High order sensitivity analysis of a mistuned blisk including intentional mistuning

Small deviations between turbine blades exist due to manufacturing tolerances or material
inhomogeneities. This effect is called mistuning and usually causes increased vibration amplitudes
and also a lower service life expectancy of bladed disks or so called blisks (bladed
integrated disk). The major resulting problem is to estimate the maximum amplitude with
respect to these deviations. Due to the probability distribution of these deviations, statistical
methods are used to predict the maximum amplitude. State of the art is the Monte-Carlo
simulation which is based on a high number of randomly re-arranged input parameters. The
aim of this paper is to introduce a useful method to calculate the probability distribution of
the maximum amplitude of a mistuned blisk with respect to the random input parameters.
First, the applied reduction method is presented to initiate the sensitivity analysis. This
reduction method enables the calculation of the frequency response function (FRF) of a
Finite Element Model (FEM) in a reasonable calculation time. Based on the Taylor series
approximation, the sensitivity of the vibration amplitude depending on normally distributed
input parameters is calculated and therewith, it is possible to estimate the maximum
amplitude. Calculating only a single frequency response function shows a good agreement
with the results of over 1000 Monte-Carlo simulations.