Modal Curves of Pre-Twisted Beams of Rectangular Cross-Section

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Abstract
An important aspect of the theoretical study of the vibrational characteristics of turbine and compressor blading is the prediction of the modal curves from which the stresses along the length of the blading can be determined. The accurate prediction of the modal curves allowing for such factors as pre-twist, camber, size of cross-section, centrifugal tensile effects, aerodynamic effects, etc., is still not possible. However, a better understanding of the effects of some of these parameters can be obtained by a study of the modal curves of relatively simple idealized models. In this work the theoretical mode shapes of vibration of pre-twisted rectangular cross-section beams for various width to depth ratios and pre-twist angle in the range 0-90° are examined. The theoretical results are obtained by the transformation method given by Carnegie, Dawson and Thomas (1)† and the accuracy of these results is verified by comparison with results obtained by Dawson (2) using the Ritz method. The theoretical results are compared to modal curves determined experimentally and good agreement is shown between them. A physical explanation of the effects of the pre-twist angle upon the modal curves is given for the first three modes of vibration.

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