内共振对斜拉索面内瞬时相频特性的影响

为研究内共振对斜拉索的瞬时相频特性的影响,利用多尺度法对拉索面内分布激励下的运动方程进行摄动求解,分别得到不计内共振和计内共振2种状态下面内主共振响应的近似解析式以及其稳态方程,最后采用Hilbert变换分别得到两者面内响应与激励的瞬时相位差及其幅值.同时在小垂度条件下,研究了不同索力下内共振对拉索面内响应与激励的瞬时...

Influence of internal resonance on in-plane instantaneous phase-frequency characteristics of stay cables

In order to study the influence of internal resonance on the instantaneous phase frequency characteristics of stay cables,the multi-scale method is used to solve the motion equation of stay cables under in-plane distributed excitation.The approximate analytical expressions of the internal main resonance response and the steady state equation are obtained under the two states of excluding internal resonance and counting internal resonance respectively.Finally,the instantaneous phase difference between the in-plane response and excitation of stay cables is obtained by Hilbert transform and its amplitude.At the same time,under the condition of Small Sag,the influence of internal resonance on the instantaneous phase difference of in-plane response and excitation under different cable forces is studied.The results show that the change of cable force will cause a sharp change of instantaneous phase difference between response and excitation,and it is more significant when internal resonance is considered.The main reason is that the internal resonance makes the frequency doubling component and the drift term caused by the out of plane response exist in the in-plane approximate solution,and the latter has a significant influence on the instantaneous phase difference,and the proportion of the drift term caused by the out of plane response in the overall drift term is the key parameter to measure the influence of the internal resonance on the instantaneous phase difference.