In a previous paper (Chen and Bogy, 1992) we studied the effects of various load parameters, such as friction force, transverse mass, damping, stiffness and the analogous pitching parameters, of a stationary load system in contact with the spinning disk on the natural frequencies and stability of the system when the original eigenvalues of interest are well separated. This paper is a follow-up investigation to deal with the situations in which two eigenvalues of the freely spinning disk are almost equal (degenerate) and strong modal interactions occur when the load parameters are introduced. After comparing an eigenfunction expansion with the finite element numerical results, we find that for each of the transverse and pitching load parameters, a properly chosen two-mode approximation can exhibit all the important features of the eigenvalue changes. Based on this two-mode approximation we study the mathematical structure of the eigenvalues in the neighborhood of degenerate points in the natural frequency-rotation speed plane. In the case of friction force, however, it is found that at least a four-mode approximation is required to reproduce the eigenvalue structure. The observations and analyses presented provide physical insight into the modal interactions induced by various load parameters in a spinning disk-stationary load system.
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June 1992
Research Papers
Mathematical Structure of Modal Interactions in a Spinning Disk-Stationary Load System
Jen-San Chen,
Jen-San Chen
Department of Mechanical Engineering, Computer Mechanics Laboratory, University of California, Berkeley, CA 94720
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D. B. Bogy
D. B. Bogy
Department of Mechanical Engineering, Computer Mechanics Laboratory, University of California, Berkeley, CA 94720
Search for other works by this author on:
Jen-San Chen
Department of Mechanical Engineering, Computer Mechanics Laboratory, University of California, Berkeley, CA 94720
D. B. Bogy
Department of Mechanical Engineering, Computer Mechanics Laboratory, University of California, Berkeley, CA 94720
J. Appl. Mech. Jun 1992, 59(2): 390-397 (8 pages)
Published Online: June 1, 1992
Article history
Received:
April 10, 1991
Revised:
July 11, 1991
Online:
March 31, 2008
Citation
Chen, J., and Bogy, D. B. (June 1, 1992). "Mathematical Structure of Modal Interactions in a Spinning Disk-Stationary Load System." ASME. J. Appl. Mech. June 1992; 59(2): 390–397. https://doi.org/10.1115/1.2899532
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