The general dynamic equation is:

(1–1)

where [M], [C] and [K] are the mass, damping and stiffness matrices, and {f} is the external force vector.

In rotordynamics, this equation gets additional contributions from the gyroscopic effect [G], and the rotating damping effect [B] leading:

(1–2)

This equation holds when motion is described in a stationary reference frame, which is the scope of this guide. See Rotating Structure Analysis in the Advanced Analysis Guide for a discussion of rotating reference frame dynamics.

The gyroscopic matrix, [G], depends on the rotational velocity (or velocities if parts of the structure have different spins) and is the major contributor to rotordynamic analysis. This matrix is unique to rotordynamic analyses, and is addressed specifically by certain commands and elements.

The rotating damping matrix, [B] also depends upon the rotational velocity. It modifies the apparent stiffness of the structure and can produce unstable motion.

For more information on those matrices, see Gyroscopic Matrix in the Mechanical APDL Theory Reference