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首页> 外文期刊>International journal of non-linear mechanics >Transverse vibrations of rotating shafts: Probability density and first-passage time of whirl radius
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Transverse vibrations of rotating shafts: Probability density and first-passage time of whirl radius

机译：旋转轴的横向振动：概率密度和回旋半径的第一次通过时间

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摘要

Transverse vibrations are considered for a single mass/two-degrees-of-freedom rotating shaft with linear internal or "rotating" damping and nonlinear external damping. The shaft is excited by external random forces. Analysis of resulting random vibrations is based on stochastic averaging method which yields separated (in the linear approximation) equations for complex amplitudes of forward and backward whirling motions. The former of these motions is shown to be dominant at rotation speeds in the vicinity of the instability threshold. Using this approximation an analytical solution is obtained for probability density of squared radius of the shaft's whirl. This solution can be used to detect on-line shaft's instability from its observed response. Solution is also obtained for expected time for reaching given level by the squared whirl radius of the shaft.
机译：对于具有线性内部或“旋转”阻尼和非线性外部阻尼的单质量/二自由度旋转轴，应考虑横向振动。轴由外部随机力激励。对产生的随机振动的分析基于随机平均方法，该方法针对正向和反向旋转运动的复杂幅度得出分离的（线性近似）方程。这些运动中的前者显示为在不稳定阈值附近的转速下占主导地位。使用该近似值，可以得到轴旋转半径的平方半径的概率密度的解析解。该解决方案可用于从观察到的响应中检测在线轴的不稳定性。还可以通过轴的旋转涡旋半径平方求出达到给定水平所需时间的解决方案。

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