CHARACTERIZATION OF TORSIONAL INSTABILITIES IN A HOOKE'S JOINT DRIVEN SYSTEM VIA MAXIMAL LYAPUNOV EXPONENTS

Dynamic instabilities in a torsional system which incorporates a Hooke's joint are investigated by means of Lyapunov exponents. Linearized analytical models for the torsional system are established for the purpose of stability analysis. The resulting two-degree-of-freedom system is parametrically excited due to an inherent non-linear velocity ratio across the Hooke's joint. Instabilities which correspond to sub-harmonic as well as combination resonances have been identified by studying the sign of the top Lyapunov exponent. An efficient forward difference scheme is employed to simulate directly the Lyapunov exponents. Instability conditions have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. Predicted instability conditions are adequate for the design of two-degree-of-freedom Hooke's joint driven systems.