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

小拱形索的混沌振动分析

基本信息

批准号：
09650531
负责人：
TAKAHASHI Kazuo
金额：
$ 1.98万
依托单位：
Nagasaki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09650531/
关键词：
Nonlinear vibration Chaos Subharmonic response Arch Cable Geometric nonlinearity Thin plate

项目摘要

(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.

（1）讨论了带有小河拱的非线性振动和混乱。基本运动的基本方程是通过Galerkin方法求解的，并且通过谐波平衡法解决了周期性振动和runge-kutta-gill方法的谐波平衡方法，以解决混乱的振动。单度自由方法被激发了。混沌振动是通过使用分叉图，Poincare图和功率谱来获得的。获得并讨论了非线性振动和混沌振动。在一半的亚谐波共振附近发现了混乱的振动。通过间歇性地进行NT周期性振动，通过重复进行混乱的途径。（2）讨论了带有小的rize的拱门的非线性振动和混乱。多重自由的方法被激发了。第三模式的非线性游离振动和第一个固有频率范围附近的非线性强制振动讨论了各种Rie率和阻尼常数。较高模式对第一种模式的非线性振动行为和混沌振动的影响是CHCK的。（3）检查了带有小河的矩形板的非线性振动特性。用盖金方法分析了使用Marguerre方程来描述最初偏转板的大挠度的方程式。对于各种Rize比率和纵横比，获得了第一种模式的非线性自由振动和强制振动。（4）研究了结构特性的影响，例如跨度长度，塔形，横截面，横截面和停留电缆布置对电缆停留桥的局部振动的局部振动。 28日本的有线桥梁正在检查。通过谐波平衡方法分析了受支持激发的电缆的非线性振动。各种参数显示了全局振动与局部振动之间的关系，不稳定区域的宽度和参数共振的幅度。