Dynamic Simulation of Gyroscopic Rigid Rotor with Anisotropy of Elastic Support Restoring and Damping Characteristics

Abstract

This paper considers a gyroscopic rigid rotor with restoring and damping characteristics of an elastic support. Differential equations of the rotor motion, which take into account the anisotropy of stiffness and damping, are solved analytically by the harmonic balance method. It is found that if the linear stiffness of the elastic support material differs in two mutually perpendicular directions, there are two critical velocities and corresponding resonance regions. Each critical velocity is defined by two resonance curves, the principal direction and the perpendicular direction, respectively. The area limited by the principal direction resonance curve is larger than the area limited by the second direction resonance curve. Linear damping or non-linear cubic damping suppresses the maximum amplitudes of these resonant curves. If damping acts only in one direction, then its effect is observed in the resonance curves of the corresponding critical velocity. In the case of the presence of a non-linear component of the rigidity of the support material, the resonance curves of the main directions are accompanied by jumps. Combined linear and non-linear cubic damping suppresses the oscillation amplitude more significantly than linear damping. The equations of rotor motion were also solved numerically and the results are in good agreement with the results of the analytical solution at the initial stage of time.