多档输电线非线性建模及面内自由振动分析

Nonlinear modelling and in-plane free vibrations of multi-span transmission lines

考虑边界条件和耦合连接条件,基于Hamilton变分原理,建立了多档输电线结构的精细化动力学模型。对两档输电线系统的特征值问题进行了研究;根据面内特征值方程,确定结构的模态函数,分析了垂跨比、跨度比等参数对面内固有频率的影响。研究结果表明,随着跨度比和垂度比的增大,各档之间横向振动耦合增强,模态频率会发生频率穿越现象。本文结合模态局部化因子描述体系的局部模态、整体模态、混合模态行为,输电线档间通过连续条件耦合,产生混合模态。结果表明,在Veering区和频率穿越区附近,某些频率接近相等,存在1:1内共振和2:1内共振模式。

Considering the boundary conditions and the coupling connection conditions, the nonlinear model of multi-span transmission lines are obtained based on the Hamilton principle. Moreover, the eigenvalue problem of two-span transmission lines is studied. According to the in-plane eigenvalue equations, the mode function is determined. The variation of the in-plane natural frequencies of the two-span transmission lines versus the span ratios and sag-to-span ratios are obtained. Results show that with the increase of the span ratio and the sag-to-span ratio, the coupling vibration between the transmission lines increases, and the frequency veering phenomena are occurred. The modal localized factors are used to describe the local modal, the global modal and the hybrid modal behavior of the system. The internal resonances such as 1:1 and 1:2 are discussed also.