Abstract
This paper presents the dynamic response and stability of an asymmetric rotating shaft supported by a flexible base near the major critical speed and the secondary critical speed. In this system, the base is movable only in a direction transversal to the shaft. In the theoretical analysis, taking into account the effects of damping, the unstable vibrations near the major critical speed are mainly considered, and also the behavior of the forced oscillations near the major and secondary critical speeds is investigated. From the theoretical analysis, the unstable region is found to be divided into at most six subregions which depend on the mass of the base, the stiffness of the base, and the asymmetry of the shaft. In addition, the resonance curves near unstable subregions are calculated. It is found that there exist two shapes of resonance curves. In experiments, five types of response curves, which contained n unstable subregion (n = 1, 2, ¨, 5) near the major critical speed, were obtained by changing the mass of the base. It was ascertained that the theoretical results for the behavior near the major critical speed agreed quantitatively with the experimental results.
Similar content being viewed by others
References
Taylor, H. D., 'Critical-speed behavior of unsymmetrical shafts', Journal of Applied Mechanics 7, 1940, A71–A79.
Dimentberg, F. M., Flexural Vibrations of Rotating Shaft, Butterworths, London, 1961.
Yamamoto, T. and Ota, H., 'On the vibrations of the shaft carrying an unsymmetrical rotating body', Bulletin of the JSME 6, 1963, 29–36.
Foote, W. R., Poritsky, H., and Slade, Jr., J. J., 'Critical speeds of a rotor with unequal shaft flexibilities, mounted in bearings of unequal flexibility – I', Journal of Applied Mechanics 10, 1943, A77–A84.
Messal, E. E. and Bonthron, R. J., 'Subharmonic rotor instability due to elastic asymmetry', ASME, Journal of Engineering for Industry 94, 1972, 185–192.
Hull, E. H., 'Shaft whirling as influenced by stiffness asymmetry', ASME, Journal of Engineering for Industry 83(2), 1961, 219–226.
Okijima, K. and Kondo, Y., 'On the critical speed regions of an asymmetric rotating shaft supported by asymmetrically elastic pedestals (1st report, On the unstable regions)', Bulletin of the JSME 18, 1975, 587–596.
Ardayfio, D. and Frohrib, D. A., 'Instabilities of an asymmetric rotor with asymmetric shaft mounted on symmetric elastic supports', ASME, Journal of Engineering for Industry 98, 1976, 1161–1165.
Ota, H. and Mizutani, K., 'Influence of unequal pedestal stiffness on the instability regions of a rotating asymmetric shaft', ASME, Journal of Applied Mechanics 45, 1978, 400–408.
Kotera, T., Nanba, S., and Fujimoto, T., 'Unstable regions of a disc supported by an asymmetric flexible shaft in asymmetric bearings', Transactions of the JSME, Series C 46, 1980, 1033–1043 [in Japanese].
Ota, H. and Mizutani, K., 'Influence of unequal pedestal stiffness on the instability regions of a rotating asymmetric shaft (3rd report, Mechanism for occurrence of two types of unstable vibrations)', Bulletin of tithe JSME 24, 1981, 700–707.
Kondo, Y. and Kimura, H., 1992, 'Vibration of an asymmetric rotating shaft supported by asymmetrically elastic pedestals', Transactions of the JSME 58, 1992, 317–322 [in Japanese].
Kondo, Y. and Okijima, K., 'On the critical speed regions of an asymmetrical rotating shaft supported by asymmetrically elastic pedestals (2nd report, On the forced oscillations)', Bulletin of the JSME 18, 1975, 597–604.
Yamamoto, T. and Ota, H., 'On the unstable vibrations of a shaft carrying an unsymmetrical rotor', ASME, Journal of Applied Mechanics 31, 1964, 515–522.
Seyranian, A. P. and Pederson, P., 'On interaction of eigenvalue branches in non-conservative multiparameter problems', in Dynamics and Vibration of Time-Varying Systems and Structures, ASME Design Engineering Technical Conference, Vol. 56, ASME, New York, 1993, pp. 19–31.
Ishida. Y., Ikeda, T., Yamamoto, T., and Esaka, T., 'Parametrically excited Oscillations of a rotating shaft under a periodic axial force', JSME International Journal, Series III 31, 1988, 698–704.
Meirovitch, L., Elements of Vibration Analysis, 2nd edn., McGraw-Hill, New York, 1986, pp. 270–285.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ikeda, T., Murakami, S. Dynamic Response and Stability of a Rotating Asymmetric Shaft Mounted on a Flexible Base. Nonlinear Dynamics 20, 1–19 (1999). https://doi.org/10.1023/A:1008302203981
Issue Date:
DOI: https://doi.org/10.1023/A:1008302203981