Analysis and Experiment on Nonlinear Response through Bifurcation and Chaotic Behavior of Cables

采用理论分析和实验研究相结合的方法，对拉索的分岔和混沌非线性响应进行了研究。结果如下。（1）研究了扁垂索在轴向周期力作用下的动力稳定性。被调查的。索的运动方程用伽辽金法求解。不稳定区域首先提出了各种垂跨比和波速比。利用非线性索理论得到了不稳定运动的幅值。（2）分析了面内时变荷载作用下斜拉索通过分叉的反对称响应。采用伽辽金法求解索在对称力作用下的面内非线性运动方程。首先给出了出现反对称响应的频率范围。在此基础上，利用Runge-Kutta-Gill方法计算了非线性对称响应和不稳定区域内的反对称响应 ...更多信息 架在特定的垂跨比下，对称响应和反对称响应之间存在非线性耦合。反对称反应。（3）研究了简谐荷载作用下悬索平面线性响应的动力稳定性。运动方程表明，切向端部载荷同时产生横向响应的参数激励和外部载荷。基本方程在空间坐标系下用Galekin方法求解，在时间坐标系下用Runge-Kutta-Gill方法求解。响应曲线显示为各种垂跨比和阻尼常数。所得结果与固定支承的结果进行了比较。(4)1研究了水平拉索在均布正弦时变载荷作用下的1/2亚谐共振和1/2亚谐共振附近的混沌行为。用Galerkin方法求解了该问题。用谐波平衡法求解了1/2亚谐共振。用龙格-库塔-吉尔法分析了系统的混沌运动。结果表明，在不同垂跨比下，拉索出现1/2亚谐共振和混沌行为。少

Analysis and Experiment on nonlinear response through bifurcation and chaotic behavior of cables is analyzed by using analytical and experimental approaches. The results are as follows.(1)Dynamic stability of a flat sag cable subjected to an axial periodic force is investigated. The investigated. The equation of motion of the cable is solved by the Galerkin method. Unstable regions are presented first for various sag-to-span ratios and ratios of wave speeds. Amplitudes of unstable motions are obtained using the nonlinear cable theory.(2)Anti-symmetric response of a cable through bifurcation under in-plane symmetrictime-varying load is analyzed. The in-plane nonlinear equations of motion of a cable under symmetric forcing are solved by a Galerkin method. The frequency range where the anti-symmetric responses occur is shown at first. Then, nonlinear symmetric response and the corresponding anti-symmetric response within the unstable region are calculated by using the Runge-Kutta-Gill met … More hod. Nonlinear coupling between symmetric and and anti-symmetric responses are observed in the particular sag-to-span ratios. Antisymmetric responses in the present problem.(3)Dynamic stability of planner, linear response of a suspended cable driven by harmonic end load is presented. The equation of motion reveals that the tangential end-loading creats simultaneous parametric excitation and external loading for the transverse response. The basic equation is solved by a Galekin method in space co-ordinate and the Runge Kutta-Gill method in time co-ordinate. Response curves are shown for various sag-to-span ratios and damping constants. The results are compared with the results obtained for fixed supports.(4)1/2 subharmonic resonance and chaotic behaviors near the 1/2 subharmonic resonance of a horizontal cable subjected to uniformly distributed sinusoidally time-varying load are presented. The problem is solved by a Galerkin method. 1/2 subharmonic resonances are solved by the harmonic balance method. Chaotic motions are analyzed by the Runge-Kutta-Gill method. 1/2 subharmonic resonaces and chaotic behaviors are shown for various sag-to-span ratios of cables. Less