Abstract
The present work presents an improvement of a computational methodology for the uncertainty quantification of structures in presence of geometric nonlinearities. The implementation of random uncertainties is carried out through the nonparametric probabilistic framework from a nonlinear reduced-order model. With such usual modeling, it is difficult to analyze the influence of uncertainties on the nonlinear part of the operators with respect to its linear counterpart. In order to address this problem, an approach is proposed to take into account uncertainties for both the linear and the nonlinear operators. The methodology is then validated in the context of the linear and nonlinear mistuning of an industrial integrated bladed-disk.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Pai, P.F., Nayfeh, A.H.: A fully nonlinear-theory of curved and twisted composite rotor blades accounting for warpings and 3-dimensional stress effects. Int. J. Solids Struct. 31 (9), 1309–1340 (1994)
Tang, D.-M., Dowell, E.H.: Nonlinear response of a non-rotating rotor blade to a periodic gust. J. Fluids Struct. 10 (7), 721–742 (1996)
Grolet, A., Thouverez, F.: Free and forced vibration analysis of a nonlinear system with cyclic symmetry: application to a simplified model. J. Sound Vib. 331 (12), 2911–2928 (2012)
Hodges, D.-H., Shang, X.-Y., Cesnik, C.E.S.: Finite element solution of nonlinear intrinsic equations for curved composite beams. J. Am. Helicopter Soc. 41 (4), 313–321 (1996)
Huang, H., Han, Q.: Research on nonlinear postbuckling of functionally graded cylindrical shells under radial loads. Compos. Struct. 92 (6), 1352–1357 (2010)
Capiez-Lernout, E., Soize, C., Mignolet, M.-P.: Computational stochastic statics of an uncertain curved structure with geometrical nonlinearity in three-dimensional elasticity. Comput. Mech. 49 (1), 87–97 (2012)
Capiez-Lernout, E., Soize, C., Mignolet, M.-P.: Post-buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation. Comput. Methods Appl. Mech. Eng. 271, 210–230 (2014)
Capiez-Lernout, E., Soize, C., Mbaye, M.: Mistuning analysis and uncertainty quantification of an industrial bladed disk with geometrical nonlinearity. J. Sound Vib. 356 (10), 124–143 (2015)
Wei, S.-T., Pierre, C.: Localization phenomena in mistuned assemblies with cyclic symmetry part ii: forced vibrations. ASME J. Vib. Acoust. Stress. Reliab. Des. 110 (4), 439–449 (1988)
Mignolet, M.-P., Przekop, A., Rizzi, S.A., Spottswood, M.S.: review of indirect/non-intrusive reduced-order modeling of nonlinear geometric structures. J. Sound Vib. 332 (10), 2437–2460 (2013)
Soize, C.: Stochastic Models of Uncertainties in Computational Mechanics. Lecture Notes in Engineering Mechanics, vol. 2. American Society of Civil Engineers (ASCE), Reston (2012)
Mignolet, M.-P., Soize, C.: Stochastic reduced-order models for uncertain geometrically nonlinear dynamical systems. Comput. Methods Appl. Mech. Eng. 197, 3951–3963 (2008)
Crisfield, M.A.: Non-Linear Finite Element Analysis of Solids and Structures, vol. 1: Essentials. Wiley, Chichester (1997)
Capiez-Lernout, E., Soize, C., Mbaye, M.: Uncertainty quantification for an industrial mistuned bladed disk with geometrical nonlinearities. In: Paper GT2015-42471, Proceedings of the ASME Turbo Expo 2015: Turbine Technical Conference and Exposition GT2015, Montréal, 15–19 June 2015
Acknowledgements
This work was supported by the DGA (French defence procurement agency) in the context of the TURBODYNA project (project number ANR-13-ASTR-0008-01) related to the ANR ASTRID research program (specific support scheme for research works and innovation defence). SAFRAN Turbomeca is also acknowledged for giving permission to publish this work.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Capiez-Lernout, E., Soize, C., Mbaye, M. (2016). Uncertainty Quantification for Nonlinear Reduced-Order Elasto-Dynamics Computational Models. In: Atamturktur, S., Schoenherr, T., Moaveni, B., Papadimitriou, C. (eds) Model Validation and Uncertainty Quantification, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-29754-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-29754-5_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29753-8
Online ISBN: 978-3-319-29754-5
eBook Packages: EngineeringEngineering (R0)