A LUMPED MASS MODEL FOR PARAMETRIC INSTABILITY ANALYSIS OF CANTILEVER SHAFT–DISK SYSTEMS

A lumped mass model is proposed to study the parametric instability of a cantilever shaft–disk system subjected to axial and follower loads, respectively. In the present study, a set of linearized stiffness influence coefficients of a longitudinally loaded cantilever shaft is derived. The mathematical model also takes into account the effect of shear deformation. Because linearized stiffness influence coefficients are used, the governing differential equations of the system become a set of coupled Mathieu–Hill equations. By the use of Bolotinʹs method, the equation of boundary frequencies can be obtained and is used to determine the boundaries between stable and unstable regions. As compared to the unstable regions obtained from finite element method, the present results show not only good agreement with them, but also much easier to construct the unstable regions. From the result of numerical simulations, several destabilizing factors of the rotational cantilever shaft–disk system are found.