Uncertainty quantification in nonlinear structural dynamics for mistuned bladed disks

The recent improvements in turbomachinery design combined to the unavoidable requirements of kerosene savings require to analyze the exceptional operating regime of bladed disks, for which large deformations and large displacements can occur. It seems then quite appropriate to consider the geometrically nonlinear effects in the computational models dedicated to the analysis of mistuned turbomachinery bladed-disks. A special attention has to be first given to the case of geometrically nonlinear tuned bladed disks. The large set of nonlinear coupled differential equations issued from the finite element model of the tuned structure has to necessarily be solved in the time domain, leading us to establish a reduced-order strategy. The operators of the corresponding mean nonlinear reduced-order model are then deduced from its explicit construction as shown in the context of three-dimensional solid finite elements. One also has to focus on the modeling of the external load, corresponding to a frequency band chosen for the excitation, which has to be selected according to usual turbomachinery criterions. The external load has to be defined in the time domain but has to represent a uniform sweep in the frequency domain. We then propose to implement the mistuning uncertainties by using the nonparametric probabilistic framework . We then obtain a stochastic reduced-order model, which requires to solve a reasonable set of uncertain nonlinear coupled differential equations in the time domain, yielding appropriate efficient and dedicated algorithms to be constructed. Such computational strategy provides an efficient computational tool, which is applied on a finite element model of an industrial centrifugal compressor with a large number of degrees of freedom. This allows new high complex dynamical behaviors to be put in evidence.