Parametric instability of spinning pretwisted beams subjected to sinusoidal compressive axial loads

Abstract

The equations of motion of a spinning pretwisted beam under pulsating compressive axial loads are formulated using Euler beam theory and the assumed mode method. Unstable regions of flutter instability are found to exist for beams with non-zero pretwist angles, within the stable critical speed zones. The narrower regions of flutter instability separate the stable critical speed zones into smaller stable sub-regions. The compressive axial force is assumed to consist of a steady state value and a time-dependent portion. The multiple scale method is used to determine the regions of instability due to the resulting parametric excitations. As the spin speed varies within the stable sub-regions, consistent shifts and widening of unstable regions due to axial load perturbation are observed. Widths of the unstable regions are found to decrease with decreasing pretwist angle and compressive axial force as well as increasing aspect ratio towards unity. © 1998 Elsevier Science Ltd. All rights reserved.