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

采用解析和实验相结合的方法，对拉索的分叉非线性响应和混沌行为进行了分析和实验研究。研究结果如下：(1)研究了扁平垂索在轴向周期力作用下的动力稳定性。被调查者。用Galerkin法求解拉索的运动方程。对于不同的垂跨比和波速比，首先给出了不稳定区域。利用非线性拉索理论分析了面内对称时变荷载作用下拉索通过分叉的反对称响应。用Galerkin方法求解了对称荷载作用下拉索的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，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更多的头巾。在特定的垂跨比下，对称和反对称响应之间的非线性耦合被观察到。(3)规划器的动力稳定性，给出了端部简谐荷载作用下悬索的线性响应。运动方程表明，切向端部载荷对横向响应产生同时的参数激励和外部载荷。基本方程在空间坐标系下用Galekin法求解，在时间坐标系下用Runge Kutta-Gill法求解。给出了不同垂跨比和阻尼常数下的响应曲线。(4)研究了均布正弦时变荷载作用下水平拉索的1/2亚谐共振和1/2亚谐共振附近的混沌行为。该问题用Galerkin方法求解。用谐波平衡法求解1/2亚谐共振。混沌运动采用Runge-Kutta-Gill方法分析。不同垂跨比的拉索均表现出1/2的亚谐共振和混沌行为。较少

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