Computational modeling strategies for the nonlinear mistuning of an industrial bladed disk
Résumé
In this research, we are interested in the dynamical analysis 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. More specifically, the present research explores several computational modeling strategies for the mistuning.
First, a nonlinear reduced-order model of the structure has to be obtained [1]. Then, the implementation of the mistuning uncertainties through the nonparametric probabilistic framework is straightforward for the linear part of the operators. Until now, the nonlinear mistuning analysis of bladed disks has been only carried out, by introducing the mistuning uncertainties on the linear part of the reduced operators [2]. Moreover, it has been shown that the nonparametric probabilistic approach was adapted to the geometrical nonlinear case, by introducing a dedicated stiffness positive-definite operator self-containing the integrality of the information concerning the nonlinear geometric stiffness contributions [3]. Nevertheless, the dimension of such dedicated stiffness operator increases with the square of the dimension of the nonlinear-reduced order model, requiring a consequent number of uncertain random germs. The main idea for reducing the size of the random germ is to keep the essential information contained in the dedicated stiffness operator. This is achieved by performing a second reduction-order model from this operator. With such strategy and with a given nonlinear reduced-order model of dimension, the random germ matrix has a reasonable size. The methodology is applied on an industrial rotating integrated bladed disk with about 2 000 000 dof