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Research Papers

Stochastic Reduced-Order Model in Low-Frequency Dynamics in Presence of Numerous Local Elastic Modes

[+] Author and Article Information
C. Soize

 Laboratoire Modélisation et Simulation Multi-Echelle (MSME), UMR 8208 CNRS, Université Paris-Est, 5 bd Descartes, 77454 Marne-la-Vallée, Francechristian.soize@univ-paris-est.fr

A. Batou

 Laboratoire Modélisation et Simulation Multi-Echelle (MSME), UMR 8208 CNRS, Université Paris-Est, 5 bd Descartes, 77454 Marne-la-Vallée, Franceanas.batou@univ-paris-est.fr

J. Appl. Mech 78(6), 061003 (Aug 22, 2011) (9 pages) doi:10.1115/1.4002593 History: Received August 26, 2009; Accepted September 20, 2010; Revised September 20, 2010; Published August 22, 2011; Online August 22, 2011

This paper deals with the nonusual case in structural dynamics for which a complex structure exhibits both the usual global elastic modes and numerous local elastic modes in the low-frequency range. Despite the presence of these local elastic modes, we are interested in constructing a stochastic reduced-order model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. In the first part, a formulation and an algorithm, which allow the “global elastic modes” and the “local elastic modes” to be calculated, are presented. The second part is devoted to the construction of the stochastic reduced-order model with the global elastic modes and in taking into account the uncertainties on the effects of the local elastic modes by the nonparametric probabilistic approach. Finally, an application, which validates the proposed theory is presented.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry of the dynamical system

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Figure 2

First elastic mode

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Figure 3

Second elastic mode

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Figure 4

Distribution of the number of eigenfrequencies for the global elastic modes (black histogram) and for the local elastic modes (grey histogram) as a function of the frequency in Hz

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Figure 9

Modulus in log scale of the frequency response for Pobs1. Comparisons between different projection bases: initial elastic modes (solid thick line), global elastic modes only (mixed line), local elastic modes only (dashed line), and global and local elastic modes (solid thin line superimposed to the solid thick line.

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Figure 10

Modulus in log scale of the frequency response for Pobs2. Comparisons between different projection bases: initial elastic modes (solid thick line), global elastic modes only (mixed line), local elastic modes only (dashed line), and global and local elastic modes (solid thin line superimposed to the solid thick line).

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Figure 11

Random frequency response functions for Pobs1. Confidence region (lower and upper lines), mean response (middle line), and deterministic response calculated with the initial elastic modes (solid thick line).

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Figure 12

Random frequency response functions for Pobs2. Confidence region (lower and upper lines), mean response (middle line), and deterministic response calculated with the initial elastic modes (solid thick line).

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