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

采用分析与实验相结合的方法，对索的分岔非线性响应和混沌行为进行了分析与实验。结果如下：(1)研究了轴向周期性力作用下扁平垂拉索的动力稳定性。的调查。用伽辽金法求解了索的运动方程。首先给出了不同垂跨比和波速比的不稳定区域。利用非线性索理论得到了不稳定运动的幅值。(2)分析了面内对称时变荷载作用下索通过分岔的反对称响应。用伽辽金法求解了索在对称受力作用下的平面内非线性运动方程。首先给出了发生反对称响应的频率范围。然后，利用龙格-库塔-吉尔法计算了不稳定区域内的非线性对称响应和相应的反对称响应。在特定的垂跨比下，观察到对称和反对称响应之间的非线性耦合。本问题中的反对称响应。(3)给出了谐波端部负载驱动下悬索规划器线性响应的动态稳定性。运动方程表明，切向端载荷对横向响应同时产生参数激励和外载荷。在空间坐标系下用伽辽金法求解，在时间坐标系下用龙格-库塔-吉尔法求解。给出了不同垂跨比和阻尼常数下的响应曲线。并将计算结果与固定支座的计算结果进行了比较。(4)研究了均匀分布正弦时变荷载作用下水平索的1/2次谐波共振和1/2次谐波附近的混沌行为。用伽辽金方法解决了这个问题。采用谐波平衡法求解1/2次谐波共振。用龙格-库塔-吉尔方法分析了混沌运动。不同垂跨比下的索呈现出1/2次谐波共振和混沌行为。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