索受外激励作用下索拱结构非线性动力学分析

NONLINEAR DYNAMICS OF CABLE-STAYED ARCH UNDER CABLES SUBJECTED TO EXTERNAL EXCITATION

研究索拱结构中索受外激励作用下索拱之间非线性动力学问题.利用已建立的索拱结构非线性动力学耦合面内运动微分方程,采用Galerkin方法把索拱结构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索主共振情况下的平均方程,研究在索受到外激励作用下索振动对拱的振动产生的影响,同时对索拱结构内共振时的稳定、分叉及混沌情况进行了分析.结果表明:索某阶频率与拱某阶频率接近时可能出现内共振现象,能量在索拱之间相互传递,原本静止的拱也可能出现共振现象,共振频域区间内索拱振动将出现跳跃、分叉及混沌等复杂的非线性动力学行为.

The nonlinear dynamics of the cable-stayed arch under cables subjected to external excitation was investigated. The coupling nonlinear dynamics equations of the cable-stayed arch derived by using Hamilton principle were used. First ,the Galerkin method was used to discrete the nonlinear equation of planar motion. Then the method of multiple scales was applied to perturb the discrete equations of motion, and the averaged equation under the primary resonances of cables was obtained. The impact of the vibration of cables over the vibration of arch under cables subjected to external excitation was studied ,and the equilibrium solution ,the period solution and chaotic solution of averaging equations were examined. The analysis results indicate that the internal resonance of the cable-stayed arch possibly appears when the frequency of cables approaches close to the frequency of arch, the energy is transferred mutually between cables and arch, and the cable-stayed arch presents complicated nonlinear dynamics behavior such as leap ,bifurcation and chaos within the resonance frequency region.