Coupled Bending-Bending Vibrations of Pre-Twisted Cantilever Blading Treated by the Rayleigh-Ritz Energy Method

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Abstract
The Rayleigh-Ritz method is used to determine the natural frequencies and mode shapes of vibration of pre-twisted rectangular cross-section beams. The method is dependent upon a good choice of approximating functions for the dynamic deflection curves. In the present analysis, series of the characteristic functions representing the normal modes of vibration are taken as the approximating functions for the bending displacements in the directions of the co-ordinate axes. The choice of this particular series leads to a considerable reduction in the number of elements in the final matrix equation and also considerably reduces the computing time. The natural frequencies of vibration are obtained for various width-to-thickness ratio beams with pre-twist angle in the range 0-90°, and the mode shapes of vibration are presented for one particular width to thickness ratio beam. The results are compared to results obtained by other methods and to experimental results, and good agreement is shown to exist.

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