Dynamic stability of a shaft system connected through a Hookeʹs joint

Dynamic stability of the torsional vibrations of a shaft system consisting of two torsionally elastic shafts interconnected through a Hookeʹs joint is investigated by means of a two degree-of-freedom model. The linearized equations of motion are shown to consist of a set of Mathieu–Hill equations and stability of their solutions is analyzed by means of a monodromy matrix method. Results are presented in the form of stability charts constructed on various parameter planes visualizing the effect of various selected pairs of system parameters on the stability.