moving loads.

Key words: dynamic response analysis, power transmission line, moving load, nonlinear effectiveness

中图分类号:

TM75

张申廷, 雷金, 贾文兴, 张昕煜, 金鹏, 秦新燕. 移动载荷作用下输电线路的动力响应分析[J]. 中国机械工程, 2025, 36(9): 2126-2139.

Shenting ZHANG, Jin LEI, Wenxing JIA, Xinyu ZHANG, Peng JIN, Xinyan QIN. Dynamic Response Analyses of Power Transmission Lines under Moving Loads[J]. China Mechanical Engineering, 2025, 36(9): 2126-2139.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2025.09.025

https://www.cmemo.org.cn/CN/Y2025/V36/I9/2126

图/表 19

图1 自然悬垂状态下单跨输电线的一般模型

Fig.1 Model of a single-span power line in natural sag configuration

图2 架空输电线路结构示意图

Fig.2 Schematic diagram of overhead transmission line structure

图3 输电线路巡检机器人工作原理

Fig.3 Working principle of power transmission line inspection robot

图4 移动载荷作用下单跨输电线模型

Fig.4 Analytical model of a single-span power transmission line under moving load

图5 移动载荷作用下输电线系统简化模型

Fig.5 Simplified model of a power transmission line system under moving load

图6 用物理摆模拟巡线机器人

Fig.6 Physical pendulum model representation of an inspection robot

图7 作用在示例单元上的重力及惯性力

Fig.7 Gravitational and inertial forces acting on a sample unit

表1 找形计算结果

Tab.1 The results of form finding

		本文计算模型	悬链线解析解
高差 h=0	最大弧垂/m	2.496	2.233
高差 h=0	安装应力/MPa	88.7	90.0
高差 h=10 m	最大弧垂/m	1.153	1.027
高差 h=10 m	安装应力/MPa	88.7	90.0

表2 非线性效应对承载输电线所选截面最大静、动位移wmax和umax影响的比较

Tab.2 Comparison of nonlinear effects inﬂuence on maximum static and dynamic displacements wmax and umax in selected cross-sections of carrying cable

输电线截面		横向位移						纵向位移
		静力学			动力学			静力学			动力学
		$w m a x l / m$	$w m a x n l / m$	$ψ s$	$w m a x l / m$	$w m a x n l / m$	$ψ d$	$u m a x l / m$	$u m a x n l / m$	$ψ s$	$u m a x l / m$	$u m a x n l / m$	$ψ d$
高差 0	x=0.25l_c	-1.943	-1.943	1.000	-1.967	-1.997	1.015	-0.102	-0.121	1.186	-0.114	-0.132	1.158
	x=0.50l_c	-2.508	-2.486	0.991	-2.548	-2.528	0.992	-0.138	-0.152	1.102	-0.139	-0.154	1.108
	x=0.75l_c	-1.944	-1.946	1.001	-1.975	-2.002	1.014	-0.106	-0.123	1.160	-0.117	-0.134	1.145
高差 10 m	x=0.25l_c	-2.234	-2.236	1.001	-2.275	-2.283	1.004	-0.093	-0.109	1.172	-0.098	-0.112	1.143
	x=0.50l_c	-2.902	-2.861	0.986	-2.941	-2.879	0.979	-0.124	-0.138	1.113	-0.127	-0.143	1.126
	x=0.75l_c	-2.216	-2.219	1.001	-2.258	-2.262	1.002	-0.107	-0.129	1.206	-0.111	-0.132	1.189

表2 非线性效应对承载输电线所选截面最大静、动位移wmax和umax影响的比较

Tab.2 Comparison of nonlinear effects inﬂuence on maximum static and dynamic displacements wmax and umax in selected cross-sections of carrying cable

输电线截面		横向位移						纵向位移
		静力学			动力学			静力学			动力学
		$w m a x l / m$	$w m a x n l / m$	$ψ s$	$w m a x l / m$	$w m a x n l / m$	$ψ d$	$u m a x l / m$	$u m a x n l / m$	$ψ s$	$u m a x l / m$	$u m a x n l / m$	$ψ d$
高差 0	x=0.25l_c	-1.943	-1.943	1.000	-1.967	-1.997	1.015	-0.102	-0.121	1.186	-0.114	-0.132	1.158
	x=0.50l_c	-2.508	-2.486	0.991	-2.548	-2.528	0.992	-0.138	-0.152	1.102	-0.139	-0.154	1.108
	x=0.75l_c	-1.944	-1.946	1.001	-1.975	-2.002	1.014	-0.106	-0.123	1.160	-0.117	-0.134	1.145
高差 10 m	x=0.25l_c	-2.234	-2.236	1.001	-2.275	-2.283	1.004	-0.093	-0.109	1.172	-0.098	-0.112	1.143
	x=0.50l_c	-2.902	-2.861	0.986	-2.941	-2.879	0.979	-0.124	-0.138	1.113	-0.127	-0.143	1.126
	x=0.75l_c	-2.216	-2.219	1.001	-2.258	-2.262	1.002	-0.107	-0.129	1.206	-0.111	-0.132	1.189

图8 跨中横向位移线性与非线性解的比较

Fig.8 Comparison of linear and nonlinear solutions of transverse displacement in mid-span

图9 跨中纵向位移线性与非线性解的比较

Fig.9 Comparison of linear and nonlinear solutions of longitudinal displacement in mid-span

图10 跨中轴向力静力和动力增量线性与非线性解的比较

Fig.10 Comparison of linear and nonlinear solutions of static and dynamic increments of axial force in mid-span

表3 非线性效应对承载输电线所选截面轴向力最大静、动力增量影响的比较

Tab.3 Comparison of nonlinear effects influence on maximum static and dynamic increments of axial forces in selected cross-sections of carrying cable

输电线截面		静力学				动力学
输电线截面		$N 0 / k N$	$Δ N m a x l / k N$	$Δ N m a x n l / k N$	$ψ s$	$Δ N m a x l / k N$	$Δ N m a x n l / k N$	$ψ d$
高差 0	x=0.25l_c	18.071	5.237	8.557	1.634	5.206	7.615	1.463
	x=0.50l_c	18.071	4.784	6.884	1.439	4.823	6.931	1.437
	x=0.75l_c	18.071	5.242	8.563	1.634	5.210	7.617	1.462
高差 10 m	x=0.25l_c	18.023	5.018	8.414	1.677	5.106	7.482	1.465
	x=0.50l_c	18.045	4.680	6.502	1.389	4.721	6.544	1.386
	x=0.75l_c	18.090	5.036	8.423	1.673	5.126	7.523	1.468

表3 非线性效应对承载输电线所选截面轴向力最大静、动力增量影响的比较

Tab.3 Comparison of nonlinear effects influence on maximum static and dynamic increments of axial forces in selected cross-sections of carrying cable

输电线截面		静力学				动力学
输电线截面		$N 0 / k N$	$Δ N m a x l / k N$	$Δ N m a x n l / k N$	$ψ s$	$Δ N m a x l / k N$	$Δ N m a x n l / k N$	$ψ d$
高差 0	x=0.25l_c	18.071	5.237	8.557	1.634	5.206	7.615	1.463
	x=0.50l_c	18.071	4.784	6.884	1.439	4.823	6.931	1.437
	x=0.75l_c	18.071	5.242	8.563	1.634	5.210	7.617	1.462
高差 10 m	x=0.25l_c	18.023	5.018	8.414	1.677	5.106	7.482	1.465
	x=0.50l_c	18.045	4.680	6.502	1.389	4.721	6.544	1.386
	x=0.75l_c	18.090	5.036	8.423	1.673	5.126	7.523	1.468

图11 不同移动速度下跨中横向位移的比较

Fig.11 Comparison of transverse displacement in mid-span at varying moving speeds

图12 不同移动速度下跨中纵向位移的比较

Fig.12 Comparison of longitudinal displacement in mid-span at varying moving speeds

图13 不同移动速度下跨中轴向力增量的比较

Fig.13 Comparison of axial force increment in mid-span at varying moving speeds

图14 不同安装高差下跨中横向位移的比较

Fig. 14 Comparison of transverse displacement in mid- span under different installation height difference

图15 不同安装高差下跨中纵向位移的比较

Fig. 15 Comparison of longitudinal displacement in mid- span under different installation height difference

图16 不同安装高差下跨中轴向力增量的比较

Fig. 16 Comparison of axial force increment in mid-span under different installation height difference

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