考虑气动力作用的载流覆冰导线主共振及谐波共振分析

针对载流导线的非线性振动问题,在以往只考虑安培力的载流导线振动方程中引入了气动荷载。在此基础上进一步引入了受迫激励荷载,以研究动态风或相邻档导线对载流覆冰导线非线性振动特征的影响,建立了一种新的气动力-安倍力-受迫激励联合作用下的载流覆冰导线系统。推导出非线性振动方程,利用Galerkin方法将该振动方程转变为有限维度的常微分方程,采用多尺度法求解得到系统的非线性受迫主共振和亚谐波共振的幅-频响应函数。通过数值计算,分析了参数变化对系统受迫共振响应的影响以及受迫主共振定常解的稳定性。结果表明,考虑气动力的振动幅值和系统非线性较未考虑气动力时更小和更弱;线路参数的变化对导线的响应幅值和系统的非线性都有一定程度的影响;主共振和亚谐波共振的响应幅值随着激励幅值的增大而增大,共振峰值向着调谐参数σ的负值方向偏移,呈现出软弹簧特征并伴随着多值和跳跃现象;主共振时,随着调谐参数的变化,响应幅值则出现同步和失步现象。

Analysis of primary resonance and harmonic resonance of current-carrying iced conductors with considering aerodynamic forces

Aiming at the problem of nonlinear vibration of current-carrying conductors,the aerodynamic forces were introduced into the previous vibration equation of current-carrying conductors that only considered Ampere'' s forces.On this basis,in order to study the influence of dynamic wind on the nonlinear vibration characteristics of current-carrying iced conductors,an excitation load was further introduced,and a new nonlinear vibration system of current-carrying iced conductors under the combined action of ampere''s forces,excitation forces and aerodynamic forces was established.The nonlinear vibration equation was derived,and the vibration equation was transformed into a finite dimensional ordinary differential equation by using the Galerkin method.The amplitude-frequency response functions of the primary resonance,super and sub-harmonic resonance were obtained by using the multi-scale method.Through numerical calculation,the influences of parameters on the forced resonance of the system and the stability of the steady-state solutions of the primary resonance were analyzed.The results show that the response amplitudes under the action of aerodynamic forces are smaller and the nonlinear system is also weaker than without considering the action of aerodynamic forces;the change of line parameters has a certain influence on the response amplitudes and the nonlinearity of system;as the excitation amplitudes increase,the response amplitudes of the primary resonance and sub-harmonic resonance will increase,and the tuning parameter corresponding to the resonance peak will offset towards the negative axis,showing the characteristics of soft spring and the response amplitudes display multi-values and jump.The nonlinearity of the system is also enhanced with the increase of wind velocity.In the primary resonance,with the changes of tuning parameter,synchronization and loss of step appear in the response amplitudes.