Random vibrations of a rotating shaft with non-linear damping

摘要

Bending vibrations of a rotating shaft due to external random excitation are considered for the case of potential instability of the shaft's linear model due to the presence of internal or "rotating" damping. A two-degree-of-freedom model is studied which accounts for non-linearity in external or "non-rotating" damping. An explicit expression is obtained for a stationary joint probability density of displacements and velocities as an exact analytical solution to the corresponding Fokker-Planck-Kolmogorov equation. The results are used to develop criterion for on-line detection of instability for the operating shaft from its measured response.