Nonlinear random vibrations of a rotating shaft

Abstract

AbstractBending 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 presence of internal or “rotating” damping. A two‐degree‐of‐freedom model with nonlinear elastic restoring forces is studied. 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.