Stochastic reduced order models for uncertain infinite-dimensional geometrically nonlinear dynamical systems-stochastic excitation cases

X. Q. Wang, Marc Mignolet, C. Soize, V. Khanna

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

The application of the nonparametric stochastic modeling technique to reduced order models of geometrically nonlinear structures recently proposed is here further demonstrated. The complete methodology: selection of the basis functions, determination and validation of the mean reduced order model, and introduction of uncertainty is first briefly reviewed. Then, it is applied to a cantilevered beam to study the effects of uncertainty on its response to a combined loading composed of a static inplane load and a stochastic transverse excitation representative of earthquake ground motions. The analysis carried out using a 7-mode reduced order model permits the efficient determination of the probability density function of the buckling load and of the uncertainty bands on the power spectral densities of the stochastic response, transverse and inplane, of the various points of the structure.

Original languageEnglish (US)
Title of host publicationSolid Mechanics and its Applications
Pages293-302
Number of pages10
Volume29
DOIs
StatePublished - 2011
EventIUTAM Symposium on Nonlinear Stochastic Dynamics and Control - Hangzhou, China
Duration: May 10 2010May 14 2010

Publication series

NameSolid Mechanics and its Applications
Volume29
ISSN (Print)18753507

Other

OtherIUTAM Symposium on Nonlinear Stochastic Dynamics and Control
CountryChina
CityHangzhou
Period5/10/105/14/10

Fingerprint

Nonlinear dynamical systems
dynamical systems
excitation
static loads
Power spectral density
buckling
probability density functions
Probability density function
Buckling
Earthquakes
earthquakes
methodology
Uncertainty

Keywords

  • Geometrically nonlinear srructures
  • Nonparametric stochastic modeling
  • Random matrices
  • Reduced order models
  • Uncertainty

ASJC Scopus subject areas

  • Aerospace Engineering
  • Automotive Engineering
  • Civil and Structural Engineering
  • Mechanical Engineering
  • Acoustics and Ultrasonics

Cite this

Wang, X. Q., Mignolet, M., Soize, C., & Khanna, V. (2011). Stochastic reduced order models for uncertain infinite-dimensional geometrically nonlinear dynamical systems-stochastic excitation cases. In Solid Mechanics and its Applications (Vol. 29, pp. 293-302). (Solid Mechanics and its Applications; Vol. 29). https://doi.org/10.1007/978-94-007-0732-0_29

Stochastic reduced order models for uncertain infinite-dimensional geometrically nonlinear dynamical systems-stochastic excitation cases. / Wang, X. Q.; Mignolet, Marc; Soize, C.; Khanna, V.

Solid Mechanics and its Applications. Vol. 29 2011. p. 293-302 (Solid Mechanics and its Applications; Vol. 29).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Wang, XQ, Mignolet, M, Soize, C & Khanna, V 2011, Stochastic reduced order models for uncertain infinite-dimensional geometrically nonlinear dynamical systems-stochastic excitation cases. in Solid Mechanics and its Applications. vol. 29, Solid Mechanics and its Applications, vol. 29, pp. 293-302, IUTAM Symposium on Nonlinear Stochastic Dynamics and Control, Hangzhou, China, 5/10/10. https://doi.org/10.1007/978-94-007-0732-0_29
Wang XQ, Mignolet M, Soize C, Khanna V. Stochastic reduced order models for uncertain infinite-dimensional geometrically nonlinear dynamical systems-stochastic excitation cases. In Solid Mechanics and its Applications. Vol. 29. 2011. p. 293-302. (Solid Mechanics and its Applications). https://doi.org/10.1007/978-94-007-0732-0_29
Wang, X. Q. ; Mignolet, Marc ; Soize, C. ; Khanna, V. / Stochastic reduced order models for uncertain infinite-dimensional geometrically nonlinear dynamical systems-stochastic excitation cases. Solid Mechanics and its Applications. Vol. 29 2011. pp. 293-302 (Solid Mechanics and its Applications).
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