A Harmonic Balance Approach for the Analysis of Flexible Rotor Bearing Systems on Non-Linear Support

Abstract. The purpose of this article is to describe the theoretical background to the Harmonic
Balance approach; adopted and further developed for the analysis of general multi degree of freedom
rotor bearing systems with nonlinear supports. System equations of motion are prepared for dynamic
systems with any number of degrees of freedom. Nonlinear behaviour can be associated with any number
of these freedoms. A computer program which uses the harmonic balance method to solve the system
equations of motion is also written. These equations are partitioned into linear and nonlinear parts. The
nonlinear sets of equations need to be solved prior to solving the linear sets of equations. Verication of
the proposed method of solution is justied through two examples. The frequency response of a well known
rotor bearing, the so called Jefcott rotor, is examined and tested against data reported by some other
researchers. Also, the versatility of this method is tested by comparing the harmonic balance approach
with the transient solution and some experimental measurements involving the nonlinear squeeze lm
bearing supports, which have already been reported by this author. It is shown that by utilizing harmonic
balance with appropriate condensation, it is possible to considerably reduce the number of simultaneous
nonlinear equations inherent to such systems. The stability (linear) of the equilibrium solutions may be
conveniently evaluated using the Floquet theory.