Nonparametric Modeling of Random Uncertainties for Dynamic Response of Mistuned Bladed Disks

Capiez‐Lernout, Evangéline; Soize, Christian

doi:10.1115/1.1760527

Cited by 44 publications

(24 citation statements)

References 22 publications

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“…Using the methodology derived from [3,20], the nonparametric probabilistic approach consists in modeling the reduced dynamic stiffness matrix for sector p as the random matrix …”

Section: Random Reduced Matrix Model For the Bladeddiskmentioning

confidence: 99%

Robust Analysis of Design in Vibration of Turbomachines

Mbaye

Soize

Ousty

et al. 2012

Journal of Turbomachinery

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“…Using the methodology derived from [3,20], the nonparametric probabilistic approach consists in modeling the reduced dynamic stiffness matrix for sector p as the random matrix …”

Section: Random Reduced Matrix Model For the Bladeddiskmentioning

confidence: 99%

Robust Analysis of Design in Vibration of Turbomachines

Mbaye

Soize

Ousty

et al. 2012

Journal of Turbomachinery

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“…This prior probability distribution is constructed by using the Maximum Entropy Principle [20] (from Information Theory [21]) for which the constraints are defined by the available information [13,14,22,15]. Since the paper [13], many works have been published in order to validate the nonparametric probabilistic approach of model uncertainties with experimental results (see for instance [23,24,25,26,27,28,15,29]), to extend the applicability of the theory to other areas [30,31,32,33,34,35,36,37,38,39,40,41], to extend the theory to new ensembles of positive-definite random matrices yielding a more flexible description of the dispersion levels [42], to apply the theory for the analysis of complex dynamical systems in the medium-frequency range, including vibroacoustic systems, [43,44,23,45,25,26,27,28,46,47,48,39], to analyze nonlinear dynamical systems (i) for local nonlinear elements [49,50,37,…”

Section: Types Of Approach For Stochastic Modeling Of Uncertaintiesmentioning

confidence: 99%

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Soize

2013

Journal of Sound and Vibration

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140

106

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To cite this version:Christian Soize. Stochastic modeling of uncertainties in computational structural dynamics -Recent theoretical advances. Journal of Sound and Vibration, Elsevier, 2013, 332 (10) AbstractThis paper deals with a short overview on stochastic modeling of uncertainties. We introduce the types of uncertainties, the variability of real systems, the types of probabilistic approaches, the representations for the stochastic models of uncertainties, the construction of the stochastic models using the maximum entropy principle, the propagation of uncertainties, the methods to solve the stochastic dynamical equations, the identification of the prior and the posterior stochastic models, the robust updating of the computational models and the robust design with uncertain computational models. We present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties, and for their identification with experimental data. We also present the construction of the posterior stochastic model of uncertainties using the Bayesian method when experimental data are available.

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“…The geometric nonlinearities are taken into account through the quadratic and cubic stiffness contributions K (2) αβγ and K (3) αβγδ which are written as…”

Section: Mean-nl-rommentioning

confidence: 99%

“…Such phenomena, referred to mistuning, can generate localization effects combined to a dynamic amplification of the forced response [1]. Many research efforts have been carried out on this subject, including reduced-order models with probabilistic approaches in the numerical modeling, for taking into account the random character of mistuning [2,3] and giving rise to strategies for the robust design of such structures [4]. Another essential aspect is to consider the geometric nonlinear effects in the computational models occurring when exceptional operating speeds of bladed disks are analyzed due to geometric nonlinearities induced by large deformations and large displacements [5,6].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification in Nonlinear Structural Dynamics for Mistuned Bladed Disks

Capiez‐Lernout¹,

Soize²,

Mbaye³

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. 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.

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Nonparametric Modeling of Random Uncertainties for Dynamic Response of Mistuned Bladed Disks

Cited by 44 publications

References 22 publications

Robust Analysis of Design in Vibration of Turbomachines

Robust Analysis of Design in Vibration of Turbomachines

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Uncertainty Quantification in Nonlinear Structural Dynamics for Mistuned Bladed Disks

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