双索非线性振动瞬时相位差及其来源

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (1) : 66-73.

论文

双索非线性振动瞬时相位差及其来源

孙测世1，林俊强1，邓正科2

作者信息 +

Instantaneous phase difference between nonlinear vibrations of double cables and its origin

SUN Ceshi1, LIN Junqiang1, DENG Zhengke2

Author information +

文章历史 +

摘要

为探究拉索间的同步或异步振动现象，对参数存在差异的双索的瞬时相频特性展开研究。推导了双索-质量块模型的无量纲动力学运动方程，采用伽辽金法得到离散的常微分方程，利用多尺度法进行求解。采用Runge-Kutta法和有限元法进行对比验证，三者结果均吻合良好。对不同参数双索的瞬时相位差来源进行了分析，结果表明：在某些频率范围内，高阶近似项对瞬时相位的影响不容忽略。双索的瞬时相位差来源于两个方面：一是线性解中相移值γ的差异；二是高阶近似解中漂移项占比参数𝛽的差异。

Abstract

In order to ascertain the phenomenon of synchronous and asynchronous vibration between cables, the instantaneous phase-frequency characteristics of double cables with different parameters are studied. The dimensionless dynamic equations of motion for the dual-cable-mass model were derived. The discrete ordinary differential equations were obtained using the Galerkin method and solved by the Method of Multiple Scales. The Runge-Kutta method and the Finite Element method are used parallelly to execute verification, and the results agree well with each other. The sources of the instantaneous phase difference of two cables with different parameters are analyzed, which show that the influence of high-order approximation on instantaneous phase cannot be ignored in some frequency range. The instantaneous phase difference of the double cables comes from two aspects: one is the difference in the phase shift value γ in the linear solution; the other is the difference in the proportion of the drift term parameters 𝛽 in the high-order approximate solution.

导出引用

孙测世1，林俊强1，邓正科2. 双索非线性振动瞬时相位差及其来源[J]. 振动与冲击, 2023, 42(1): 66-73

SUN Ceshi1, LIN Junqiang1, DENG Zhengke2. Instantaneous phase difference between nonlinear vibrations of double cables and its origin[J]. Journal of Vibration and Shock, 2023, 42(1): 66-73

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