周期荷载激励下覆冰输电线的主共振及谐波共振分析  

Analysis of primary resonance and harmonic resonanceof ice-coated transmission line excited by periodic load

作　　者：刘小会[1,2] 杨曙光 蔡萌琦 邹明 孙测世 LIU Xiaohui;YANG Shuguang;CAI Mengqi;ZOU Ming;SUN Ceshi(State key laboratory of Bridges and Tunnels in Mountainous Areas,Chongqing Jiaotong University,430074 Chongqing,China;College of Civil Engineering,Chongqing Jiaotong University,430074 Chongqing,China;College of Architecture and Civil Engineering,Chengdu University,610106 Chengdu,China)

机构地区：[1]重庆交通大学省部共建山区桥梁及隧道工程国家重点实验室,重庆430074 [2]重庆交通大学土木工程学院,重庆430074 [3]成都大学建筑与土木工程学院,成都610106

出　　处：《应用力学学报》2022年第1期54-64,共11页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助(No.51308570,51808085);重庆市自然科学基金资助(No.cstc2021jcyj-msxmX0166);重庆市科委基础与前沿项目资助(No.cstc2017jcyjAX0246);重庆市教委科学技术研究项目资助(No.KJ201600712182);重庆市研究生科研创新项目资助(No.CYS19240);重庆市创新训练项目资助(No.S201910618016)。

摘　　要：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。In order to study the influence of dynamic wind on the nonlinear galloping characteristics of ice-coated transmission lines,a periodic excitation load was added to the galloping govern equation of ice-coated transmission lines under the condition of stable wind,and a new forced-self-excited vibration govern equation was established.The equation is also suitable for describing the influence of adjacent gear wires on the motion characteristics of galloping gear wires.Using the method of multiple scales to solve the self-excited system under weak excitation and strong excitation,respectively,the amplitude frequency function of the primary resonance and harmonic resonance is obtained,and the primary,super-harmonic and subharmonic resonances of the forced self-excited system are analyzed.The results show that the primary resonance under weak excitation,the increase of wind speed or excitation amplitude will enhance the hard spring characteristics and nonlinear characteristics of the system.In a self-excited system under strong excitation,when the excitation frequency is close to integer multiples and fractional multiples of the natural frequency,the 2 super-harmonic resonance and 1/2 subharmonic resonance are more likely to occur.When 1/2 sub-harmonic resonance occurs,as the excitation amplitude increases,the response amplitude also increases.The tuning parameter corresponding to the resonance peak inclines to the positive axis,showing hard spring characteristics,and the increase in wind speed enhance the nonlinearity and hard spring characteristics of the system.

关 键 词：非线性振动 输电线舞动 主共振 谐波共振 

分 类 号：TM753[电气工程—电力系统及自动化]