时滞影响下受控斜拉索的参数振动稳定性

Parametric Vibration Stability of Controlled Stay Cables With Time Delays

研究了轴向激励作用下受控斜拉索系统主参数共振的时滞效应,考虑了拉索垂度和几何非线性的影响,基于Hamilton变分原理建立了受控斜拉索系统轴向激励下的非线性参数振动方程,利用Galerkin方法得到时滞动力系统,运用多尺度法对受控系统的主参数共振进行了分析,得到了不同时滞值、控制增益时参数振动稳定域和受控拉索的时程曲线.研究表明,时滞影响下斜拉索振动控制系统的效果变差,参数共振的稳定域发生偏移,对受控斜拉索系统的控制效果随着时滞的增大而变差,从而对控制系统的参数设计起到指导作用.

The effects of time delays on the primary parametric vibration of controlled stay cables under axial excitation were studied.In view of cable sag and geometric nonlinearity-the nonlinear parametric vibration equation for the controlled stay cable system under axial excitation was built based on the Hamiltonian principle.Then the dynamic system with time delay was formulated by means of the Galerkin method.The multi-scale method was used to analyze the primary parametric resonance of the controlled stay cable system and obtain the effects of different time delays and control gains on the time histories of the parametric vibration and the stability region of the controlled stay cable.The study shows that time delay weakens the vibration controlling effects on the stay cable-and the stability region of the parametric vibration is shifted.The larger the time delay is-the worse the controlling effects will be.The work plays a guiding role in the parametric design of the control system for stay cables.