Analytical modeling of the coupled nonlinear free vibration response of a rotating blade in a gas turbine engine.

In this paper, we investigate the free vibration response of a rotating blade in a gas turbine engine. The blade is modeled as a tapered Timoshenko beam with nonlinear variations in its cross-section properties. The governing equations of motions are derived using Lagrangian mechanics and Rayleigh-Ritz method. These equations take into account centrifugal stiffening, axial and lateral coupling due to Coriolis effect, shear deformation, and rotary inertia. We examine the effect of the beam geometry upon its axial and lateral free vibration response. The effects of rotational speed, taper ratio, chord ratio, hub radius, and slenderness ratio on the natural frequencies are analyzed. The results of our analysis indicate that the taper ratio, slenderness ratio, and rotational speed of the beam govern its free lateral vibration response. The axial vibration of the beam is significantly affected by the slenderness ratio, but it is found to be independent of the hub radius. [ABSTRACT FROM AUTHOR]