摘要
研究完全参数激励下弹性拉索与悬臂梁耦合结构的非线性动力学问题。建立索梁耦合结构力学模型,利用Hamilton原理建立索-梁耦合系统的非线性动力学方程,利用Galerkin方法将索-梁耦合系统的非线性运动偏微分方程离散为一组常微分方程。利用多尺度法分析研究索-梁耦合动力学系统的非线性振动,用Runge-Kutta法对数学模型进行数值计算,得到当梁与索的频率比为2:1时,系统发生严重的参数共振,同时探讨阻尼参数对索-梁耦合系统非线性动力学的影响,并提出对工程有实际意义的结论。
The nonlinear dynamic analysis for the coupled structure of cable-stayed beam subject to fully parametric excitation is provided. The mechanical model of cable-stayed beam is established. The non-linear partial differential equations are derived for a coupled structure of cable-stayed beam subject to fully parametric excitation by using Hamilton principle. The Galerkin method is adopted to obtain ordinary differential equations of the coupling motion in stayed system. The non-linear vibration of coupled structure is analyzed with the help of multi-scale method. By means of Runge-Kutta method, the numerical solutions of differential equations are obtained which indicate that there is serious parametric resonance when the cable-stayed beam frequency ratio is 2：1. Through the analysis of relative response curves, the damping parameters are concluded which have significant influence on the coupling vibration of the cable-stayed beam. The conclusion having actual meaning to engineering is proposed.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2009年第9期19-23,共5页
Journal of Mechanical Engineering
基金
国家自然科学基金资助项目(10372039)
关键词
参数激励
非线性振动
索梁耦合
GALERKIN法
多尺度法
Parametric excitation Non-linearvibration Coupling of cable-stayed beam Galerkinmethod Multi-scalemethod
