Nonstationary Vibration during Acceleration through Two Critical Speeds : Without damping

Abstract

The nonstationary vibration of a rotating shaft which passes through two critical speeds successively under conditions of uniform acceleration is theoretically analyzed by both an exact solution and approximate expressions for the vibration, neglecting the damping force. The analytical results show that the nonstationary vibration is characterized by one parameter containing both the critical speed ratio and the acceleration rate, and that the vibration is directly affected by the unbalance distribution in the case of fast acceleration. Furthermore, formulae for evaluating the maximum amplitudes and the rotational speeds of the nonstationary response are derived, and the evaluated values are compared with those obtained from the exact solution.