The stability of three known exact solutions to the nonlinear equations governing free transverse motions of spinning membrane disks is investigated for a particular choice of perturbations. A wave which travels circumferentially in the disk in the direction opposite to its rotation is shown to be infinitesimally unstable. A wave traveling in the direction of disk rotation and a nonlinear vibration are not shown to be unstable.
Stability of Transverse Waves in a Spinning Membrane Disk
P. Z. Bulkeley
Department of Mechanical Engineering, Stanford University, Stanford, Calif.
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Bulkeley, P. Z. (March 1, 1973). "Stability of Transverse Waves in a Spinning Membrane Disk." ASME. J. Appl. Mech. March 1973; 40(1): 133–136. https://doi.org/10.1115/1.3422911
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