Internal resonance between a pair of forward and backward modes of a spinning disk under space-fixed pulsating edge loads is investigated by means of multiple scale method. It is found that internal resonance can occur only at certain rotation speeds at which the natural frequency of the forward mode is close to three times the natural frequency of the backward mode and the excitation frequency is close to twice the frequency of the backward mode. For a light damping case the trivial solution can lose stability via both pitchfork as well as Hopf bifurcations when frequency detuning of the edge load is varied. On the other hand, nontrivial solutions experience both saddle-node and Hopf bifurcations. When the damping is increased, the Hopf bifurcations along the trivial solution path disappear. Furthermore, there exists a certain value of damping beyond which no nontrivial solution is possible. Single-mode resonance is also briefly discussed for comparison.
On the Internal Resonance of a Spinning Disk Under Space-Fixed Pulsating Edge Loads
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, May 15, 2000; final revision, May 31, 2001. Associate Editor: R. C. Benson. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Chen, J. (May 31, 2001). "On the Internal Resonance of a Spinning Disk Under Space-Fixed Pulsating Edge Loads ." ASME. J. Appl. Mech. November 2001; 68(6): 854–859. https://doi.org/10.1115/1.1408616
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