The focus of this investigation is on the formulation and validation of a novel approach for the inclusion of uncertainty in the modeling of the boundary conditions of linear structures and of the coupling between linear substructures. This work is particularly relevant to complex structures assembled from simpler substructures as in aerospace applications. First, a mean structural dynamic model that includes boundary condition/coupling flexibility is obtained using classical substructuring concepts. The application of the nonparametric stochastic modeling approach to this mean model is next described and thus permits the consideration of both model and parameter uncertainty.

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This paper focuses on the determination of the effects on the bladed disk forced response of small variations (mistuning) in the blade-disk interface properties as may result from blade seating. A blade-interface-disk mean model is first developed that relies on both the Craig-Bampton approach and a local modeling of the interface. Then, both model and data uncertainties are introduced in this model using the nonparametric stochastic modeling approach. An example of application is presented that indicates a difference in physical behavior of a bladed disk with mistuned interfaces as compared to one with mistuned blade alone frequencies. Most notably, it is shown that at equal variability on the blade frequencies, the variations in blade-disk interface properties lead to a higher amplification factor.

The response of blades in bladed disks can be represented as a sum of modal contributions from their cantilevered modes and a component induced by the motion of the disk and its interface with the blades. This last contribution referred to here as the disk-induced blade motions is generally considered to be tuned when performing mistuning analysis of bladed disks. Yet, as most of the blade properties, its structural coupling to the disk is likely to be uncertain, for example due to variations in thickness at the blade filet. One thus expects a mistuning of the interface stiffness and mass matrices in particular. The effect of this mistuning on the blade response, which does not appear to have received significant attention, is the focus of the present investigation. A Craig-Bampton methodology is introduced to highlight the disk-blade interface and a mistuning modeling of its stiffness matrix is introduced following the nonparametric modeling method. The analysis with various mistuning models is carried out on a 15-blade impeller finite element model at several resonances. It is found that a small mistuning of the disk-induced blade does not alter notably the mistuned response of the blades.

This paper addresses the stochastic modeling of the stiffness matrix of slender uncertain curved beams that are forced fit into a clamped-clamped fixture designed for straight beams. Because of the misfit with the clamps, the final shape of the clamped-clamped beams is not straight and they are subjected to an axial preload. Both of these features are uncertain given the uncertainty on the initial, undeformed shape of the beams and affect significantly the stiffness matrix associated with small motions around the clamped-clamped configuration. A modal model using linear modes of the straight clamped-clamped beam with a randomized stiffness matrix is employed to characterize the linear dynamic behavior of the uncertain beams. This stiffness matrix is modeled using a mixed nonparametric-parametric stochastic model in which the nonparametric (maximum entropy) component is used to model the uncertainty in final shape while the preload is explicitly, parametrically included in the stiffness matrix representation. Finally, a maximum likelihood framework is proposed for the identification of the parameters associated with the uncertainty level and the mean model, or part thereof, using either natural frequencies only or natural 2 frequencies and mode shape information of the beams around their final clamped-clamped state.To validate these concepts, three simulated, computational experiments were conducted within Nastran to produce populations of natural frequencies and mode shapes of uncertain slender curved beams after clamping. The three experiments differed from each other by the nature of the clamping condition in the in-plane direction. One experiment assumed a no-slip condition (zero in-plane displacement), another a perfect slip (no in-plane force), while the third one invoked friction. The first two experiments gave distributions of frequencies with similar features while the latter one yielded a strong deterministic dependence of the frequencies on each other, a situation observed and explained recently and thus not considered further here. Then, the application of the stochastic modeling concepts to the no-slip simulated data was carried out and led to a good matching of the probability density functions of the natural frequencies and the modal components, even though this information was not used in the identification process.These results strongly suggest the applicability of the proposed stochastic model.