Introduction

The purposes of this chapter are primarily to alert readers to the limitations of the analysis provided in previous chapters, to highlight the more complex behavior of certain types of rotor, and to indicate where detailed descriptions of the analysis of these systems can be found.

Chapters 3, 5, and 6 consider the behavior of rotor–bearing systems when the rotor vibrates laterally; that is, the rotor whirls due to the actions of initial radial disturbances or, more important, radial forces. The rotor is modeled as an assembly of shaft elements and rigid disks. The shaft elements include the effects of inertia, bending and shear deflection, rotary inertia, and gyroscopic couples; the disks include the effects of inertia and gyroscopic couples. Bearings and foundations are modeled essentially as assemblies of axial springs and damping elements. Similarly, in Chapter 9, we examine the axial and torsional vibration of rotors and, in each case, we model the system as an assemblage of masses and inertias and axial or torsional springs.

There are three basic assumptions in the aforementioned analysis: (1) the rotor– bearing–foundation system is linear; this assumption is present even in Chapter 7, in which instabilities of various types are examined; (2) although the rotor can deflect laterally, axially, and in torsion, it cannot otherwise deform; the shape of its cross section is fixed and plane cross sections remain plane; and (3) although the rotor can deflect laterally, axially, and in torsion, there is no coupling between these deflections; thus, an axial force can produce an axial deflection of the rotor, but it causes neither a lateral nor a torsional deflection.