Modeling of nonlinear vibrations for analysis and control of cylinder gyroscopes

We propose a dynamic model for a cylinder gyroscope which includes geometric nonlinearities. We show how these nonlinearities lead to modal interactions in a form of superharmonic responses. These effects which appear when the excitation amplitude of the gyroscope is large, are unwanted and cannot be explained by using linear vibration theory. Simulation of the model is shown to agree well with the experimental result. This work is intended to be a basis for developing vibration damping controllers which reduce the effect of these unwanted higher harmonic responses