In the design of gas turbine engines, the analysis of nonlinear vibrations of mistuned and frictionally damped blade-disk assembly subjected to random excitation is highly complex. The transitional probability density function (PDF) for the random response of nonlinear systems under white or coloured noise excitation (delta-correlated) is governed by both the forward Fokker-Planck (FP) and backward Kolmogorov equations. This paper presents important improvement and extensions to a computationally efficient higher order, finite difference (FD) technique for the solution of higher dimensional FP equation corresponding to a two degree of freedom nonlinear system representative of vibration of tip shrouded frictionally damped bladed disk assembly subjected to Gaussian white noise excitation. Effects of friction damping on the mean square response of a blade are investigated. The friction coefficient of the damper is assumed to be a function of the sliding velocity of the contact surface. The effects of stiffness and damping mistuning on the forced response of frictionally damped bladed disk are investigated. Numerical studies are presented for a pair of mistuned blades of cyclic assemblies. The response and reliability of a blade subjected to random excitation is also obtained. With time averaged probability density as an invariant measure, the probability of large excursion in case of damping mistuning is also presented. The results of the FD method are validated by comparing with Monte Carlo Simulation (MCS) results.

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