Nonlinear transient dynamic response of a blade subject to a pulsating load in a decaying centrifugal force field

This study is concerned with an analytical solution for the nonlinear transient dynamic response of a rotating blade in a gas turbine engine experiencing dynamic unbalance due to a blade-off scenario leading to rotor unbalance. As a consequence of rotor unbalance, the blade experiences a pulsating load at its tip due to contact with the casing and a decaying centrifugal force field due to the rotor deceleration. The governing equations of motion consider the blade as an elastic Timoshenko beam of varying thickness subject to changing rotational speeds. The analysis takes into account the variation in the thickness of the beam, the coupled axial and lateral displacements of the beam as a result of Coriolis component of acceleration, shear deformation, rotary inertia, and friction resulting from the contact between the blade and the casing. Our findings indicate that the thickness profile of the beam plays a significant role in the transient response. It further reveals that the decaying centrifugal force field leads to a dramatic change in the dynamic response and the resulting forces on the blade.