The determination of model frequencies and mode shapes of rotating blades, which are either straight or tapered, is usually accomplished via application of conventional assumed displacement finite element or assumed modes methodologies. To ensure accuracy of modal information at low mode num bers, a large number of elements or admissible functions must be utilized in the model. Modal frequencies converge to the exact solutions from above with the increase of number of elements or assumed admissible functions. To apply the resulting large degree-of-freedom model in a dynamic simulation (forced or transient), or to embed such a model in a real-time model-based control problem, can be impractical. As a result, the model order must be reduced via static or dynamic condensation procedures to a practical number of degrees-of-freedom, which is constrained by simulation time, or the control interval in a digital control system. Therefore, a method is proposed, based on a spectral finite element technique, to develop such a low degree-of-freedom dynamic model directly and without resorting to a condensation procedure. The method exploits semi-analytical progressive wave solutions of the governing partial differential equations. We have calculated such results for a number of examples such as a straight beam and beams with uniform taper or compound tapers. Only one single spectral finite element is needed to obtain any modal frequency or mode shape, which is as accurate or better than other approaches reported in the literature for a straight or uniformly tapered beams. The minimum number of such spectral finite element correspond to the number of substructures (i.e., beam sections with different uniform tapers) in a rotating beam in order to capture the complete system dynamic characteristics. The element assembly procedure is accomplished in the same fashion as the conventional finite element approach. Overall, for a rotating blade system, our spectral finite element method provides highly accurate predictions for any modal frequency using a single element or very few elements corresponding to the number of uniform taper changes in the blade system.

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