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

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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