Self-Excited Harmonic and Solitary Waves in a Spinning Disk (With Video Presentation)

Abstract

Solitary waves have been reported in many applications in physics and engineering. While these waves are of relatively simple shape, the mechanisms that control them are highly nonlinear and often not completely understood. In this study a flexible disk spinning against a stationary base plate and interacting with the surrounding air-field exhibits both harmonic as well as solitary waves and this, depending on the spin rate of the disk. Preliminary experimental results indicate that-in contrast with harmonic waves, the speed with which the solitary waves propagate does not depend upon the spin rate of the disk. This appears to be a lock-in phenomenon that is characteristic of well known nonlinear fluid-structure interaction problems. Furthermore, and despite the presence of dispersion in the fluid/disk medium, all solitary waves propagate with the same speed. While a full model capable of predicting these solitons has yet to be developed, a discussion is presented on both the linear model that is currently accepted in the literature, as well as on the nonlinear mechanisms that may control such interesting waves.

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

“…Finally, Renshaw (1998) has used Lyapunov's second method to determine the critical speed of a flexible disk spinning inside an enclosure. Boulahbal and Crandall (1997) (also see Boulahbal (1995)) recently reported on very interesting experiments for a disk spinning close to a base plate. They carried the experiments into post-critical region at rotational speeds much above the critical speeds.…”

Nonlinear Vibration of Heated Co-rotating Disks

“…When the rotation speed reaches a critical value, the laminar flow becomes turbulent near the edge of the disk. With further increase in rotational speed, both laminar and turbulent fluid flows appear near the center and edge of the rotating disk (Boulahbal and Crandall, 1997). For much higher rotational speeds, the fluid-flow near the rotating disk surface becomes fully turbulent.…”