Abstract
The present research concerns the dynamical analysis of mistuned rotating bladed-disks for which nonlinear geometrical effects exist. The present methodology requires the construction of an adapted reduced-order basis from which a nonlinear reduced-order model is constructed. The mistuning phenomenon is taken into account by considering a nonparametric probabilistic approach based on the information theory. In the present context the uncertainty is introduced by replacing the reduced-order basis with a stochastic reduced-order basis (SROB). This latter one is obtained by using a new nonparametric probabilistic approach of model-form uncertainties so that each realization of the SROB respects some mathematical properties linked to the available information under constraints concerning the specified boundary conditions and the usual orthogonality properties. With such strategy, the computational effort is focused on the stochastic nonlinear reduced internal forces and the related tangential operator which are explicitly constructed using the SROB combined with the finite element method. The numerical application is a rotating mistuned bladed-disk subjected to a load for which geometrical nonlinearities effects occur. The uncertainty propagation in this nonlinear dynamical system is then analyzed.
Highlights
Nowadays, a main challenge in engineering structural dynamics concerns the development of computational strategies for constructing stochastic nonlinear reduced-order models that are able to accurately reproduce dynamical structural responses that occur in nonlinear vibrational operating ranges
In the context of the finite element method, the nonlinear finite element computational model that describes the nonlinear dynamical forced response of the considered structure is characterized in the time domain by the following set of nonlinear coupled differential equations such that
It is chosen to solve this set of nonlinear differential equations in order to construct the nonlinear dynamical response that will be considered as the reference response
Summary
A main challenge in engineering structural dynamics concerns the development of computational strategies for constructing stochastic nonlinear reduced-order models that are able to accurately reproduce dynamical structural responses that occur in nonlinear vibrational operating ranges. In the context of the finite element method, the nonlinear finite element computational model that describes the nonlinear dynamical forced response of the considered structure is characterized in the time domain by the following set of nonlinear coupled differential equations such that [M ]U(t) + ([D] + [CG(Ω)])U (t) + [K(Ω)]U(t) + FNL(U(t)) = F(t) ,. It is chosen to solve this set of nonlinear differential equations in order to construct the nonlinear dynamical response that will be considered as the reference response In this case, the nonlinear algorithms require to construct the nonlinear internal finite element forces and the related tangential operator with the finite element model. In such a case, [A] is not computed and the eigenvalue problem is replaced by a singular value decomposition of [Y] or [Y]T
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