Effects of warping and pretwist on torsional vibration of rotating beams

The effect of pretwist and warping on the torsional vibration of short-aspect-ratio rotating beams is examined for application to the modeling of turbofan, turboprop, and compressor blades. The equations of motion and the associated boundary conditions by using both Wagner's hypothesis and Washizu's theory are derived and a few minor limitations of the Wagner's hypothesis, as applied to thick blades, are pointed out and discussed. The equations for several special cases are solved in a closed form. Results are presented indicating the effect of warping, pretwist, and rotation on torsional vibration of beams as aspect ratio is varied. The results show that the structural warping and pretwist terms have a significant effect on torsional frequency and mode shapes of short-aspect-ratio blades whereas the inertial warping terms have negligible effect. Since the torsional frequencies and mode shapes are very important in aeroelastic analyses by using modal methods, the structural warping terms should be included in modeling turbofan, turboprop, compressor, and turbine blades.