Abstract
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 if the resulting equations are to be consistent. Elastic displacements are typically modelled using mode shapes and generalized coordinates, an approach that neglects displacement effects that are higher than second order in the generalized coordinates. 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 the second order elastic displacements. The model 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 this model with and without foreshortening effects and some conclusions are drawn as to the relative importance of such terms in rotor disk modelling.
