两跨输电线非线性主共振响应分析

Nonlinear main resonance response analysis of two-span transmission lines

研究两跨输电线非线性共振响应问题,应用Hamilton变分原理推导了两跨输电线的振动微分方程以及对应的边界条件。利用Galerkin离散方法和多尺度法,得到了单模态主共振响应。研究结果表明:幅频响应曲线表现出软、硬弹簧性质,随着外激励幅值的增大,输电线系统响应由软弹簧性质向硬弹簧性质转换;系统阻尼减小或外激励幅值增大时,系统幅值个数也随之发生变化,表现出多值和跳跃现象。

In this paper,the problem of nonlinear resonance of two-span transmission lines is studied.The Hamilton differential variation principle is used to derive the differential equations and the corresponding boundary conditions of two-span transmission lines.Through the Galerkin technique,a differential equation of motion with a single degree of freedom of two span transmission lines is obtained.According to the multi-scale method,the fourth-order modal frequency and the single-mode primary resonance response are obtained.Results obtained show that the amplitude-frequency curve shows the properties of the soft and hard springs.With the increase of the external excitation amplitude,the response of the transmission line system changes from soft spring to hard spring.When the system damping decreases or the external excitation amplitude increases,the number of systemamplitudes also changes,showing multiple values and jumping phenomena.