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Research Papers

Deterministic and Stochastic Model Order Reduction for Vibration Analyses of Structures With Uncertainties

[+] Author and Article Information
Ji Yang

School of Mechanical and
Manufacturing Engineering,
UNSW Australia,
Sydney, New South Wales 2052, Australia
e-mail: passion@zju.edu.cn

Béatrice Faverjon

School of Mechanical and
Manufacturing Engineering,
UNSW Australia,
Sydney, New South Wales 2052, Australia;
CNRS INSA-Lyon,
LaMCoS UMR5259,
Université de Lyon,
Lyon F-69621, France
e-mail: beatrice.faverjon@insa-lyon.fr

Herwig Peters

School of Mechanical and
Manufacturing Engineering,
UNSW Australia,
Sydney, New South Wales 2052, Australia
e-mail: herwig.peters@outlook.com

Steffen Marburg

Faculty of Mechanical Engineering,
Institute of Vibroacoustics of Vehicles
and Machines,
Technische Universität München,
Munich 85748, Germany
e-mail: steffen.marburg@tum.de

Nicole Kessissoglou

Mem. ASME
School of Mechanical and
Manufacturing Engineering,
UNSW Australia,
Sydney, New South Wales 2052, Australia
e-mail: n.kessissoglou@unsw.edu.au

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 22, 2016; final manuscript received October 20, 2016; published online February 6, 2017. Assoc. Editor: Matthew Brake.

J. Vib. Acoust 139(2), 021007 (Feb 06, 2017) (13 pages) Paper No: VIB-16-1260; doi: 10.1115/1.4035133 History: Received May 22, 2016; Revised October 20, 2016

To reduce the computational effort using polynomial chaos expansion to predict the dynamic characteristics of structures with several uncertain parameters, hybrid techniques combining stochastic finite element analysis with either deterministic or stochastic model order reduction (MOR) are developed. For the deterministic MOR, the Arnoldi-based Krylov subspace technique is implemented to reduce the system matrices of the finite element model. For the stochastic MOR, a stochastic reduced basis method is implemented in which the structural modal and frequency responses are approximated by a small number of basis vectors using stochastic Krylov subspace. To demonstrate the computational efficiency of each reduced stochastic finite element model, variability in the natural frequencies and frequency responses of a simply supported flexible plate randomized by uncertain geometrical and material parameters is examined. Results are compared with both Monte Carlo (MC) simulations and nonreduced stochastic models. Using the reduced models, the effects of the individual uncertain parameters as well as the combined uncertainties on the dynamic characteristics of the plate are examined.

Copyright © 2017 by ASME
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References

Figures

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Fig. 1

Flowchart diagram of the block Arnoldi algorithm for the generation of the transformation matrix

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Fig. 2

Finite element model of the simply supported plate

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Fig. 3

Uncertain Young's modulus δE=5%: (a) PCE coefficients and (b) PDF

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Fig. 4

Convergence analysis for the frequency response with uncertain Young's modulus δE=5%: (a) deterministic MOR for different PCE orders and (b) stochastic MOR for different number of basis vectors

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Fig. 5

(a) Mean and (b) variance of the frequency response using nonreduced PCE () and MC simulations () for uncertain Young's modulus (δE=5%)

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Fig. 6

(a) Mean and (b) variance of the frequency response using deterministic MOR, () stochastic MOR, () and MC simulations () for uncertain Young's modulus (δE=5%)

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Fig. 7

(a) Mean and (b) variance of the frequency response using stochastic MOR (), combined MOR (), and MC simulations () for uncertain Young's modulus (δE=5%)

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Fig. 8

(a) Mean and (b) variance of the frequency response using deterministic MOR (), combined MOR (), and MC simulations () for uncertain Young's modulus (δE=2%)

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Fig. 9

(a) Mean and (b) variance of the frequency response using deterministic MOR (), combined MOR (), and MC simulations () for uncertain Young's modulus (δE=10%)

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Fig. 10

(a) Mean and (b) variance of the frequency response using deterministic MOR (), combined MOR (), and MC simulations () for uncertain thickness (δh=0.1%)

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Fig. 11

(a) Mean and (b) variance of the frequency response using deterministic MOR (), combined MOR (), and MC simulations () for uncertain thickness (δh=1%)

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Fig. 12

Convergence analysis for frequency response with two uncertain parameters (δE=2% and δh=0.1%): (a) deterministic MOR for different PCE orders and (b) combined MOR for different number of basis vectors

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Fig. 13

(a) Mean and (b) variance of the frequency response using deterministic MOR (), combined MOR (), and MC simulations () for two uncertain parameters (δE=2% and δh=0.1%)

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Fig. 14

(a) Mean and (b) variance of the frequency response using deterministic MOR (), combined MOR (), and MC simulations () for two uncertain parameters (δE=2% and δh=1%)

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Fig. 15

(a) Mean and (b) variance of the frequency response using deterministic MOR (), combined MOR (), and MC simulations () for two uncertain parameters (δE=5% and δh=0.1%)

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