Modelling of an Elastic Disk With Finite Hub Motions and Small Elastic Vibrations With Application to Rotordynamics

In the modelling of flexible structures undergoing large overall motion and small elastic vibrations, it is necessary to include elastic displacement effects up to second order in the kinematical equations if the resulting differential equations are to be consistent. Elastic displacements are typically modelled using mode shapes and generalized coordinates, and second and higher order elastic effects (sometimes referred to as foreshortening) are often neglected in the development of kinematical relations. This study examines the implications of such effects in the modelling of an elastic disk with arbitrary base motions and small elastic vibrations. A general modelling procedure is described that is appropriate for the development of simulation models for such structures. An approximate technique is used to account for second order elastic terms in the kinematical relations. The modelling procedure is specialized to the case of an elastic disk undergoing a constant axial spin and infinitesimal displacements for all other degrees of freedom. Comparisons are made between the natural frequencies of a disk model with and without these elastic foreshortening effects and some conclusions are drawn as to the relative importance of such terms in rotor disk modelling.