Dynamic stability analysis of torsional vibrations of a shaft system connected by a Hooke׳s joint through a continuous system model

Stability of parametrically excited torsional vibrations of a shaft system composed of two torsionally elastic shafts interconnected through a Hooke׳s joint is studied. The shafts are considered to be continuous (distributed-parameter) systems and an approximate discrete model for the torsional vibrations of the shaft system is derived via a finite element scheme. The stability of the solutions of the linearized equations of motion, consisting of a set of Mathieu–Hill type equations, is examined by means of a monodromy matrix method and the results are presented in the form of a Strutt–Ince diagram visualizing the effects of the system parameters on the stability of the shaft system.