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

(1)讨论了小里泽肋的非线性振动和混沌问题。运动的基本方程求解的Galerkin方法和由此产生的时间变量求解的谐波平衡法的周期性振动和龙格-库塔-吉尔方法的混沌振动。采用单自由度方法。利用分岔图、Poincare映射和功率谱分析了系统的混沌振动。得到了非线性振动和混沌振动，并进行了讨论。半次谐波共振附近存在混沌振动。得到了通过间歇重复nT周期振动进入混沌的途径。(2)讨论了小里泽肋的非线性振动和混沌问题。采用多自由度方法。讨论了不同里泽比和阻尼常数下第三阶非线性自由振动和第一阶固有频率附近的非线性强迫振动。研究了高阶振型对一阶振型非线性振动和混沌振动的影响。(3)研究了带小里泽矩形板的非线性振动特性。用Galerkin方法分析了用Marguerre方程描述初始挠度板大挠度的方程。得到了不同里泽比和纵横比下的一阶和高阶非线性自由振动和强迫振动。(4)研究了斜拉桥跨长、塔型、截面及斜拉索布置等结构特性对斜拉索局部振动的影响。对日本的28座斜拉桥进行了检测。采用谐波平衡法分析了索在支座激励下的非线性振动。的整体振动和局部振动，不稳定区域的宽度和参数共振的振幅之间的关系示出的各种参数。

(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.