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IssuesArchive of Issues2007-4pp.530-539

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V. I. Gulyayev and I. L. Solovjov, "Critical states of thin-walled hyperbolic gyros elastically connected to a rotating platform," Mech. Solids. 42 (4), 530-539 (2007)
Year 2007 Volume 42 Number 4 Pages 530-539
Title Critical states of thin-walled hyperbolic gyros elastically connected to a rotating platform
Author(s) V. I. Gulyayev (National Transport University, Suvorova 1, Kiev, 01010, Ukraine, valery@gulyayev.com.ua)
I. L. Solovjov (National Transport University, Suvorova 1, Kiev, 01010, Ukraine, solovjov@gala.net)
Abstract We analyze effects related to the origination of critical states of thin-walled rigid and elastic axisymmetric hyperbolic gyros (shells) elastically connected by the smaller base to a rotating carrier body. We consider the cases of simple and compound rotations of the body and show that, in the case of simple rotation, the specific features of origination of critical states of solid and elastic shells are determined by the ratio of their axial moments of inertia. In the case of compound rotation, the first frequency of precession resonance vibrations of elastic shells generated by the gyroscopic forces of inertia is independent of the elastic compliance of the body-shell joint.
References
1.  V. I. Gulyayev, "Dynamics of Elastic Systems in Compound Motion," Prikl. Mekh. 39 (5), 28-51 (2003).
2.  A. Tondl, Dynamics of Turbogenerator Rotors (Energiya, Leningrad, 1971) [in Russian].
3.  H. Ziegler, Principles of Structural Stability (Blaisdell Publishing Company, Waltham, MA, 1968; Mir, Moscow, 1971).
4.  V. I. Gulyayev, A. A. Grom, and N. A. Snezhko, "Precession Vibration of Conic Shells in Complex Rotation," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 156-163 (1999) [Mech. Solids (Engl. Transl.)].
5.  M. A. Belova, V. I. Gulyayev, and I. L. Solovjov, "Static and Dynamical Critical States of Parabolic Shells in Simple and Compound Rotations," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 152-163 (2004) [Mech. Solids (Engl. Transl.)].
6.  V. I. Gulyayev, I. L. Solovjov, and P. Z. Lugovyy, "Analysis of Precession Vibrations of Thin-Wall Elastic Shells in Compound Rotation," J. Sound and Vibrat. 246 (3), 491-504 (2001).
7.  V. I. Gulyayev, I. L. Solovjov, and M. A. Belova, "Interconnection of Critical States of Parabolic Shells in Simple and Compound Rotations with Values of Their Natural Precession Vibrations Frequencies," Inter. J. Solids and Structures 41 (13), 3565-3583 (2004).
8.  V. I. Gulyayev, I. L. Solovjov, and M. A. Belova, "Critical States of Thin Ellipsoidal Shells in Simple and Compound Rotations," J. Sound and Vibrat. 270 (1/2), 323-339 (2004).
9.  A. I. Lurie, Analytical Mechanics (Fizmatgiz, Moscow, 1961; Springer, Berlin, 2001).
10.  K. R. Sivadas, "Vibrations Analysis of Prestressed Rotating Thick Circular Conical Shell," J. Sound and Vibrat. 186 (1), 99-109 (1995).
Received 08 February 2005
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