Bladed disc system or rotor, which is an integral part of turbines and compressors, exhibits
very complex vibrations during operation. Typically, these bladed disc structures are designed
to be rotationally periodic i.e. a sector repeats itself comprising of a blade and a part of the hub.
However, because of imperfections in manufacturing tolerances, wear and tear during
operation the sectors are no longer identical. This results in the loss of periodicity and the
system is referred to a mistuned system. The sectors of mistuned system are assumed to have
random spatial fluctuations in system parameters. Consequently, it leads to mode localization
in the bladed disc system and results in localized stresses leading to failure.
This study focusses on modelling a sector with the material properties having spatial random
inhomogeneities. These inhomogeneities result in a system that is inherently mistuned as cyclic
symmetry is lost. A surrogate stochastic reduced order model is developed for the analysis of
randomly parametered structural systems with complex geometries. It is assumed that the
mathematical model is available in terms of large ordered finite element (FE) matrices. The
structure material properties are assumed to have spatial random inhomogeneities and are
modelled as non-Gaussian random fields. A polynomial chaos expansion (PCE) based
framework is developed for modeling the random fields directly from measurements and for
uncertainty quantification of the response. Difficulties in implementing PCE due to geometrical
complexities are circumvented by adopting PCE on a geometrically regular domain that bounds
the physical domain and are shown to lead to mathematically equivalent representation. The
static condensation technique is subsequently extended for stochastic cases based on PCE
formalism to obtain reduced order stochastic FE models. The efficacy of the method is
illustrated through two numerical examples.