Forced Response of Turbine Engine Bladed Disks and Sensitivity to Harmonic Mistuning

The mistuned forced response of turbine engine bladed disks is treated using harmonic perturbations in the properties of a continuous ring. A continuous shear spring is attached to the ring in which the stiffness is allowed to vary along the ring annulus. The modes of such a structure with a single harmonic mistuning pattern are shown to obey the Mathieu equation, which is solved to obtain the natural frequencies and modes of the mistuned system. The forced response of the system is then examined to determine the sensitivity of the system to small mistuning. The model is extended to include multiple harmonics, allowing for the possibility of general mistuning. An expression for the maximum amplitude magnification due to small mistuning is developed by showing that high response is caused by distortion of the structural modes. A method to intentionally mistune systems for maximum forced response is demonstrated, and numerical results demonstrate the accuracy of the analytical prediction. The intentionally mistuned system response is shown to be robust with respect to small random mistuning. Such a result might be useful for designing a test rotor for screening new bladed disk designs or for establishing the root cause of fatigue problems.