Stability analysis of rotating blade bending vibration due to torsional excitation

This paper studies the forced vibrations of a flexible rotating blade under the excitation of shaft torsional vibration. A reduced order nonlinear dynamic model is adopted, wherein the torsional vibration degree of freedom is substituted by a simple harmonic motion with a frequency that is function of the system rotating speed. The resulting system of second-order ordinary differential equation with harmonically varying coefficients is solved using the method of harmonic balance. The forced response solution is compared to the numerical integration results. Agreement is found with respect to stable and unstable regions of the blade vibrations. The solution is useful for defining dangerous operating speed ranges and for quantifying the relationship between shaft torsional and blade bending natural frequencies.