ANALYTICAL DETERMINATION OF COUPLED BENDING VIBRATIONS OF ROTATING TWISTED CANTILEVER BEAMS BY MEANS OF STATION FUNCTIONS

The work by Mendelson and Gendler on the application of station functions to the treatment of coupled bending vibrations of cantilever beams is extended to include centrifugal effects. The effect of centrifugal forces is obtained by the introduction of additional terms into the loading functions of the governing integral equations. The use of station functions is made possible by integrations by parts of the centrifugal terms.

The analysis was applied to several rectangular beams of variable geometry, representative of the automotive type turbine and compressor blading. The increase in the natural frequencies due to shaft rotation was found to be very pronounced in the fundamental mode, diminishing rapidly in significance with the increasing order of frequencies. Furthermore, it is shown that this effect is considerably influenced by the geometry of the beam.

Experimental work with several stationary beams was initiated to check the accuracy of the method of analysis. The degree of correlation obtained was well within the engineering accuracy.