Parametric instability of spinning pretwisted beams subjected to spin speed perturbation

Abstract

The equations of motion of a spinning pretwisted beam under compressive loads and subjected to spin speed perturbations 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 spin speed consists of a steady state value and a time-dependent portion. The resulting dimensionless equations of motion are reduced to matrix differential equations with time-dependent coefficients. A modal analysis method is employed to uncouple the equations followed by application of the multiple scale method to determine the regions of instability due to parametric excitations. Parameters investigated include pretwisted angles, aspect ratio of the beam cross-sections, steady-state spin speed and axial loads. Dynamic instability due to both the summed and difference-type resonance were studied.