Squeeze film dampers introduce nonlinear motion dependent damper forces into otherwise linear rotor bearing systems, thereby considerably complicating their analysis. Noncircular orbit type dampers, such as unsupported or uncentralized dampers, have generally necessitated transient solutions, which are computationally prohibitive for design studies of large order systems, particularly for systems with low damping. By utilizing harmonic balance with appropriate condensation, it is possible to considerably reduce the number of simultaneous nonlinear equations inherent to this approach. The stability (linear) of the equilibrium solutions may be conveniently evaluated using Floquet theory, particularly if the damper force components are evaluated in fixed, rather than rotating, reference frames. The versatility of this technique is illustrated on systems of increasing complexity with and without damper centralizing springs. Of particular interest, is its applicability to unsupported systems illustrating how such systems can lift off and, with further increase in speed, the damper forces can be linearized about the orbit center.

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