悬索在考虑1:3内共振情况下的动力学行为

研究了悬索在受到外激励作用下考虑1∶3内共振情况下的两模态非线性响应.对于一定范围内悬索的弹性-几何参数而言,悬索的第三阶面内对称模态的固有频率接近于第一阶面内对称模态固有频率的三倍,从而导致1∶3内共振的存在.首先利用Galerkin方法把悬索的面内运动方程进行离散,然后利用多尺度法对离散的运动方程进行摄动得到主共振情况下的平均方程.接下来对平均方程的稳态解、周期解以及混沌解进行了研究.最后利用Runge-Kutta法研究了悬索两自由度离散模型的非线性响应.

DYNAMIC BEHAVIOR OF SUSPENDED CABLES WITH ONE-TO-THREE INTERNAL RESONANCES

The two-mode nonlinear response of the suspended cable subjected to external excitation with one-to-three internal resonance is investigated.The natural frequency of the third symmetric in-plane mode is approximately three times as large as the natural frequency of the first symmetric in-plane mode for a range of geometry-elasto parameter,resulting in a one-to-three internal resonance.Firstly,the Galerkin method is used to discrete the governing equation to a discrete form of the equations of motion.Then the method of multiple scales is applied to attack the equations of motion leading to averaging equations.The equilibrium solution,the period solution and chaotic solution of averaging equations are examined in this paper.Finally,the non-linear response of the two-degree-of-freedom discretized model is investigated by using the Runge-Kutta algorithm.