AERODYNAMICALLY EXCITED VIBRATION OF A ROTATING-DISK

The stability of a rotating disk coupled to the surrounding fluid is i nvestigated analytically and experimentally. Dimensional analysis of t he equations governing transverse motion of a centrifugally tensioned, Kirchhoff plate and irrotational flow of a compressible fluid identif ies three dimensionless parameters that characterize the state of stab ility of the fluid-plate system. They are the ratio of the fluid and p late densities, LAMBDA, the Mach number of the periphery of the disk, M, and the ratio of the stiffness of the disk in bending to that deriv ed from centrifugal stresses, epsilon. Numerical analysis of these equ ations for subsonic speeds (M < 0.3) predicts flutter instability that depends primarily on LAMBDA and the geometry of the fluid enclosure, secondarily on epsilon, and does not depend on M. Experimental results for a relatively fixed geometry, however, show that the onset of inst ability is completely described by LAMBDA and M, even though M much le ss than 1. The experimental measurements show that instability is inde pendent of epsilon for values of epsilon ranging over several orders o f magnitude.