Modal analysis of a distributed parameter rotating shaft

Forced response analysis of an undamped distributed parameter rotating shaft is investigated by using a modal analysis technique. The shaft model includes rotary inertia and gyroscopic effects, and various boundary conditions are allowed (not only the simply supported case). Presented here is a study of the resulting non-self-adjoint eigenvalue problem and its characteristics in the case of rotor dynamics. In addition to the modal analysis, Galerkin's method is applied to analyze the forced response of an undamped gyroscopic system. Both methods are illustrated in a numerical example and the results are compared and discussed.