Nonlinear Motion Control of a Column Using a Coupled Gyroscope

AbstractIn this paper, a system of the gyroscopes coupled via the massless torsional springs and the massless torsional dampers mounted on the tip mass of a column subjected to a vibrating base is considered. The coupled gyroscopes are assumed to have reverse angular speeds Ω, and the rotations θ to eliminate the torques due to the springs and the dampers. Taking advantage of the angular momentum of the rotating gyroscope, gyrostabilizer systems are expected to become more widely actualized as theyprovide an effective means of motion control with several significant advantages for various structures. The non-linearmotions of the gyro-column system and the equations of motion for the system are derived following energy (Lagrange) based approaches and examples provided. On the other hand, the effect of the angular velocities of the gyroscopes are studied, and it is shown that the angular velocity (spinvelocity) Ω of a gyroscope has a significanteffect on the behavior of the dynamicmotion. It is alsoshown how the dampers an dspringsdue to the motion between the suporting gimbals influence the dynamic behavior of the column

Optimum Tuning of a Gyroscopic Vibration Absorber Using Coupled Gyroscopes for Vibration Control of a Vertical Cantilever Beam

This paper deals with the investigation of optimum values of the stiffness and damping which connect two gyroscopic systems formed by two rotors mounted in gimbal assuming negligible masses for the spring, damper, and gimbal support. These coupled gyroscopes use two gyroscopic flywheels, spinning in opposing directions to have reverse precessions to eliminate the forces due to the torque existing in the torsional spring and the damper between gyroscopes. The system is mounted on a vertical cantilever with the purpose of studying the horizontal and vertical vibrations. The equation of motion of the compound system (gyro-beam system) is introduced and solved to find the response measured on the primary system. This is fundamental to design, in some way, the dynamic absorber or neutralizer. On the other hand, the effect of the angular velocities of the gyroscopes are studied, and it is shown that the angular velocity (spin velocity) of a gyroscope has a significant effect on the behavior of the dynamic motion. Correctness of the analytical results is verified by numerical simulations. The comparison with the results from the derivation of the corresponding frequency equations shows that the optimized stiffness and damping values are very accurate