Abstract
The nonlinear dynamics of the parametrically excited vibrations of a class of generalized gyroscope systems under delayed feedback control is investigated by the averaging method and simulations in this paper. The influence of feedback control on the stability of the trivial solution and the amplitude of the periodic vibrations is presented based on Routh-Hurwitz criterion and the Levenberg-Marquardt method respectively. It is shown that the stability of the trivial solution can be varied when feedback control and time delay are employed. The amplitudes of periodic solutions can also be modulated greatly by feedback gain and time delay. However, the influence of time delay on amplitudes is periodic. The simulations obtained by numerically integrating the original system are in good agreement with the analytical results.
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