Solution to the Backward-Kolmogorov Equation for a Nonstationary Oscillation Problem

The solution of a backward-Kolmogorov equation is presented. This equation is associated with a Markov approximation of the response amplitude of a lightly damped linear oscillator driven by an evolutionary random excitation.

Passage of a Rotor Through a Critical Speed

This paper deals with a nonstationary oscillation of a rotor passing through a critical speed. The analysis is based on the method of multiple scales and the method of matched asymptotic expansion. The peak amplitude of the response and the criteria for the onset of the stalling (inability to pass through the critical speed) are derived. These results are compared with those of digital computer simulation.