The general dynamic equation is:

where , , and are the mass, damping, and stiffness matrices, and is the external force vector.

A Fourier decomposition of the solution and the load vector is used:

where is the Fourier matrix, and and are harmonic indices displacement and load quantities.

Using the transformation matrix, the dynamics equation reduces to:

This set of uncoupled cyclic sector equations is solved while enforcing the compatibility boundary conditions between the sectors.

For more information about the matrices, see Analysis of Cyclically Symmetric Structures in the Mechanical APDL Theory Reference.