Effects of Nonconstant Spin Rate on the Vibration of a Rotating Beam

Abstract

The effects of a time-dependent angular velocity upon the vibration of a rotating Euler beam are presented. It is assumed that the angular velocity can be expressed as the sum of a steady-state value and a relatively small periodic perturbation. Equations of motion are derived for a beam oriented parallel to the spin axis. Terms with time-dependent coefficients appear in the equations of motion due to the nonconstant spin rate resulting in a nonautonomous system possessing parametric instabilities. A perturbation technique called the KBM method is used to derive general expressions for approximate solutions and instability region boundaries. A simple perturbation function is assumed for the purpose of illustrating the use of the derived general expressions.