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 ca ntilever shaft-disk system subjected to axial and follower loads, respectiv ely. In the present study, a set of linearized stiffness influence coeffici ents of a longitudinally loaded cantilever shaft is derived. The mathematic al model also takes into account the effect of shear deformation. Because l inearized stiffness influence coefficients are used, the governing differen tial equations of the system become a set of coupled Mathieu-Hill equations . By the use of Bolotin's method, the equation of boundary frequencies can be obtained and is used to determine the boundaries between stable and unst able regions. As compared to the unstable regions obtained from finite elem ent method, the present results show not only good agreement with them, but also much easier to construct the unstable regions. From the result of num erical simulations, several destabilizing factors of the rotational cantile ver shaft-disk system are found. (C) 2000 Academic Press.