TY - GEN
T1 - Stochastic reduced order models for uncertain infinite-dimensional geometrically nonlinear dynamical systems-stochastic excitation cases
AU - Wang, X. Q.
AU - Mignolet, Marc
AU - Soize, C.
AU - Khanna, V.
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Geometrically nonlinear srructures
KW - Nonparametric stochastic modeling
KW - Random matrices
KW - Reduced order models
KW - Uncertainty
UR - http://www.scopus.com/inward/record.url?scp=84861051682&partnerID=8YFLogxK
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U2 - 10.1007/978-94-007-0732-0_29
DO - 10.1007/978-94-007-0732-0_29
M3 - Conference contribution
AN - SCOPUS:84861051682
SN - 9789400707313
T3 - Solid Mechanics and its Applications
SP - 293
EP - 302
BT - IUTAM Symposium on Nonlinear Stochastic Dynamics and Control - Proceedings of the IUTAM Symposium
T2 - IUTAM Symposium on Nonlinear Stochastic Dynamics and Control
Y2 - 10 May 2010 through 14 May 2010
ER -