Chaos in a Forced Vibratory System with an Asymmetric Restoring Force

具有不对称恢复力的受迫振动系统中的混沌

基本信息

批准号：
13650249
负责人：
NAKAI Mikio
金额：
$ 1.34万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650249/
关键词：
Piecewise Linear System Chaos Gear Vibration Contact Vibration Interval Analysis Conley Index

项目摘要

(1) A generalized solution methodology based on piecewise linear vector fields has been proposed for piecewise linear systems with boundaries for both displacement and time. This methodology is applied in analyzing dynamic responses of torsional vibration through bilinear spring stiffness with changing hysteretie torque in the rotating machinery system, which has boundaries for both displacement and velocity. For asymmetric torque with hysteresis. two cases exist when restoring torque changes smoothly and discontinuously. Our present method can be applied to dynamic responses of piecewise linear systems having velocity and displacement boundaries.(2) In rolling contact vibration of two discs, their dynamic responses can be predicted employing the second-order averaging method of which validity has been confirmed for nonlinear vibrations.(3) Topological methods are employed to extract unstable fixed points in phase space from numerical and experimental time series data. Conley index of … More an isolated invariant subset and the R-B method can determine unstable fixed points contained in strange attractor from numerical time series data. For experimental time series, the theorem for the relationship between index pair and Conley index enables one to predicted unstable fixed points with acceptable accuracy.(4) For the experimental model, a driven disc with smoothed surface is in rolling contact with another driving disc having wavy roughness. As a driving disc with wavy surface, a spur gear, 0.5 module, was used. Accelerations in the radial direction of the disc were measured at different rotational speeds and contact loads. As a result, non-linear responses including additional and differential harmonic resonances and chaotic motion occur in connection with the corrugation frequency, contact resonance frequency and the natural frequencies of the disc. It was found that the topological method (3) can find an unstable fixed point contained in Poincare map obtained from measured time series data. Less

(1) 针对具有位移和时间边界的分段线性系统，提出了一种基于分段线性矢量场的广义求解方法，该方法应用于通过旋转中滞后扭矩变化的双线性弹簧刚度来分析扭转振动的动态响应。对于具有位移和速度边界的机械系统，当恢复扭矩平滑和不连续变化时，存在两种情况。 (2)在两个圆盘的滚动接触振动中，可以采用二阶平均法来预测它们的动态响应，该方法对于非线性振动的有效性已被证实。(3)采用拓扑方法提取不稳定不动点数值和实验时间序列数据的相空间中孤立不变子集的康利指数和 R-B 方法可以从数值时间序列数据中确定奇异吸引子中包含的不稳定不动点。对和康利指数(4) 对于实验模型，具有光滑表面的从动盘与另一个具有波状粗糙度的驱动盘滚动接触作为具有波状表面的驱动盘，正齿轮，0.5模数。，在不同的旋转速度和接触载荷下测量了圆盘径向方向的加速度，因此，会出现与波纹频率相关的非线性响应，包括附加和微分谐振和混沌运动。发现拓扑方法（3）可以从测量的时间序列数据中找到包含在庞加莱图中的不稳定不动点。