Analysis on Chaotic Vibrations an Arch with Small Rize and a Cable

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(1) Nonlinear vibrations and chaos of an arch with a small rize are discussed. The basic equation of motion is solved by a Galerkin method and the resulting time variable is solved by the harmonic balance method for periodic vibrations and Runge-Kutta-Gill method for chaotic vibrations. The single-degree-of freedom approach is emplyed. Chaotic vibration is obtained by using bifurcation diagrams, Poincare map and power spectrums. Nonlinear vibrations and chaotic vibrations are obtained and discussed. Chaotic vibrations are found near the one-half subharmonic resonance. The route to chaos through repeating intermittently nT-periodic vibration is obtained.(2) Nonlinear vibrations and chaos of an arch with a small rize are discussed. The multiple-degrees-of freedom approach is emplyed. Nonlinear free vibration of the third mode and nonlinear forced vibrations near the first natural frequency range are discussed for various rize ratios and damping constants. The effect of the higher mode on nonlinear vibration behaviors and chaotic vibrations of the first mode is chcked.(3) The nonlinear vibration properties of a rectangular plate with a small rize are examined. The equations describing the large deflection of the initially deflected plate using the Marguerre equation are analyzed by a Galerkin method. Nonlinear free vibrations and forced vibrations of the first mode and higher nodes are obtained for various rize ratios and aspect ratios.(4) Effects of structural properties such as the span length, tower shape, the cross section and the stay cable arrangement on local vibrations of stay cables of cable stay bridges are studied. 28 cable stay bridges in Japan are examined. Nonlinear vibrations of the cable subjected to the support excitations are analyzed by the harmonic balance method. The relations between global vibrations and local vibrations, widths of unstable regions and amplitudes of parametric resonances are shown for various parameters.