On using a distributed-parameter model for modal analysis of a mistuned bladed disk rotor and extracting the statistical properties of its in-plane natural frequencies

In this paper, mistuning of bladed-disk systems is investigated. The blades are considered as continuous Euler-Bernoulli beams with transverse and longitudinal degrees of freedom. The governing equations of motion for the tuned and mistuned bladed disk systems are derived and discretized by use of Galerkin method. The obtained equations have time-varying coefficients and cannot directly be used for calculating the system critical speeds and Campbell diagram. For the tuned case, by use of Coleman and complex transformations one can transform the time varying system to a time-invariant system. Further transformations are required for the mistuned system to change into a time-invariant system. Next, a four-bladed disk system supported by bearings was considered. The modal analysis was performed and the critical speeds and the Campbell diagram were calculated. The results indicate that both coupled modes and conjugate modes appear in the Campbell diagram which are changing with the rotating speed. Finally, a probabilistic analysis was performed on the mistuned parameters by use of Monte Carlo method. It was found that the disk dominant modes are insensitive to the various mistuning realizations. However, the blade dominant modes are sensitive to the mistuning parameters and have a coefficient of variation one order of magnitude less than the mistuning coefficient of variation. It was also seen that the probability density functions of whirl speeds for different mistuned properties are able to be considered Gaussian.