Mistuning analysis and uncertainty quantification of an industrial bladed disk with geometrical nonlinearity

Abstract

a b s t r a c tThis paper deals with the dynamical analysis and uncertainty quantification of a mistuned industrial rotating integrally bladed disk, for which the operating regime under consideration takes into account the nonlinear geometrical effects induced by large displacements and deformations. First, a dedicated mean nonlinear reduced-order model of the tuned structure is explicitly constructed using the finite element method. The random nature of the mistuning is then modeled by using the nonparametric probabilistic approach extended to the nonlinear geometric context. Secondly, a detailed dynamic analysis and uncertainty propagation are conducted in order to quantify the impact of the nonlinear geometrical effects on the mistuned structure. The results show that the dynamic amplification in the frequency band is significant outside the frequency band of excitation due to the presence of geometric nonlinearities combined with mistuning effects.

Uncertainty Quantification for Nonlinear Reduced-Order Elasto-Dynamics Computational Models

“…Recently, a complete methodology has been proposed for the geometric nonlinear analysis of mistuned bladed disks [8], for which all the terms including the rotational motion of the bladed-disk are taken into account. Below, the main steps of such methodology are briefly summarized.…”

“…Construction of the external load in the time domain corresponding to a uniform sweep of the frequency band of excitation [8] 4. Choosing the projection basis as the linear eigenmodes of the tuned structure [10] 5.…”

“…Solving the stochastic nonlinear equations in the time-domain with efficient algorithms based on the arc-length methods [7,8] All the details concerning the theoretical construction of such methodology and its application to a large finite element model of an industrial bladed-disk can be found in [8].…”

“…Until now, it has been assumed in the industrial application [8] that the mistuning only affects the linear operators. In this case, that means that linear mistuning in presence of deterministic geometric nonlinearities is considered.…”

“…Uncertainties have then to be taken into account in the computational models by using probabilistic models as soon as the probability theory can be used. Recently, a computational methodology adapted to the uncertainty quantification of structures in presence of geometric nonlinearities has been proposed and validated in the context of structural dynamics [6,7,8]. The implementation of random uncertainties is carried out through the nonparametric probabilistic framework from a nonlinear reduced-order model.…”