There are two kinds of assembly procedures: the finite
element method and the transfer matrix method. Ruhl and
Booker (1972) used a finite element model to study the
dynamic characteristic of a turbo rotor. In their model, only
elastic bending and translational kinetic energy were
included, whereas the effects of rotatory inertia, gyroscopic
effects, shear deformation, axial torque, axial load, and
internal damping were neglected. Dimaragonas (1975) presented
a more general model that included rotatory inertia,
gyroscopic effects, and internal damping. Gasch (1976)
presented a model that was similar to Dimaragonas’s but
included the effect of distributed eccentricity. At the same
time, Nelson and McVaugh (1976) published their model
that included rotatory inertia, gyroscopic moments, and
axial load. The detailed equations for the elements are
expressed in both a fixed and a rotating reference frame.
Their work was generalized by Zorzi and Nelson (1977),
who included internal damping. Nelson (1980) presented a
model that included the shear deformation effects. In general,
the governing equation of motion of a flexible rotor
can be written as (Lalanne and Ferraris, 1998)