Gyroscopic modes decoupling method in parametric instability analysis of gyroscopic systems

Traditional procedures to treat vibrations of gyroscopic continua involve direct application of perturbation methods to a system with both a strong gyroscopic term and other weakly coupled terms. In this study, a gyroscopic modes decoupling method is used to obtain an equivalent system with decoupled gyroscopic modes having only weak couplings. Taking the axially moving string as an example, the instability boundaries in the vicinity of parametric resonances are detected using both the traditional coupled gyroscopic system and our system with decoupled gyroscopic modes, and the results are compared to show the advantages and disadvantages of each method.