Abstract
The bifurcations of a thin-walled shell rotor during simple and complex rotation are analyzed. The similarity and difference of the problem formulations and solution techniques are pointed out. In both cases, the buckling mode is described by the first circumferential harmonic. The dependence of rotor bifurcations on natural frequencies is studied
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REFERENCES
V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of Differentiable Maps, Vol. II, Birkhauser, Boston, MA (1988).
A. T. Vasilenko and N. I. Klimenko, “Stress state of rotating inhomogeneous anisotropic cylinders,” Int. Appl. Mech., 35, No.8, 778–783 (1999).
V. I. Gulyaev, A. A. Grom, and N. A. Snezhko, “Precession of conical shells during complex rotation,” Mekh. Tverd. Tela, No. 2, 156–163 (1999).
V. I. Gulyaev, P. Z. Lugovoi, I. L. Solov’ev, and M. A. Belova, “On the bifurcational states of rotating spherical shells,” Int. Appl. Mech., 38, No.9, 1131–1137 (2002).
A. I. Lur’e, Analytical Mechanics [in Russian], Fizmatgiz, Moscow (1961).
T. Poston and I. N. Stewart, Catastrophe Theory and Its Applications, Pitman, London-San Francisco (1978).
R. Gilmore, Catastrophe Theory for Scientists and Engineers, Dover, New York (1993).
A. Tondl, Some Problems of Rotor Dynamics, Chapman & Hall, London (1965).
H. Ziegler, Principles of Structural Stability, Blaisdell, London (1968).
V. I. Gulyaev, “Complex motion of elastic systems,” Int. Appl. Mech., 39, No.5, 525–545 (2003).
V. I. Gulyaev, P. Z. Lugovoi, and I. L. Solov’ev, “Elastic vibrations of a single-support thin-walled rotor (compound shell) during complex rotation,” Int. Appl. Mech., 39, No.8, 969–975 (2003).
V. I. Gulyayev, I. L. Solovjov, and P. Z. Lugovoy, “Analysis of precession vibrations of thin-wall elastic shells in compound rotation,” J. Sound Vibr., 246, No.3, 491–504 (2001).
Y. Padovan, “Natural frequencies in rotating prestressed cylinders,” J. Sound Vibr., 31, 469–482 (1973).
K. R. Sivadas, “Vibration analysis of prestressed rotating thick circular conical shell,” J. Sound Vibr., 186, No.1, 99–109 (1995).
A. T. Vasilenko and G. K. Sudavtsova, “Stress analysis of anosotropic inhomogenous shells of revolution subjected to centrifugal forces,” Int. Appl. Mech., 39, No.7, 862–869 (2003).
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 127–134, March 2005.
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Gulyaev, V.I., Solov’ev, I.L. & Belova, M.A. Bifurcations of a Single-Support Elastic Thin-Walled Rotor. Int Appl Mech 41, 330–335 (2005). https://doi.org/10.1007/s10778-005-0092-6
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DOI: https://doi.org/10.1007/s10778-005-0092-6