Warping of stationary and rotating heavy disks

Abstract

A flexible circular plate with gravity as its main source of external loading is called a heavy disk. This paper studies the non-axisymmetric warping of a clamped-free heavy disk. In the theoretical formulation, von Karman’s plate model is adopted to derive the equations of motion of a rotating heavy disk. In the experiment, a 5 1 4 -inch floppy disk is used to demonstrate the non-axisymmetric deformations when the disk is either stationary or rotating. We first measured the shape of the floppy disk when it was stationary. It was observed that two non-axisymmetric deformations coexisted, one with shape cos 2 θ and the other cos 3 θ. We next rotated the floppy disk. It was observed that when the floppy disk started with shape cos 2 θ, the deformation switched to shape cos 3 θ as the rotation speed increased to 303 rpm. As the speed continued to increase, the shape cos 3 θ persisted all the way up to 1010 rpm. Beyond that the disk deformation became axisymmetric until 1313 rpm. Beyond 1313 rpm, aeroelastic flutter started to kick in and equilibrium state was no longer achievable. The rotation speed was then reduced gradually from high speed to 0. It was found that the deformation remained cos 3 θ all the way, instead of switching back to the cos 2 θ shape the disk started out with in the first place. The coexistence of two stable non-axisymmetric deformations of the stationary disk and the hysteresis behavior of the rotating disk observed in the experiment are consistent with theoretical predictions.