高压输电导线非线性振动分析

Response Analysis of Non-linear Vibration of High-Voltage Transmission Conductors

为研究高压输电线路导线由几何非线性引起的非线性振动特点,采用扩展的Hamilton原理建立水平悬垂输电导线的三维运动方程,并将其约化为二维振动方程,应用Galerkin方法对其进行模态截断,得到有限自由度的离散运动方程,然后使用四阶的Runge-Kutta方法对离散方程进行数值求解,得到了导线在简谐激励作用时的面内响应和面外响应.数值分析结果表明:当考虑由垂度引起的几何非线性因素时,输电导线不仅会发生主共振,还会发生次谐波共振和超谐波共振,且面外振动与面内振动之间由于发生密频内共振致使输电导线在实际振动中发生能量传递,引起非直接受激的面内产生大幅振动,同时非线性振动也会对线路振动产生调频作用.

To investigate the nonlinear vibration characteristics of high-voltage transmission conductors caused by geometrical nonlinearity, the 3D dynamical equations of the horizontal suspended transmission conductors are derived through the expanded Hamilton＇ s principle. Then the equations are reduced to 2D dynamical e- quations and are diverted into a set of ordinary differential equations through Galerkin procedure by assuming a model deflection shape. Coupled out-of-plane and in-plane responses of the conductors under harmonic exter- nal excitation are studied by means of fouth-order Runge-Kutta method. The results show that the nonlinearity produces the primary resonance, the subharmonic resonance and the superharmonic resonance. Energy transi- tion phenomena may take place between out-of-plane vibrations and in-plane vibrations because of the internal resonance due to closely spaced natural frequencies. When the out-of-plane vibration is initiated, the in-plane vibration can be excited and the response is periodic, changing the natural vibration characteristics of the sys- tem simultaneously.