Sensitivity and Hessian Matrix Analysis of Evolutionary PSD Functions for Nonstationary Random Seismic Responses
Publication: Journal of Engineering Mechanics
Volume 138, Issue 6
Abstract
This paper describes a numerical method for calculation of the sensitivity and Hessian matrix of the response evolutionary power spectral density (PSD) functions of structures subjected to uniformly modulated evolutionary random seismic excitation. The method is formulated based on the pseudoexcitation method and the Gauss precise time step integration method. The evolutionary nonstationary random response analysis is converted into step-by-step integration computations using the pseudoexcitation method. The formulas of the pseudoresponses and their first and second derivatives with respect to the structural design variables are derived based on the Gauss precise time step integration method. The evolutionary PSD functions, their sensitivity, and the Hessian matrix are calculated using the pseudoresponses and their first and second derivatives, respectively. Finally, the evolutionary PSD functions’ sensitivity and Hessian matrix analysis of a three-story, two-bay planar frame subjected to uniformly modulated evolutionary random earthquake ground motion has been studied to elucidate the proposed method.
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Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 6 • June 2012
Pages: 716 - 720
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Jan 24, 2011
Accepted: Dec 12, 2011
Published online: Dec 14, 2011
Published in print: Jun 1, 2012
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