Gyroscopic rotor dynamics simulation with anisotropy of elastic and damping characteristics of the support

In the work, the differential equations of motion of the gyroscopic rotor, built taking into account the anisotropy of stiffness and damping of the flexible support, are solved analytically, by the method of harmonic balance, convenient for obtaining separately amplitude-frequency and phase-frequenc...

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Bibliographic Details
Published in:Advances in mechanical engineering 2024-09, Vol.16 (9)
Main Authors: Abduraimov, Azizbek, Iskakov, Zharilkassin, Kamal, Aziz, Kalybayeva, Akmaral
Format: Article
Language:English
Subjects:
Amplitudes
Curves
Damping
Differential equations
Elastic anisotropy
Elastic supports
Equations of motion
Exact solutions
Geometric nonlinearity
Linear damping
Nonlinear control
Oscillations
Rotor dynamics
Stationary processes
Stiffness
Citations: Items that this one cites
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Summary:In the work, the differential equations of motion of the gyroscopic rotor, built taking into account the anisotropy of stiffness and damping of the flexible support, are solved analytically, by the method of harmonic balance, convenient for obtaining separately amplitude-frequency and phase-frequency characteristics in the direction of oscillations. The equations of the non-stationary process are obtained by the method of changing amplitudes. It has been found that when the linear stiffness of the elastic support is different in two orthogonal directions, two critical velocities and the corresponding resonant regions arise. In the area of each critical speed, there are two amplitude-frequency curves of oscillations of the main direction and the direction perpendicular to it, respectively. The geometric nonlinearity of damping suppresses the elevations of these amplitude-frequency curves more significantly than linear damping. If only one of the two directions has a damping nonlinearity, then its effect is on the amplitude-frequency curves of the corresponding critical speed. It is more efficient to control resonant amplitudes for smooth resonant transitions by enhancing the linear damping with geometrically nonlinear damping. The results of the analytical solution of the equations of motion agree well with the results of direct modeling and experimental studies.
ISSN:1687-8132
1687-8140
DOI:10.1177/16878132241272189