Experimental results are reported and a simple model proposed to explain a phenomenon in which the equilibrium deflection of a flexible disk rotating inside a narrow housing undergoes an abrupt jump when the rotation speed is varied slightly. Discontinuous jumps are observed in a small fraction (25%) of Zip disks rotating between 3000 rpm and 4500 rpm. For those disks exhibiting jumps, the jumps are repeatable for both increases and decreases in rotation speed during a test; no hysteresis is observed. A disk that initially exhibits the jump phenomenon may fail to exhibit jumps several days or weeks later and vice versa. Numerical results for a rotating membrane hydrodynamically coupled to the surrounding flow show that the number of possible equilibria is a sensitive function of the radial flows above and below the disk. In particular, a small change in radial flow from a radially inward flow to a radially outward flow can abruptly change the number of possible equilibria from two to one. The characteristics of this transition are compatible with the experimental observations.
Multiple Equilibria of a Hydrodynamically Coupled Flexible Disk Rotating Inside a Thin Housing
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, December 16, 2001; final revision, July 26, 2002. Associate Editor: O. O’Reilly.
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Warner and , G. M., and Renshaw , A. A. (January 23, 2003). "Multiple Equilibria of a Hydrodynamically Coupled Flexible Disk Rotating Inside a Thin Housing ." ASME. J. Appl. Mech. January 2003; 70(1): 142–147. https://doi.org/10.1115/1.1526121
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