Numerical Simulations of Flutter Instability of a Flexible Disk Rotating Close to a Rigid Wall

Abstract

In this paper, we present a numerical study of flutter instability of a flexible disk rotating near a rigid wall. The disk is modeled using linear plate theory, and the air flow between the disk and the rigid plate is modeled using the Reynolds equation of lubrication for thin-film flows. The coupled disk-fluid equations are solved numerically. The spatial derivatives are approximated using finite-difference schemes and the time integration is performed using the Runge-Kutta numerical scheme. The transient numerical simulation is used to determine approximations to the exact stability boundaries for stable operation of the disk. The stability boundaries for the disk-fluid system are captured for a wide range of circumferential mode numbers (16-30) and disk rotational speeds, and these predictions are compared to the predictions of an approximate single-mode analysis.