Whirling prediction with geometrical shaft profiling

Distributed parameter shaft–rotor models are considered. The multivariable irrational, hyperbolic and circular function, input–output relationship for the system, is derived. Arbitrary, geometrical shaft profiling may be accommodated within the analytical techniques outlined. Conventional frequency response methods are employed in the determination of the critical speed condition. Specific studies, incorporating cantilevered rotors with non-linear shaft length–diameter configurations are detailed. The general applicability of the procedures outlined is emphasised.