Natural frequency of rotating beams using non-rotating modes

A Lagrangian approach is formulated for predicting the rotating natural frequencies of a beam from the nonrotating modes and frequencies. Using the first two nonrotating mode shapes in one case and the first four such modes in the other case the frequencies of the rotating modes are calculated for a short tapered beam and a typical helicopter blade, respectively. In each case the beam is represented by lumped parameters. The number of mass points representing the beam and the accuracy of the calculated slopes of the nonrotating mode shapes at those points are both shown to affect the accuracy of the resulting frequencies, but the number of stations is shown to be more important.