索-梁耦合系统非线性振动分析

Nonlinear vibration analysis for coupled structure of cable-stayed beam

研究了在惯性参考系中弹性斜拉索与悬臂梁耦合结构的非线性振动问题,利用Hamilton原理建立了索-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,然后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,同时探讨了各种参数对索-梁耦合系统非线性振动的影响,并提出对工程有实际意义的结论。

The nonlinear partial differential equations are studied for a coupled structure of a cable-stayed beam by using Hamilton＇ s principle. The Galerkin＇ s method is adopted to obtain ordinary differential equations of the coupled motion. The non-linear vibration of coupled structure is analyzed with the multi-scale method, and by means of Runge-Kutta＇ s method, the numerical solutions of the differential equations at the frequency ratio of 2 ： 1 are obtained. Through the analysis of relative response curves, the dominative factors are concluded which have significant influences on the coupled vibration of the cablestayed beam. The conclusions are useful for engineering application.